Page 1
Selection at the AMSE Conference-2017
Valencia, Spain, July 13-14, 2017
- Venture Capital Research: A Bibliometric Analysis
C.A. Cancino, J.M. Merigó, D. Díaz, J.P. Torres (Chile)…………………………………………………………....1
- Fuzzy Logic Measures and Non-Monotonic Distances Applied to Color Psychology
Flor Madrigal Moreno, Andreia Cristina Müller, Jaime Gil Lafuente, José M. Merigó Lindahl (Mexico, Spanish,
Chile)…………………………………………………………………………………………………………..…....11
- Linguistic Measures of Subjective and Objective Poverty
Maria Jose Fernandez (Argentine)………………………………………………………………..………………...23
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Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 1-10
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Venture Capital Research: A Bibliometric Analysis
*C.A. Cancino, **J.M. Merigó, ***D. Díaz, ****J.P. Torres
Department of Management Control and Information Systems and Department of Business,
University of Chile
Av. Diagonal Paraguay 257, 8330015 Santiago, Chile
(*[email protected] , **[email protected] , ***[email protected] ,
****[email protected] )
Abstract
Venture capital research is becoming very significant during the last decades. The aim of
this study is to present a general overview of the leading journals, articles and authors in
venture capital research between 1990 and 2014. Different analyses were performed, all of
them at a general level for the described period. In order to do so, as is usual in bibliometric
analysis, this work uses the Web of Science database. The article provides several
bibliometric indicators, that includes the total number of publications, the total number of
citations, and the h-index. The main contribution of this work is to develop a general
overview of the leading journals, authors, universities in venture capital research, which
leads to the development of a future research agenda for bibliometric analysis, such as the
review of the most productive and influential authors, universities, and countries in venture
capital research.
Keywords: Venture Capital; Bibliometrics; Journals; Authors, Universities; Web of
Science.
1. Introduction
Venture Capital (VC) is an instrument for supporting the development and growth of new
enterprises through the provision of financial resources and also offers business expertise,
customer networks and good management practices (Hochberg et al., 2010). According to
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Cornelius and Persson (2006), venture capitalists are financial intermediaries who collect
excess capital from those who have it, and provide it to those who require it for the
development of a business venture. In general, in the decades, venture capital research has
grown considerably in proportion to other disciplines.
This article develops a way to analyze venture capital research over the last 25 years by
using bibliometric indicators. Bibliometric studies are becoming very popular in the
scientific literature (Merigó et al., 2016), strongly motivated by the access to bibliographic
information. Some studies have developed bibliometric analyses in a wide range of fields
including: entrepreneurship (Landström, 2012), innovation (Cancino et al., 2017a, 2017b),
health economics (Wagstaff and Culyer, 2012), among others.
The article develops a journal and authors analysis identifying the leading ones in the field.
In particular, this work describe that there are certain specialized journals that publish more
in venture capital research with respect to other journals, for example, Journal of Business
Venturing, Entrepreneurship Theory and Practice, and Small Business Economics. It also
highlights other journals for having a high number of citations, even if they publish a large
number of articles in VC research, such as the Journal of Finance, Journal of Financial
Economics, Research Policy, Strategic Management Journal, Academy of Management
Journal, Administrative Science Quarterly, among others. Moreover, a temporal analysis is
developed in order to see which journals have been the most influential ones throughout
time.
2. Literature Review
According to Gompers et al. (2008), Venture Capital (VC) research explores different
steps, which involve the pre-investment phase of VC, the management of VC, and the exit
strategies of VC. In the first step, pre-investment phase, VC research explores how changes
in public market signals affected VC, or the conditions to facilitate the creation of greater
firm value after receiving VC (Dushnitsky and Lenox, 2006). Research in this stage also
analyses the process of creating relationships between venture capitalists and entrepreneurs
(Hochberg et al., 2010). In the second step, research in the management stage focused its
attention on companies when they receive VC. For examples, researchers have explored the
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links between the influence and control of VC firms (Bottazzi, Da Rin & Hellmann, 2008)
and the management skills and expertise of entrepreneurs and new ventures, such as
entrepreneurial orientation (Stam & Elfring, 2008). Finally, research in the exit step
reviews how firms can develop either their initial public offering (IPO) or their buyout.
Nahata (2008) suggests that companies backed by more reputable VCs by initial public
offering (IPO) capitalization share, are more likely to exit successfully, access public
markets faster, and have higher asset productivity at IPOs.
Even though VC research has three stages of analysis, VC research encompasses wide
range of academic areas, without a particular discipline leading scientific research in this
field. Academics from disciplines such as Finance, General Management, Innovation, Law,
Public Policy, Sociology and Economics present a wide range of research on venture
capital, which is very valuable because it brings different perspectives to analyze the
problem of financing new businesses.
The above shows that the analysis of VC research is varied and can derive from different
disciplines. It could be positive to have different perspectives to try to understand the
problem.
3. Methods
Bibliometric research is a field that quantitatively studies bibliographic material (Broadus,
1987) providing a general overview of a research field according to a wide range of
indicators. There are different ways of ranking material in a bibliometric analysis. The most
common approaches use the total number of articles or the total number of citations.
Another useful indicator is the h-index (Hirsch, 2005) that combines articles with cites
indicating the number of studies X that have received X or more citations. Normally, the
information about citations, total number of articles or h-index can be obtained from
academic databases as Web of Science (WoS), Scopus or Google Scholar. WoS is one of
the most popular databases for classifying scientific research worldwide. The assumption is
that it only includes those journals that are evaluated with the highest quality.
In order to search for articles that have focused on venture capital research, the study uses
the keywords “venture capital*” or “business venturing” or “corporate venturing” in the
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title, abstract and keywords of any work available in WoS between 1990 and 2014, in order
to capture as many possible combinations of terms related to venture capital. This search
finds 2.086 articles that have become 1.820 studies by only considering articles, reviews,
letters and notes. The search was developed in October 2015 and January 2016.
4. Results
There are many journals in the scientific community that publishes material related to
venture capital research. Table 1 presents a list of the twenty journals with the highest h-
index in venture capital research.
R Journal Venture Capital
TPV TCV HV TP
1 Journal of Business Venturing 164 6976 48 836
2 Journal of Finance 23 2923 21 1972
3 Journal of Financial Economics 35 2884 21 1791
4 Entrepreneurship Theory and Practice 49 1070 21 515
5 Research Policy 37 1609 20 2059
6 Small Business Economics 67 833 16 1252
7 Strategic Management Journal 25 1477 15 1726
8 Journal of Management Studies 23 624 14 1252
9 Journal of Banking Finance 25 1024 13 3561
10 Journal of Corporate Finance 35 569 13 723
11 Technovation 30 396 13 1538
12 Academy of Management Journal 19 916 11 1490
13 Review of Financial Studies 26 763 10 1377
14 Harvard Business Review 26 634 10 4847
15 Management Science 14 966 9 3247
16 Entrepreneurship and Regional Development 18 300 9 381
17 Administrative Science Quarterly 8 1050 8 512
18 Organization Science 16 613 8 1301
19 Financial Management 14 494 8 832
20 Journal of International Business Studies 11 260 8 1162
Table 1: Most influential journals in venture capital research according to WoS
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R means rank, HV means h-index in venture capital research, TPV means the total number
of publications in venture capital research, TCV means the total number of citations
in venture capital research, and TP means the total number of publication of the journal.
The first journal of the Table 1, Journal of Business Venturing, publishes about 20% of the
total articles on venture capital research,
Also, Table 1 show that scientific analysis on venture capital comes from many disciplines,
and it is not possible to identify a specific group of journals leading the discipline. This is
evident if the group of the twenty most cited papers in venture capital research is analyzed
(Table 2).
R Authors Year Journal
1 Stuart, TE; Hoang, H; Hybels, RC 1999 Administrative Science Quarterly
2 Zucker, LG; Darby, MR; Brewer, MB 1998 American Economic Review
3 Sahlman, WA 1990 Journal of Financial Economics
4 Megginson, WL; Weiss, KA 1991 Journal of Finance
5 Powell, WW; White, DR; Koput, KW; Owen-Smith, J 2005 American Journal of Sociology
6
Krueger, NF; Reilly, MD; Carsrud, AL
2000 Journal of Business Venturing
7 Berger, AN; Udell, GF 1998 Journal of Banking & Finance
8 Lee, C; Lee, K; Pennings, JM 2001 Strategic Management Journal
9 Sorenson, O; Stuart, TE 2001 American Journal of Sociology
10 Mcdougall, PP; Shane, S; Oviatt, BM 1994 Journal of Business Venturing
11
Shane, S; Stuart, T
2002 Management Science
12 Kaplan, SN; Stromberg, P 2003 Review of Economic Studies
13 Podolny, JM 2001 American Journal of Sociology
14 Hellmann, T; Puri, M 2002 Journal of Finance
15 Black, BS; Gilson, RJ 1998 Journal of Financial Economics
16
Kortum, S; Lerner, J
2000 Rand Journal of Economics
17 Lerner, J 1995 Journal of Finance
18 Di Gregorio, D; Shane, S 2003 Research Policy
19 Zucker, LG; Darby, MR; Armstrong, JS 2002 Management Science
20 Barry, CB; Muscarella, CJ; Peavy, JW; Vetsuypens, MR 1990 Journal of Financial Economics
Table 2: Most cited articles in venture capital research according to WoS
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For this group it is possible to identify 12 different journals: Administrative Science
Quarterly, American Economic Review, American Journal of Sociology, Journal of
Banking & Finance, Journal of Business Venturing, Journal of Finance, Journal of
Financial Economics, Management Science, Rand Journal of Economics, Research Policy,
Review of Economic Studies and Strategic Management Journal. Among this group, three
journals (Journal of Financial Economics, Journal of Finance and American Journal of
Sociology) present three articles each on the list of the 20 most cited papers in venture
capital research.
Some leading authors in venture capital research stand out in this discipline, not only
because of the large number of publications which they develop but also because of their
high influence on the rest of the researchers of the world. Table 2 presents a ranking with
20 leading authors in venture capital research, which are classified according to their h-
index, which allows us to analyse their influence on other researchers.
R Name University Country TP TC H
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Lerner J
Wright M
Shepherd DA
Cumming D
Lockett A
Sapienza HJ
Mason CM
Harrison RT
Gompers P
Busenitz LW
Manigart S
Hellmann T
Keil T
Schwienbacher A
Bruton GD
Dushnitsky G
Keuschnigg C
Pollock TG
Zahra SA
Dimov D
Harvard University
Imperial College Business School
Indiana University
York University
University of Nottingham
University of Minnesota
University of Strathclyde
University Belfast
Harvard University
University of Oklahoma
School and Ghent University
University of British Columbia
Aalto University
University of Amsterdam
Christian University
London Business School
University of St. Gallen
The Pennsylvania State University
University of Minnesota
Newcastle University Business School
USA
UK
USA
Canada
UK
USA
UK
UK
USA
USA
Belgium
Canada
Finland
Netherlands
USA
UK
Switzerland
USA
USA
UK
27
42
22
29
16
13
12
11
10
10
20
8
8
11
8
7
8
7
8
8
2821
1368
966
657
604
925
311
296
860
591
481
1003
266
180
411
383
358
344
296
158
21
20
17
16
13
12
12
11
10
10
10
8
8
8
7
7
7
7
7
7
Table 3: The most influential authors in venture capital research according to WoS
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The results shown in Table 3 are that researchers from the USA and UK lead the ranking of
the most influential authors in venture capital research. Among the first 10 authors, 50%
works in USA universities and 40% works in UK universities. Also, from the total of 20
leading authors 60% works in USA and UK universities. Following the USA and UK,
researchers from Belgium, Canada, Finland, Netherlands and Switzerland are present in our
rankings. Another important highlight is that the most influential authors come from
different universities; the generation of the most influential knowledge on venture capital
research is not gathered in any particular university. In fact, among U.S. universities, only
Harvard University presents two authors in our rankings.
5.- Conclusions
This work presents a general overview of the leading journals, articles and authors in
venture capital research between 1990 and 2014. Different analyses were performed, all of
them at a general level for the described period.
First, the analysis focused on studying a ranking of 20 leading journals that present a
greater h-index in the discipline. In this ranking, it is possible to observe an interesting
discussion that reveals that the most productive journals, i.e., those who have a greater
quantity of published work, are not necessarily the most influential, i.e. those who have a
greater number of citations by the scientific community. Only one case, Journal of Business
Venturing which is the most productive, is also the most influential journal. Evidently, this
is the only specialized journal in venture capital research. Interestingly, some cases, such as
Journal of Finance, Strategic Management Journal and Journal of Banking & Finance,
present an important number of citations (more than 1000) in fewer than 25 papers. These
three journals, despite not being specialized in venture capital research, publish very
influential papers. The work also develops ranking of the more cited articles in venture
capital research and a list with most influential authors in the discipline under study.
Clearly, venture capital research will continue growing and it is necessary to deepen the
analysis of the authors, countries and universities that lead research in this discipline, who
are not only the most productive players but also the most influential actors.
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References
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Venture Capital in the Creation of Public Companies”, Journal of Financial
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Berger, A. and Udell, G. (1998), “The economics of small business finance: The roles of
private equity and debt markets in financial growth cycle”, Journal of Banking &
Finance, 22(6), 613-673.
Black, BS. and Gilson, RJ. (1998), “Venture capital and the structure of capital markets:
banks versus stock markets”, Journal of Financial Economics, 47, 243-277.
Bottazzi, L., Da Rin, M., Hellmann, T. (2008). “Who are the active investors?: Evidence
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Technovation, 26(2), 142-150.
Di Gregorio, D. and Shane, S. (2003), “Why do some universities generate more start-ups
than others?”, Research Policy, 32(2), 209-227.
Dushnitsky, G., Lenox, M. J. (2006). “When does corporate venture capital investment
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Gompers, P., Kovner, A., Lerner, J., Scharfstein, D. (2008). “Venture capital investment
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Hochberg, Y., Ljungqvist, A., Lu, Y. (2010). “Networking as a Barrier to Entry and the
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Kaplan, S. and Stromberg, P. (2003), “Financial contracting theory meets the real world:
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70(2), 281-315.
Kortum, S. and Lerner, J. (2000), “Assessing the Contribution of Venture Capital to
Innovation”, Rand Journal of Economics, 31(4), 674-692.
Krueger, N., Reilly, M. and Carsrud, A. (2000), “Competing models of entrepreneurial
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Landström, H., Harirchi, G. and Aström, F. (2012), “Entrepreneurship: Exploring the
knowledge base”, Research Policy, 41(7), 1154–1181.
Lee, C., Lee, K. and Pennings, J. (2001), “Internal capabilities, external networks, and
performance: a study on technology-based ventures”, Strategic Management
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Sahlman, W. (1990), “The structure and governance of venture-capital organizations”,
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university start-ups”, Management Science, 48(1), 154-170.
Sorenson, O. and Stuart, T.E. (2001), “Syndication networks and the spatial distribution of
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performance of entrepreneurial ventures”, Administrative Science Quarterly, 44(2),
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bibliometric lens”, Journal of Health Economics, 31(2), 406-439.
Zucker, L., Darby, M. and Brewer, M. (1998), “Intellectual human capital and the birth of
US biotechnology enterprises”, American Economic Review, 88(1), 290-306.
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Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 11-22
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Fuzzy Logic Measures and Non-Monotonic Distances Applied to
Color Psychology
* Flor Madrigal Moreno, **Andreia Cristina Müller, **Jaime Gil Lafuente, ***José M. Merigó
Lindahl
* Department of Accounting and Administrative Sciences, Universidad Michoacana de San
Nicolás de Hgo., Av. J. Mújica S/N, Felicitas del Rio 58030, Michoacán, México.
[email protected]
**Department of Economy and Business Organizations, Universidad de Barcelona
Av. Diagonal 690, 08034 Barcelona, España. [email protected] / [email protected]
***Department of Management, Control and Information Systems, Universidad de Chile
Diagonal Paraguay 257, Of. 1906, 833015, Santiago, Chile. [email protected]
Summary
The intention of this paper is to shape the profile of millennials by using fuzzy logic and color
psychology, with the purpose of having a communicative approach through the use of color red.
The data were collected from the literature review, and then a mathematical assessment was
given. The distances were measured to find the communication degree that the color red has with
the millennials, since it is linked with passion, consumption, practicality, and selectivity,
elements that reveal the attitude of this market segment. The Hamming distance and the ordered
weighted average (OWA) were used. The ordered weighted average distance operator (OWAD)
was also used; and finally, calculations were made with nonmonotonic operators of NOMOWA,
which has a negative value, and which exhibit non-monotonicity.
Keywords: Fuzzy logic, non-monotonic distances, color psychology, millennials.
1. Introduction
In recent years the study of generational groups has taken relevance, the millennial generation
stands out by its own, particularly for its buying behavior in addition to consumption in digital
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environment. It is an attractive market for sensory and digital marketing since they are young
people who are accustomed to giving their opinion and being listened, guided not by established
formality, but by natural behaviors and providing credit to useful information from the interaction
between them through social networks.
Research related to the generation of communication links and the use of specific colors will
influence the millennials when making decisions. In specific, the red color is influencing them,
becoming then, an important part of their everyday decisions. Companies around the world use
signals such as colors and shapes to convey a brand image and to increase the possibility of
consumer purchase (Hess & Melnyk, 2016).
This research paper is based on the measurement of perceptions about the color red and what it
communicates, linked to the characteristics that define the millennials. When reference is made to
a subjective "sensation" or "perception" that is not possible or cannot be measured, another
concept is used: the valuation, using the theory of fuzzy numbers (Kaufmann & Gil Aluja, 1986).
Through the literature review, first the mathematization of the colors is carried out and then the
mathematization of the words that define millennials utilizing the fuzzy logic. The mathematical
framework allows modeling the uncertainty of the cognitive human processes that can be treated
by a computer (González, 2011), then the:
1.Weighted Hamming Distance (WHD) has been used to show the most definitive coincidences
between the characteristics of the millennials and the colors that communicate the values that
distinguish them, in such a way that the researchers of this generational group have more
information that allows them to approach to this group of people in specific.
2. Subsequently, the Ordered Weighted Average Distance OWAD was used;
3. After the Non-Monotonic Weighted Hamming Distance- NON-MONOTONIC-WHD;
4. The weighted average non-monotonic ordered distance is calculated. NON-MONOTONIC
OWAD. All the above tools will allow to observe that the use of the weights adjusted to the
individual characteristics, means that the degree of uncertainty in measuring is less. Therefore,
the distance is also smaller (WHD and NON- NOMOTONIC WHD). On the other hand, when
the weights are only ordered, the degree of uncertainty is more significant. Therefore, the
distance also increases (OWAD and NON-MONOTONIC OWAD).
2. Preliminaries
2.1 Color psychology
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For centuries artists, philosophers, psychologists, and scientists have studied the effects of color,
developing many theories about the use of it. The number and variety of such approaches show
that universal rules cannot be applied: the perception of color depends on individual experiences.
To Goethe, it was really important to understand the human reactions to color, and his research is
a starting point of modern color psychology (Illusion Studio, 2016).
The study made by Kauppinen‐ Räisänen & Luomala, (2010), suggests that an essential function
played by colors is communication, and the evidence also shows the role of colors as a means of
communication. The color communication is related to the context, and there is a relationship
between the meaning of the packaging color and the type of product. Similarly, marketing
research suggests that consumers make product choices based on the meanings they associate
with colors and how the colors of the product fit their overall color preferences (Madden, Hewett,
& Roth, 2000).
2.2 Millennials
Millennials use consumption to define who they are and to distinguish themselves. In a research
made by Charters et al., (2011), it is evident that amongst millennial consumers the use of image,
color, and positioning vary from one country to another. On the other hand, a research made by
Credo, Lanier, Matherne, & Cox, (2016), shows that social and service-oriented activities are
increasingly important for young people.
In addition to a study made by Elliot & Barth, (2012), it was observed that in the design of wine
labels for millennial consumers, they want a more balanced mix between mind and heart (Harris
Interactive, 2001). This can explain their attempt to satisfy emotional needs through
consumption, often choosing brands of their choice in the same way they choose their friends
(Vrontis & Papasolomou, 2007).
Millennials are individualists, they do not want to be part of a mass of consumers, they are
selective, and they like personalized treatment. This includes products with a design, color, and
characteristics suitable for each buyer. In this line, colors often play a crucial role because they
are associated with a consumer culture or a consumer subculture. The notion of an association
between colors and cultures dates back to (Luckiesh, 1927), who proposed that race, customs and
the civilization type affect color preferences.
2.3 Fuzzy Logic implementation
The use of the Fuzzy model data analysis allows to have higher authenticity in the data collection,
maximizing the validity in the interpretation of results. This model reduces the uncertainty of the
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information as it adapts to the consumer's performance and potentiates efficiency in decision-
making (Casabayó & Borja, 2010).
The complexity of the problems and the inaccuracy of the situations have made it necessary to
introduce mathematical schemes that are more flexible and adapted to reality. In this sense, the
theory of fuzzy sets, has allowed the birth of some techniques that will facilitate the solution of
those problems in which uncertainty appears (Kaufmann & Gil Aluja, 1986).
The theory of fuzzy sets is used to develop an evaluation procedure adjusted to reality. The
proposed approach makes it possible to treat impact dimensions as linguistic variables and, based
on them, formulate evaluative criteria in the form of fuzzy rules (García, Félix Benjamín, & Bello
Pérez, 2014).
2.4 Hamming Distance
The Hamming Distance is a useful technique to calculate the differences between two elements,
two sets, etc. For example, it can be useful in the fuzzy set theory to calculate the distances
between Fuzzy sets, Fuzzy value intervals, intuitionist fuzzy sets and interval intuitionist fuzzy
sets. The Hamming distance adapted from (Gil, 2012) can be described as follows:
Hamming between two fuzzy subsets and j:
Next:
To carry out this comparison, it is expected to use the so-called "Hamming relative distance." It is
obtained by dividing the absolute distance by the number of characteristics, qualities or
singularities, in this case, "n." It will be then:
D
˜
P
˜
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2.5 OWA Operators
OWA operators are tools that allow adding information. That is, from a series of data, a single
representative value of the information can be obtained. As an additional characteristic of the
OWA operators, it can be said that the elected value obtained is an added value according to
predetermined optimism/pessimism parameters (Merigó, 2008).
The ordered weighted average distance operator (OWAD) is used as a data analysis tool since it
provides a parametrized family of distance aggregation operators between the maximum distance
and the minimum distance and can be further extended using other types of ranges such as the
Euclidean distance, the Minkowski distance, and the quasi-arithmetic distance (Merigo & Gil-
Lafuente, 2012).
1
n| ai -bi |
i=1
n
åæ
èç
ö
ø÷
2.6 Non-monotonic OWA and OWAD operators
It can be defined as follows for two sets X = {x1, x2, …, xn} and Y = {y1, y2, …, yn}.
Definition 1. A non-monotonic OWAD operator of dimension n is a NOM-OWAD mapping: [0,
1]n [0, 1]n → [0, 1] that has an associated weighting vector W with 11 nj jw and wj [-1, 1]
so that:
NOM-OWAD (x1, y1, x2, y2, …, xn, yn) =
n
jjj Dw
1
,
Where Dj is the j value of the longest individual distance from | xi - yi |
It should be noted that the main difference with the NOM-OWAD is that the weighting vector wj:
can be less than 0. In definition 1 the study considers between -1 and 1. But it is also possible to
consider more general cases, heavy OWA (Yager, 1999) (Merigo & Gil-Lafuente, 2012), where
weights can move between -∞ and ∞.
3. Applications
This is a transactional qualitative research, with primary and secondary data obtained from the
analysis of books, scientific articles, and specialized marketing magazines. A selection of
literature was carried out that in an extensive and detailed way to describe the importance of
color, its general aspects, its symbolism, what it communicates, as well as the characteristics and
concepts associated to it.
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As a second stage, some scientific articles were reviewed about millennials and their
consumption habits. The articles consulted to define the characteristics that define millennials
were the following: Engagement and talent management of gen Y(Weyland, 2011); Generation Y
values and lifestyle segments, (Valentine & Powers, 2013); Millennials (Gen Y) consumer
behavior, their shopping preferences and perceptual maps associated with brand loyalty, (Ordun,
2015); Consumer expectation from online retailers in developing e-commerce market: An
investigation of developing online market in Bangladesh, (Rahman, 2015a); Optimizing digital
marketing for generation Y: An investigation of developing online market in Bangladesh,
(Rahman, 2015b); Hip to be cool: A gen Y view of counterfeit luxury products, (Francis &
Burgess, 2015); Discovering the millennials’ personal values orientation: A comparison to two
managerial populations, (Weber, 2015); Effects of consumer embarrassment on shopping basket
size and value: A study of the millennials consumer, (Satinover N., Raska, & Flint, 2015);
Adaptative use of social networking applications in contemporary organizations: Examining the
motivations of gen Y cohorts, (Shirish, Boughzala, & Srivastava, 2016); Online purchase
behavior of generation Y in Malaysia, (Muda, Mohd, & Hassan, 2016); Acceptance of online
mass customization by generation Y, (Junker, Walcher, & Blazek, 2016); Gen Y: A study on
social media use and outcomes, (Omar, 2016); Creativity and cognitive skills among millennials:
Thinking too much and creating too little, (Corgnet, Espín, & Hernán-González, 2016); Gen Y
customer loyalty in online shopping: An integrated model of trust, user experience and branding,
(Bilgihan, 2016) y Generation X vs Generation Y: A decade of online shopping, (Lissitsa & Kol,
2016).
Later a matrix of the millennials’ profile was elaborated; the words that describe their personality
were identified, where these words that characterize them are mathematically defined, generating
then a pattern. An scale was established where the numerical interval from 0 to 1, according to
the highest occurrences of each word in the articles consulted, as well as the intensity of the
description to each construct. Later, a table is developed to establish a relationship between the
words associated with the profile of the millennials and the degree of association of each of these
words with the color red.
Table 1 shows the data using Weighted Hamming Distance (WHD) and the Ordered Weighted
Average Distance (OWAD).
Table 1. Hamming Distance, WHD, and OWAD to calculate distances.
Calculations Hamming Distance WHD OWAD
Characteristics HD W W*
Results
W Ŵ Ŵ* Results Ŵ
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W1 Hope 1 0.35 0.026 0.026 0.85 0.064 0.064
W2 Technology 1 0.65 0.049 0.049 0.65 0.049 0.049
W3 Freedom 1 0.30 0.022 0.022 0.65 0.049 0.044
W4 Innovation 0.9 0.21 0.016 0.014 0.55 0.042 0.037
W5 Balance 0.9 0.21 0.016 0.014 0.35 0.026 0.024
W6 Friendship 0.9 0.21 0.016 0.014 0.35 0.026 0.024
W7 Communication 0.9 0.55 0.041 0.037 0.30 0.023 0.018
W8 Perception (interaction) 0.8 0.21 0.016 0.013 0.25 0.019 0.015
W9 Education 0.8 0.21 0.016 0.013 0.25 0.019 0.015
W10 Cooperativism 0.8 0.21 0.016 0.013 0.21 0.016 0.013
W11 Dynamism - multitasking 0.8 0.25 0.019 0.015 0.21 0.016 0.011
W12 Strong intellect /intelligence 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W13 Connectivity 0.7 0.35 0.026 0.018 0.21 0.016 0.011
W14 Leadership 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W15 Emotional sensitivy 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W16 Attention 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W17 Ethics 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W18 Egocentrism 0.7 0.35 0.026 0.018 0.21 0.016 0.010
W19 Trust 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W20 Human values 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W21 Entertain 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W22 Personal growth 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W23 Changes 0.6 0.21 0.016 0.009 0.21 0.016 0.008
W24 Joy 0.5 0.21 0.016 0.008 0.21 0.016 0.008
W25 Impersonality 0.5 0.21 0.016 0.008 0.21 0.016 0.008
W26 Pleasure 0.5 0.25 0.019 0.009 0.21 0.016 0.006
W27 Beauty 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W28 Health 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W29 Depression 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W30 Protection 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W31 Positive energy 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W32 Easy 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W33 Solvency 0.4 0.21 0.016 0.006 0.21 0.016 0.005
W34 Experience 0.3 0.65 0.049 0.015 0.21 0.016 0.005
W35 Stability 0.3 0.21 0.016 0.005 0.21 0.016 0.003
W36 Luxury/sophistication 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W37 Fidelity 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W38 Self-confidence 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W39 Activity / Anxiety 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W40 Love 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W41 Coherence 0.2 0.21 0.016 0.003 0.21 0.016 0.002
W42 Passion 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W43 Power 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W44 Work /Physical activity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W45 Selectivity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W46 Maturity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W47 Competitiveness 0.1 0.21 0.016 0.002 0.21 0.016 0.002
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W48 Consumption 0.1 0.85 0.064 0.006 0.21 0.016 0.002
W49 Commitment 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W50 Nutrition /feeding 0.1 0.21 0.016 0.002 0.21 0.016 0.000
W51 Praticity 0 0.21 0.016 0.000 0.21 0.016 0.000
W52 Bored 0 0.21 0.016 0.000 0.21 0.016 0.016
TOTAL 0.475 13.37 1 0.494 13.23 1 0.556
Source: Original from the author.
Table 1 shows how the distances are different using each method, with Hamming distance the
value is 0.475, while using weighted Hamming Distance (OWA), the result is 0.494, and with
Distance (from Hamming) ordered weighted average (OWAD), the value is 0.556. When the
weights are ordered, the degree of uncertainty is more significant therefore the distance increases.
4. Non-monotonic applications
NOMOWA operators have negative weights and exhibit non-monotonicity. While monotonicity
is undoubtedly a useful property in aggregation, there are situations in which nonmonotonicity
may be helpful. A potential application of these non-monotonic operators of OWA is in the
multi-criterion aggregation domain guided by quantizer in which the guide quantifier is not
monotonic (Yager, 1999).
The author Ovchinnikov, (1998) introduced an extension of the OWA operators that allow the
possibility of having a non-monotonicity in the aggregation process.
The following is shown in Table 2. The distinctive feature of these operators that allow negative
weights to be used in the OWA weighting vector, the application of non-monotonic tools: Non-
monotonic weighted Hamming Distance (WHD) and the weighted average distance ordered non
monotonic (OWAD), applied to color red, where the weighting was made based on the literature
review of color psychology to relate the reactions that could be extreme by red.
Table 2. Application of non-monotonic tools WHD and non-monotonic OWAD
Non-Monotonic-WHD Non-Monotonic-OWAD
Characteristic Non-Mon-WHD Non-Mon-WHD*
Results Non- Mon -
OWAD
Non- Mon -
OWAD*
Results
Non-Mon-WHD Non- Mon -
OWAD
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W8 -0.3 -0.019 -0.015 0.9 0.057 0.046
W11 -0.2 -0.013 -0.01 0.8 0.051 0.035
W15 -0.1 -0.006 -0.004 0.5 0.032 0.022
W17 -0.4 -0.025 -0.018 0.45 0.029 0.02
W19 -0.3 -0.019 -0.011 0.4 0.025 0.015
W20 -0.3 -0.019 -0.011 0.4 0.025 0.015
W28 -0.4 -0.025 -0.01 0.2 0.013 0.005
W29 -0.5 -0.032 -0.013 0.2 0.013 0.005
W34 -0.1 -0.006 -0.002 0.1 0.006 0.002
W37 -0.1 -0.006 -0.001 0.1 0.006 0.001
W41 0 0 0 -0.1 -0.006 -0.001
W42 1 0.063 0.006 -0.1 -0.006 -0.001
W43 0.9 0.057 0.006 -0.1 -0.006 -0.001
W44 0.8 0.051 0.005 -0.2 -0.013 -0.001
W45 0.2 0.013 0.001 -0.2 -0.013 -0.001
W46 0.2 0.013 0.001 0.3 0.019 0.002
W47 0.4 0.025 0.003 -0.3 -0.019 -0.002
W48 0.1 0.006 0.001 -0.3 -0.019 -0.002
W49 0 0 0 -0.3 -0.019 -0.002
W50 -0.2 -0.013 -0.001 -0.4 -0.025 0
W51 0.3 0.019 0 -0.4 -0.025 0
W52 0 0 0 -0.5 -0.032 -0.032
TOTAL 15.78 1 0.501 15.78 1 0.811
Source: Original from the author.
5. Conclusions
This research allows to know the demands of the millennial generation, and to discover the
perception they have over certain products and services. By using the fuzzy logic, the Hamming
distance, the ordered weighted average (OWA), the ordered weighted average distance operator
(OWAD) and the nonmonotonic operators of NOMOWA, it has been possible to value the
millennial's perceptions. The millennial generation has an imprecise conduct. Therefore, the
behavioral phenomenon must be contextualized to a geographical place and specific conditions.
In this context, the theory of fuzzy sets allows reducing the uncertainty when communicating
with the millennials. Fuzzy logic does not increase the difficulty of traditional mathematics and is
closer to human thinking (Canós, 2013).
It is important to clarify that shorter distances are the ideal ones since they accurately show a
slight gap between the ideal and what is sought, before this it can be established that the red color
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is not exactly the one that generates more anchoring with the millennials according to the
mathematical results. However, the color red is linked to consumption, passion, practicality and
selectivity, elements that reveal to a large extent the tastes and preferences of this market
segment, as well as its link with the brands, generating a passionate defense of the brands that
define them. And with those that they identify with, as well as those which they do not respect.
The selectivity of millennials includes friends, brands and experiences. Millennials like
distinctive brands.
This research focuses on the mathematical evaluation of the words that define the millennial and
the communication through colors, distinguishing the importance of the use of psychology color
and the analysis of phenomena related to perception through fuzzy logic as well as new non-
monotonic combination tools WHD and OWAD. Since these combinations use negative weights
for very radical aggregation cases, this analysis represents an innovation in the study of color
theory.
Finally, this document can be strengthened with future research where other colors are analyzed
and their link with millennials, as well as the integration of new combination tools.
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Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 23-34
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Linguistic Measures of Subjective and Objective Poverty
Maria Jose Fernandez
Universidad de Buenos Aires, CIMBAGE, IADCOM / CONICET
Av. Córdoba 2122, Ciudad de Buenos Aires, C1120AAQ, Argentina
[email protected]
Abstract
Last decades several studies of subjective welfare with a great diversity of approaches have
appeared. Some have focused on finding variables that determine it. Others stress the importance
on quantifying it. Some investigates the determinants that make some people declare high levels
of welfare and others do not. One of crucial social problems in the study of welfare is the
recognition, measurement and analysis of the causes of poverty.
It is necessary to complement the objective poverty analysis with subjective indicators of
welfare in order to assess the correspondence between the objective improvements and the
subjective perceptions.
In this paper, we propose an evaluation model of Economic Welfare which includes
subjective and objective poverty indicators with the use of mathematical tools for the treatment of
uncertainty, in particular, linguistic models.
Keywords
Linguistic models, poverty measures, objective poverty, subjective poverty.
1. Introduction
Welfare Economics can be defined as a branch of Economics that explains the satisfaction of the
agents and the mechanisms that generate their increase and decrease. Its study is part of
disciplines as diverse as psychology, politics, sociology, philosophy and economics.
Utilitarianism posed by Bentham [1] and Mill [2] laid the foundations from which modern
Economic Science began the study of welfare. Welfare is also an abstract concept with subjective
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connotations, but correlated with objective economic factors and individual welfare refers to each
person's perception of having covered their needs [3].
During recent years, subjective assessments of quality of life are considered when measuring
development. It is often said that subjective welfare is a necessary and sufficient condition for
human development. Subjective welfare refers to an assessment of the welfare of an individual
obtained through a survey. Subjective happiness or welfare is a global assessment of the quality
of life by each individual [4]. The employment of subjective welfare measures is based on the
basic assumption the governments needs to evaluate the improvements in the quality of life of
their citizens [5]. Traditionally, study, measurement and design of public policies have paid
attention to economic indicators. Recent studies highlighted the importance of incorporating
subjective indicators, such as care or perception of happiness [6]. During last decades several
studies of subjective welfare that present a great diversity in the type of approach that they realize
have appeared. Some have focused on finding the variables that determine welfare. Others stress
the importance on quantifying happiness, and finally a group investigates the determinants that
make some people declare high levels of welfare and others do not. Dimensions that agents
consider important regarding their welfare and quality of life are the benchmark in the study of
subjective welfare. The self-evaluation that the subjects make regarding the satisfaction and
happiness they perceive in relation to the different dimensions is taken into account [7]. Main
social problems in the study of welfare are the recognition, measurement and analysis of the
causes of poverty. It is also fundamental to be able to design effective measures to reduce it.
However, this concept presents significant difficulties when it’s intended to measuring it
accurately. Evaluation of economic welfare can be based on two types of indicators: objective-
quantitative indicators (poverty lines, unsatisfied basic needs, human development index,
anthropometric indicators, etc.) and subjective-qualitative indicators (based on surveys that reveal
perceptions of individuals or households) [8].
Subjective poverty approach defines as poor those who are not satisfied with their situation,
because it is considered excluded from the normal way of life, regardless of the economic
situation of the agent. Studying poverty from a subjective point of view means considering that
any person or family can give their judgment about the degree to which it satisfies their basic
needs. To determine whether a person or family considers themselves poor or not, two forms are
generally used. It is possible to ask directly about certain perceptions about their condition or
observe their behavior. Subjective poverty can be understood as the perception of poverty that
has a sector of the population that feels and defines itself as poor because they cannot access a set
of goods and services that they consider of great importance [9]. Recognizing what causes
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subjective poverty can be a good mechanism to improve public policies based on a better
understanding of the needs and expectations of the population and the redefinition of priorities
[10]. Measuring welfare is a frequent task, and there is a high consensus on the need to quantify
it, but there are some divergences as to which indicators use to reflect a society's welfare situation
and little information on how population evaluates what happens with their own welfare [11].
Subjective measurements are based on population surveys where they are asked to define their
situation, usually located at a point on a qualitative scale. In general, information of welfare level
of each person is obtained through simple questionnaires with simple and direct questions that
capture people's perception of their satisfaction with access to certain goods or services.
The existence of qualitative variables, inherent to human behavior, or elements of the external
environment of difficult objective quantification, makes it difficult for individuals to represent
with an exact numerical value the valuation of the different aspects related to the welfare to be
assessed. Under such circumstances, it is more appropriate to express their responses by means of
linguistic values rather than exact numerical values. This approach is based on fuzzy sets theory
and is called linguistic approach. It is applied when the variables involved are of a qualitative
nature [12, 13, 14]. It is possible to model in a more appropriate way a great number of real
situations, since they allow representing the information of the individuals, that it is not always
precise, in a more appropriate way. A linguistic variable differs from a numerical one in that its
values are not numbers, but words or sentences of the natural language, or of an artificial
language [12]. The use of the diffuse linguistic approach implies the need to operate with words
[15].
It is necessary to complement the analysis of the population living conditions with the subjective
indicators of welfare in order to assess the correspondence between the objective improvements
and the subjective perceptions that the agents perform on them. Given that the type of questions
used to define a subjective welfare indicators are qualitative in nature, the use of a linguistic
model that operates with words directly will allow aggregating opinions of the individuals
adequately without losing information. The proposed approach will let to capture the nuances and
degrees of welfare present in human perceptions, whereas the classical models allow only binary
contrasts between positive and negative perceptions, not including the variations of intensities
between them. Application of linguistic models to evaluate the population's perceptions of their
welfare makes it possible to analyse individuals’ life quality under the use of linguistic variables
belonging to the habitual language. In addition, it will allow studying and processing individual
and aggregated opinions operating with words directly without losing information nor rigorous.
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This paper is structured as follows. In first place, a Linguistic Combined Model for Economic
Welfare is presented. A Welfare Linguistic Subjective Indicator and a Linguistic Poverty Line are
combined to measure a household multidimensional poverty. Next section develops an example
and finally some conclusions are presented.
2. Linguistic Combined Model of Economic Welfare Evaluation
Poverty is a multidimensional reality that is not usually completely measured because of its
nature. Population’s living conditions are characterized by subjective and objective aspects. Thus,
poverty measures sometimes are in the need to combine subjective and objective features.
Since subjective well-being indicators are built through surveys that reveal the individual's
perception in certain areas considered using qualitative scales, is very relevant the use
of linguistic variables in their formulation [16]. Then, since poverty is a matter of degrees, a
linguistic poverty line is used to evaluate objective welfare of each household [17].
First, households' perceptions in five chosen areas will be collected using a multiple choice
survey (Appendix). With the information obtained, ILBE index will be calculated for each
household [16]. Then, the fuzzy poverty line will be calculated for that household [17]. Finally,
the subjective evaluation of the household will be contrasted with the degree of poverty for
identifying different situations on multidimensional poverty.
2.1. Welfare Linguistic Subjective Indicator
Welfare Linguistic Subjective Indicator (ILBE) takes into account five areas of welfare: 1. health,
2. education, 3. housing, 4. income and 5.employment [16]. Economic welfare is determined by
their perception about these aspects. These perceptions are taken from direct surveys of heads of
households. The questionnaire induces households to assess their access to the five areas
considered using linguistic labels. The assessment of each area will provide a component of ILBE
and aggregation enable an indicator for each household.
According to the domain of the variables involved, it is assumed the use of one of the following
sets of linguistic terms, in order to the head of household express their views on each question
made:
excellentgood,very good, mean,bad, bad,very dreadful, 65432101 sssssssS
poor}non poor,non almost
poor,somewhat poor,notorpoornor poor,rather poor, very poor,absolutely {
65
432102
ss
sssssS
important} absolutely important, very important,pretty
careless, important, little t,uninportanrather t,unimportan {
654
32103
sss
ssssS
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With the information obtained in surveys the indicator value for a family is obtained. This value
is calculated for each area of satisfaction for the selected household. The assessment of the degree
of satisfaction of each home for each area that integrates the ILBEh is obtained by
using the aggregation operator of linguistic information with the information gathered from
surveys (Appendix).
- Health Area: Evaluation will be based on household responses to questions 1 (access to
healthcare) and 2 (access to medicines and vaccination): heqq sssEAA 21
,1.
Where 11
Ssq is the response of question 1, 12Ssq is the response of question 2 and is the
evaluation of the health area of this household.
- Education Area: Evaluation will be based on household responses to questions 3 (conformity
to the educational level of the head) and 4 (access to the education system): edqq sssEAA 43
, .
Where 13
Ssq is the response of question 3, 14
Ssq is the response of question 4 and is the
evaluation of the education área of this household.
- Housing Area: Evaluation will be based on household responses to questions 5 (housing
conditions) and 6 (neighborhood general conditions): hoqq sssEAA 65
, .
Where 15
Ssq is the response of question 5, 16
Ssq is the response of question 6 and is the
evaluation of the housing área of this household.
- Income Area: Evaluation will be based on household responses to questions 7 (income) and 8
(household income need not to feel poor): iqq sssEAA 87
, .
Where 11
Ssq is the response of question 7, 11
Ssq is the response of question 8 and is the
evaluation of the income área of this household.
- Employment Area: Evaluation will be based on household responses to questions 9 (number of
hours worked) and 10 (working conditions): emqq sssEAA 109
, .
Where 11
Ssq is the response of question 9, 110
Ssq is the response of question 10 and is the
evaluation of the employment área of this household.
Since not all areas that compose the indicator are equally important for all households, the survey
includes a question which asks the degree of importance assigned to each family to each of them
(Question 13, appendix) corresponding to a linguistic label in the set 3S .
If 3Ss
jh
is the linguistic label that shows the importance allocated by the household h the area
j
1 EAA: extended arithmetic mean [16].
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28
( 5,...,1j ); the weighting, hjw , correspondent must verify that 1,0jhw
5
1
1j
jhw , and is
obtained by applying
5
1j
jjjh hhw nh ...,,1 .
Having assessed the components of the index and obtained their respective weights, the ILBEh is
obtained by the use of aggregation operator of linguistic
information hemihoedhehh ssssssEWAAILBE ,,,, 2.
If it is wanted to express the degree of aggregate welfare of each household by a term of the set
1S , the sub index of the virtual label hs is approximated to an integer
value through the usual rounding operation (round h ) and it is got a linguistic original label.
Questions 11 and 12 will be used to compare the consistency of the households’ responses,
211Ssq and
112Ssq .
2.2. Objective Poverty Evaluation
It is needed to classify the household according to their income, because it is important to
analyze how poor households perceive their welfare as how they do the non-poor ones. For
classifying the household, we will employ the Fuzzy Poverty Lines and the Poverty Degrees
developed by Fernandez [17]. In this model, poverty is considered as a matter of degree.
First, a Fuzzy Basic Food Basket (CBAF) is determined to calculate the Indigence Line to the
Equivalent Adult. To assess the CBAF for an adult fuzzy triangular numbers are expressed by its
confidence intervals and are operated with them [18]. Given nCCC ,...,1 , its cardinal is
nC monthly valuation of CBAF is given by:
n
i
ii
CBAF PQV1
/ niRPQ ii ,...,1, .
Being each n component of the basket, the quantity of component i of the basket, the
price of that good [17]. Then, a fuzzy scale is constructed to determine the units of equivalent
adults of each household, obtained from a fuzzy energy needs table [17]. Being hU the units of
equivalent adults of h-th household and CBAFV the valuation of CBAF for an equivalent adult unit,
the valuation of the CBAF for the h-th household is: CBAF
hh
CBAF VUV .
In order to obtain the fuzzy poverty line, it is indispensable to establish the fuzzy inverse of
Engel's coefficient e~ 3. Fuzzy poverty line for the equivalent adult will be determined
by: eVLP CBAFf~. .
2 EWAA: weighted arithmetic mean [16]. 3 Fuzzy inverse Engel's coefficient relates food expenditures with non-food ones using triangular fuzzy numbers [17].
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29
Being fLP the fuzzy poverty line for the equivalent adult and hU the units of equivalent adults
of h-th household, the valuation of the Poverty Line for the h-th household is: f
hh
f LPULP .
Once calculatedh
fLP , household's monthly effective total income is compared and it is
determined whether it is completely poor, not poor, or whether it is in the gray area. For
classifying households within the gray zone, it is possible to associate the degree of belonging to
the set of poor households with a set of labels. It is possible to construct a set of labels to classify
households with respect to the concept of poverty (Table 1 and Figure 1).
The use of this approach allows capturing the different degrees present when valuing a measure
that represents welfare that is intended to measure. The use of fuzzy sets theory helps to
understand the phenomenon dimensions more comprehensively.
2.3. Joint Poverty Analysis
In order to analyze the determinants of the non-poor / feeling poor and the poor / non feeling poor
families, households will be separated into four groups.
The objective poorness or non-poorness will be assessed with the fuzzy poverty lines method. A
household will be considered poor with a qualification lower than “High” (Left branch and
) and will be considered non poor in any other situation.
The subjective feeling of poverty will be determined with ILBE index. Once is approximated
to a label of the set , it will be considered feeling poor households those who gets a valuation
lower than “bad” ( , and ), and feeling non poor in any other situation.
Households will be categorized into 4 groups.
Group 1. Poor / Feeling Poor.
Objective Poverty degree: “High”, “Very High” and
“Absolute”
ILBE: “Bad”, “Very Bad” and “Dreadful”.
Group 2. Poor / Non feeling poor.
Objective Poverty degree: “High”, “Very High” and
“Absolute”
ILBE: “Mean”, “Good”, “Very Good” and “Excellent”.
Group 3. Non poor / Feeling poor. Group 4. Non poor / Non feeling poor.
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30
Objective Poverty degree: “Medium”, “Low”, “Very
Low” and “Null”
ILBE: “Bad”, “Very Bad” and “Dreadful”.
Objective Poverty degree: “Medium”, “Low”, “Very
Low” and “Null”
ILBE: “Mean”, “Good”, “Very Good” and “Excellent”.
Special attention will be paid to Group 2 and 4 in order to make deeper analysis of the
determinants of perceptions of poverty.
3. Application
A household will be evaluated in order to classify it into one of the four groups outlined above.
In first place, it will be calculated the Fuzzy poverty line for that family, and then it will be
compared with its income. For that period, the amount needed to buy the Fuzzy Basic Food
Basket for the equivalent adult will be an approximate triangular fuzzy number:
82.2031,62.1766,50.1501CBAFV [17, 19]. Fuzzy inverse of Engel's coefficient will be
50.2,41.2,30.2~ e , and the poverty line for the equivalent adult will be an approximate
triangular fuzzy number 55.5079,4.4257,45.3453~. eVLP CBAFf.
Household is structured as follows: Head of household, a female 35 years old, her son 18 years
old and her mother 61 years old. This household represents 59.2,44.2,17.2hU units of
equivalent adults. The fuzzy poverty line will be calculated and approximated to a triangular
fuzzy number 03.1315605.1038898.7493 ,,LPULP f
hh
f [17, 19].
The family declares to the interviewer that its monthly effective total income is $9500. Thus, its
income belongs to the poverty set in a 0.69 degree; household presents a high level of objective
poverty.
In a second phase, the household answer the subjective survey. The responses where:
Question Valuation Associated Linguistic Label
1 Good 141Sssq
2 Good 142Sssq 421
, sssEAAs qqhe
3 Mean 133Sssq
4 Good 144Sssq 5.343
, sssEAAs qqed
5 Bad 125Sssq
6 Bad 126Sssq 265
, sssEAAs qqho
7 Very bad 117Sssq
8 Bad 128Sssq 5.187
, sssEAAs qqi
9 Mean 139Sssq
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31
10 Mean 1310Sssq 3109
, sssEAAs qqem
11 Rather
poor 2211
Sssq
12 Bad 1212Sssq
Question 13: 1. Health Very important 351Sss
25.01 w
2. Education Very important 352Sss 25.02 w
3. Housing Careless 333Sss 15.03 w
4. Income Pretty Important 344Sss 20.04 w
5. Employment Careless 335Sss 15.05 w
1392.2,,,, SssssssssEWAAILBE hemihoedhehh → presents a mean feeling of poverty.
When classifying into one of the groups, this household belongs to Group 2 “Poor / Non feeling
poor”. Further analysis will be needed to understand why this family doesn’t perceive poverty or
maybe it weigh mostly access to certain goods or services than its own income.
4. Conclusions
Subjective welfare measures are a complementary tool of objective indicators. It is important to
understand the connection between objective and subjective improvements.
The proposed approach allows showing different groups considering objective and subjective
poverty. This disaggregated analysis will help the analysts to understand the determinants of
poverty perceptions in relation to objective well-being.
The implementation of linguistic models will help to understand the degrees inherent in the
analysis of human welfare.
In future researches it will be interesting to go deeper into the structure of the survey, the
determinants of welfare perceptions versus the objective situation of poverty, and it will be
possible to make contributions regarding the construction of a single index combining both
approaches.
Acknowledgement
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32
The authors thanks to the Secretaría de Ciencia y Técnica of the Universidad de Buenos Aires
(UBACyT Project 2016 20020150100090BA), to the Facultad de Ciencias Económicas of that
University where the Project belongs to and to the Consejo Nacional de Investigaciones
Científicas y Técnicas (CONICET).
References
[1] Bentham, J. (1948). An Introduction to the principles of morals and Legislation. Oxford
Blackwell.
[2] Mill, J.S. (1971). El Utilitarismo. Ediciones Aguilar.
[3] Iglesias Vázquez, Emma; Pena López, José Atilano; Sánchez Santos, José Manuel (2013).
“Bienestar Subjetivo, Renta Y Bienes Relacionales. Los determinantes de la felicidad en
España”. Revista Internacional de Sociología (RIS), Vol.71, nº 3. pp. 567-592.
[4] Veenhoven, R. (2009). «Measures of Gross National Happiness». Intervención Psicosocial
18(3), pp.279-299.
[5] Vargas Pérez, Andrés Mauricio (2013). “Bienestar subjetivo y políticas públicas de los
gobiernos locales”. Revista de Economía del Caribe n°12, pp. 106-129
[6] Carrasco-Campos, Ángel; Martínez, Luis Carlos; Moreno Mínguez, Almudena (2013).
“Revisión crítica de la medición del bienestar desde una perspectiva interdisciplinar”. Prisma
Social - Revista de Ciencias Sociales nº 11. Pp. 91-122.
[7] Yasuko Arita, B., Romano, S., García, N., del Refugio Félix, M. (2005). “Indicadores
objetivos y subjetivos de la calidad de vida”. Enseñanza E Investigación En Psicología
vol.10, num. 1, pp. 93-102.
[8] Aguado Quintero, L.F.; Osorio Mejía, A.M. (2006). ”Percepción subjetiva de los pobres:
Una alternativa a la medición de la pobreza”. Reflexión Política Año 8 Nº 15, pp. 26-40.
[9] Ravallion, M. (2010). “On multidimensional indices of poverty” Journal of Economic
Inequality.
[10] Giarrizo, V. (2007). Pobreza Subjetiva en Argentina. Construcción de indicadores de
Bienestar Económico. Tesis Doctoral. Facultad de Ciencias Económicas. Universidad de
Buenos Aires.
[11] Bradshaw, J., Finch, N. (2003). “Overlaps in Dimensions of Poverty”. Journal of Social
Policy 32, pp. 513-525.
[12] Zadeh, L.A. (1975). “The concept of a linguistic variable and its applications to approximate
reasoning”. Part I, Information Sciences, Vol. 8, pp.199-249. Part II, Information Sciences,
Vol. 8, pp.301-357. Part III, Information Sciences, Vol. 9, pp.43-80.
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[13] Herrera, F.; Herrera-Viedma, E. (2000). “Linguistic decision analysis: steps for solving
decision problems under linguistic information”. Fuzzy Sets and Systems, vol. 115, pp.67-
82.
[14] Lazzari, L.L. (2010). El comportamiento del consumidor desde una perspectiva fuzzy.
Editorial Edicon.
[15] Xu, Z. (2008). “Linguistic aggregation operators: An overview” en: Bustince, H. et al. (eds.),
Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Berlin: Springer-
Verlag, pp.163-181.
[16] Lazzari, L.L., Fernandez M.J., Mouliá, P.I. (2013). “Welfare Linguistic Subjective
Indicator” en Anna M. Gil Lafuente; José M. Merigó, Luciano Barcellos-Paula, F. Silva-
Marins, C. Azevedo-Ritto (editors) Decision Making Systems in Business Administration.
World Scientific, Singapore. ISBN 978-981-4452-04-5.
[17] Fernandez, M.J. (2012). Medidas de pobreza. Un enfoque alternativo. Tesis Doctoral.
Facultad de Ciencias Económicas. Universidad de Buenos Aires.
[18] Kaufmann A., Gil Aluja J., Terceño Gómez A. (1994). Matemática para la Economía y la
Gestión de Empresas. Ediciones Foro Científico. Barcelona.
[19] INDEC (2017). Condiciones de vida. Vol. 1, nº 4 Incidencia de la pobreza y la indigencia en
31 aglomerados urbanos. Segundo semestre de 2016. Instituto Nacional de Estadística y
Censos (INDEC), Buenos Aires.
Appendix. Survey form
1. You consider that your access to health care is:
Dreadful – very bad – bad – mean – good- very good – excellent.
2. You consider that your access to medication and vaccination, if needed, is:
Dreadful – very bad – bad – mean – good- very good – excellent.
3. You consider your education level is:
Dreadful – very bad – bad – mean – good- very good – excellent.
4. You consider that access to the education system is:
Dreadful – very bad – bad – mean – good- very good – excellent.
5. You consider that your housing conditions are:
Dreadful – very bad – bad – mean – good- very good – excellent
6. You think that the general conditions of their neighborhood (asphalt, lighting, sewers,etc.) are:
Dreadful – very bad – bad – mean – good- very good – excellent
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34
7. You think your income is:
Dreadful – very bad – bad – mean – good- very good – excellent
8. How much extra home income your household need not to feel poor?
Income amount Linguistic
label
Income
amount
Linguistic
label
More than double Dreadful 40 – 50%
more Good
double Very bad 10 -30 %
more Very good
80 – 90% more Bad nothing excellent
60 – 70% more Mean
9. Considering the number of the amount of hours that you work, you find it:
Dreadful – very bad – bad – mean – good- very good – excellent
10. You think that your working conditions are:
Dreadful – very bad – bad – mean – good- very good – excellent
11. Do you feel poor?
Absolutely poor – very poor – rather poor – nor poor or not poor – somewhat poor – almost non
poor – non poor.
12. How do you evaluate your level of economic welfare?
Dreadful – very bad – bad – mean – good- very good – excellent
13. Indicate the importance of each area for your welfare.
area Absolut.
important
Very
important
Pretty
important Careless
Little
important
Rather
unimportant Unimportant
1. health
2. Education
3. Housing
4. Income
5. Employment
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1
Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 1-10
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Venture Capital Research: A Bibliometric Analysis
*C.A. Cancino, **J.M. Merigó, ***D. Díaz, ****J.P. Torres
Department of Management Control and Information Systems and Department of Business,
University of Chile
Av. Diagonal Paraguay 257, 8330015 Santiago, Chile
(*[email protected] , **[email protected] , ***[email protected] ,
****[email protected] )
Abstract
Venture capital research is becoming very significant during the last decades. The aim of
this study is to present a general overview of the leading journals, articles and authors in
venture capital research between 1990 and 2014. Different analyses were performed, all of
them at a general level for the described period. In order to do so, as is usual in bibliometric
analysis, this work uses the Web of Science database. The article provides several
bibliometric indicators, that includes the total number of publications, the total number of
citations, and the h-index. The main contribution of this work is to develop a general
overview of the leading journals, authors, universities in venture capital research, which
leads to the development of a future research agenda for bibliometric analysis, such as the
review of the most productive and influential authors, universities, and countries in venture
capital research.
Keywords: Venture Capital; Bibliometrics; Journals; Authors, Universities; Web of
Science.
1. Introduction
Venture Capital (VC) is an instrument for supporting the development and growth of new
enterprises through the provision of financial resources and also offers business expertise,
customer networks and good management practices (Hochberg et al., 2010). According to
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Cornelius and Persson (2006), venture capitalists are financial intermediaries who collect
excess capital from those who have it, and provide it to those who require it for the
development of a business venture. In general, in the decades, venture capital research has
grown considerably in proportion to other disciplines.
This article develops a way to analyze venture capital research over the last 25 years by
using bibliometric indicators. Bibliometric studies are becoming very popular in the
scientific literature (Merigó et al., 2016), strongly motivated by the access to bibliographic
information. Some studies have developed bibliometric analyses in a wide range of fields
including: entrepreneurship (Landström, 2012), innovation (Cancino et al., 2017a, 2017b),
health economics (Wagstaff and Culyer, 2012), among others.
The article develops a journal and authors analysis identifying the leading ones in the field.
In particular, this work describe that there are certain specialized journals that publish more
in venture capital research with respect to other journals, for example, Journal of Business
Venturing, Entrepreneurship Theory and Practice, and Small Business Economics. It also
highlights other journals for having a high number of citations, even if they publish a large
number of articles in VC research, such as the Journal of Finance, Journal of Financial
Economics, Research Policy, Strategic Management Journal, Academy of Management
Journal, Administrative Science Quarterly, among others. Moreover, a temporal analysis is
developed in order to see which journals have been the most influential ones throughout
time.
2. Literature Review
According to Gompers et al. (2008), Venture Capital (VC) research explores different
steps, which involve the pre-investment phase of VC, the management of VC, and the exit
strategies of VC. In the first step, pre-investment phase, VC research explores how changes
in public market signals affected VC, or the conditions to facilitate the creation of greater
firm value after receiving VC (Dushnitsky and Lenox, 2006). Research in this stage also
analyses the process of creating relationships between venture capitalists and entrepreneurs
(Hochberg et al., 2010). In the second step, research in the management stage focused its
attention on companies when they receive VC. For examples, researchers have explored the
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3
links between the influence and control of VC firms (Bottazzi, Da Rin & Hellmann, 2008)
and the management skills and expertise of entrepreneurs and new ventures, such as
entrepreneurial orientation (Stam & Elfring, 2008). Finally, research in the exit step
reviews how firms can develop either their initial public offering (IPO) or their buyout.
Nahata (2008) suggests that companies backed by more reputable VCs by initial public
offering (IPO) capitalization share, are more likely to exit successfully, access public
markets faster, and have higher asset productivity at IPOs.
Even though VC research has three stages of analysis, VC research encompasses wide
range of academic areas, without a particular discipline leading scientific research in this
field. Academics from disciplines such as Finance, General Management, Innovation, Law,
Public Policy, Sociology and Economics present a wide range of research on venture
capital, which is very valuable because it brings different perspectives to analyze the
problem of financing new businesses.
The above shows that the analysis of VC research is varied and can derive from different
disciplines. It could be positive to have different perspectives to try to understand the
problem.
3. Methods
Bibliometric research is a field that quantitatively studies bibliographic material (Broadus,
1987) providing a general overview of a research field according to a wide range of
indicators. There are different ways of ranking material in a bibliometric analysis. The most
common approaches use the total number of articles or the total number of citations.
Another useful indicator is the h-index (Hirsch, 2005) that combines articles with cites
indicating the number of studies X that have received X or more citations. Normally, the
information about citations, total number of articles or h-index can be obtained from
academic databases as Web of Science (WoS), Scopus or Google Scholar. WoS is one of
the most popular databases for classifying scientific research worldwide. The assumption is
that it only includes those journals that are evaluated with the highest quality.
In order to search for articles that have focused on venture capital research, the study uses
the keywords “venture capital*” or “business venturing” or “corporate venturing” in the
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4
title, abstract and keywords of any work available in WoS between 1990 and 2014, in order
to capture as many possible combinations of terms related to venture capital. This search
finds 2.086 articles that have become 1.820 studies by only considering articles, reviews,
letters and notes. The search was developed in October 2015 and January 2016.
4. Results
There are many journals in the scientific community that publishes material related to
venture capital research. Table 1 presents a list of the twenty journals with the highest h-
index in venture capital research.
R Journal Venture Capital
TPV TCV HV TP
1 Journal of Business Venturing 164 6976 48 836
2 Journal of Finance 23 2923 21 1972
3 Journal of Financial Economics 35 2884 21 1791
4 Entrepreneurship Theory and Practice 49 1070 21 515
5 Research Policy 37 1609 20 2059
6 Small Business Economics 67 833 16 1252
7 Strategic Management Journal 25 1477 15 1726
8 Journal of Management Studies 23 624 14 1252
9 Journal of Banking Finance 25 1024 13 3561
10 Journal of Corporate Finance 35 569 13 723
11 Technovation 30 396 13 1538
12 Academy of Management Journal 19 916 11 1490
13 Review of Financial Studies 26 763 10 1377
14 Harvard Business Review 26 634 10 4847
15 Management Science 14 966 9 3247
16 Entrepreneurship and Regional Development 18 300 9 381
17 Administrative Science Quarterly 8 1050 8 512
18 Organization Science 16 613 8 1301
19 Financial Management 14 494 8 832
20 Journal of International Business Studies 11 260 8 1162
Table 1: Most influential journals in venture capital research according to WoS
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5
R means rank, HV means h-index in venture capital research, TPV means the total number
of publications in venture capital research, TCV means the total number of citations
in venture capital research, and TP means the total number of publication of the journal.
The first journal of the Table 1, Journal of Business Venturing, publishes about 20% of the
total articles on venture capital research,
Also, Table 1 show that scientific analysis on venture capital comes from many disciplines,
and it is not possible to identify a specific group of journals leading the discipline. This is
evident if the group of the twenty most cited papers in venture capital research is analyzed
(Table 2).
R Authors Year Journal
1 Stuart, TE; Hoang, H; Hybels, RC 1999 Administrative Science Quarterly
2 Zucker, LG; Darby, MR; Brewer, MB 1998 American Economic Review
3 Sahlman, WA 1990 Journal of Financial Economics
4 Megginson, WL; Weiss, KA 1991 Journal of Finance
5 Powell, WW; White, DR; Koput, KW; Owen-Smith, J 2005 American Journal of Sociology
6
Krueger, NF; Reilly, MD; Carsrud, AL
2000 Journal of Business Venturing
7 Berger, AN; Udell, GF 1998 Journal of Banking & Finance
8 Lee, C; Lee, K; Pennings, JM 2001 Strategic Management Journal
9 Sorenson, O; Stuart, TE 2001 American Journal of Sociology
10 Mcdougall, PP; Shane, S; Oviatt, BM 1994 Journal of Business Venturing
11
Shane, S; Stuart, T
2002 Management Science
12 Kaplan, SN; Stromberg, P 2003 Review of Economic Studies
13 Podolny, JM 2001 American Journal of Sociology
14 Hellmann, T; Puri, M 2002 Journal of Finance
15 Black, BS; Gilson, RJ 1998 Journal of Financial Economics
16
Kortum, S; Lerner, J
2000 Rand Journal of Economics
17 Lerner, J 1995 Journal of Finance
18 Di Gregorio, D; Shane, S 2003 Research Policy
19 Zucker, LG; Darby, MR; Armstrong, JS 2002 Management Science
20 Barry, CB; Muscarella, CJ; Peavy, JW; Vetsuypens, MR 1990 Journal of Financial Economics
Table 2: Most cited articles in venture capital research according to WoS
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For this group it is possible to identify 12 different journals: Administrative Science
Quarterly, American Economic Review, American Journal of Sociology, Journal of
Banking & Finance, Journal of Business Venturing, Journal of Finance, Journal of
Financial Economics, Management Science, Rand Journal of Economics, Research Policy,
Review of Economic Studies and Strategic Management Journal. Among this group, three
journals (Journal of Financial Economics, Journal of Finance and American Journal of
Sociology) present three articles each on the list of the 20 most cited papers in venture
capital research.
Some leading authors in venture capital research stand out in this discipline, not only
because of the large number of publications which they develop but also because of their
high influence on the rest of the researchers of the world. Table 2 presents a ranking with
20 leading authors in venture capital research, which are classified according to their h-
index, which allows us to analyse their influence on other researchers.
R Name University Country TP TC H
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Lerner J
Wright M
Shepherd DA
Cumming D
Lockett A
Sapienza HJ
Mason CM
Harrison RT
Gompers P
Busenitz LW
Manigart S
Hellmann T
Keil T
Schwienbacher A
Bruton GD
Dushnitsky G
Keuschnigg C
Pollock TG
Zahra SA
Dimov D
Harvard University
Imperial College Business School
Indiana University
York University
University of Nottingham
University of Minnesota
University of Strathclyde
University Belfast
Harvard University
University of Oklahoma
School and Ghent University
University of British Columbia
Aalto University
University of Amsterdam
Christian University
London Business School
University of St. Gallen
The Pennsylvania State University
University of Minnesota
Newcastle University Business School
USA
UK
USA
Canada
UK
USA
UK
UK
USA
USA
Belgium
Canada
Finland
Netherlands
USA
UK
Switzerland
USA
USA
UK
27
42
22
29
16
13
12
11
10
10
20
8
8
11
8
7
8
7
8
8
2821
1368
966
657
604
925
311
296
860
591
481
1003
266
180
411
383
358
344
296
158
21
20
17
16
13
12
12
11
10
10
10
8
8
8
7
7
7
7
7
7
Table 3: The most influential authors in venture capital research according to WoS
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7
The results shown in Table 3 are that researchers from the USA and UK lead the ranking of
the most influential authors in venture capital research. Among the first 10 authors, 50%
works in USA universities and 40% works in UK universities. Also, from the total of 20
leading authors 60% works in USA and UK universities. Following the USA and UK,
researchers from Belgium, Canada, Finland, Netherlands and Switzerland are present in our
rankings. Another important highlight is that the most influential authors come from
different universities; the generation of the most influential knowledge on venture capital
research is not gathered in any particular university. In fact, among U.S. universities, only
Harvard University presents two authors in our rankings.
5.- Conclusions
This work presents a general overview of the leading journals, articles and authors in
venture capital research between 1990 and 2014. Different analyses were performed, all of
them at a general level for the described period.
First, the analysis focused on studying a ranking of 20 leading journals that present a
greater h-index in the discipline. In this ranking, it is possible to observe an interesting
discussion that reveals that the most productive journals, i.e., those who have a greater
quantity of published work, are not necessarily the most influential, i.e. those who have a
greater number of citations by the scientific community. Only one case, Journal of Business
Venturing which is the most productive, is also the most influential journal. Evidently, this
is the only specialized journal in venture capital research. Interestingly, some cases, such as
Journal of Finance, Strategic Management Journal and Journal of Banking & Finance,
present an important number of citations (more than 1000) in fewer than 25 papers. These
three journals, despite not being specialized in venture capital research, publish very
influential papers. The work also develops ranking of the more cited articles in venture
capital research and a list with most influential authors in the discipline under study.
Clearly, venture capital research will continue growing and it is necessary to deepen the
analysis of the authors, countries and universities that lead research in this discipline, who
are not only the most productive players but also the most influential actors.
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Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 11-22
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Fuzzy Logic Measures and Non-Monotonic Distances Applied to
Color Psychology
* Flor Madrigal Moreno, **Andreia Cristina Müller, **Jaime Gil Lafuente, ***José M. Merigó
Lindahl
* Department of Accounting and Administrative Sciences, Universidad Michoacana de San
Nicolás de Hgo., Av. J. Mújica S/N, Felicitas del Rio 58030, Michoacán, México.
[email protected]
**Department of Economy and Business Organizations, Universidad de Barcelona
Av. Diagonal 690, 08034 Barcelona, España. [email protected] / [email protected]
***Department of Management, Control and Information Systems, Universidad de Chile
Diagonal Paraguay 257, Of. 1906, 833015, Santiago, Chile. [email protected]
Summary
The intention of this paper is to shape the profile of millennials by using fuzzy logic and color
psychology, with the purpose of having a communicative approach through the use of color red.
The data were collected from the literature review, and then a mathematical assessment was
given. The distances were measured to find the communication degree that the color red has with
the millennials, since it is linked with passion, consumption, practicality, and selectivity,
elements that reveal the attitude of this market segment. The Hamming distance and the ordered
weighted average (OWA) were used. The ordered weighted average distance operator (OWAD)
was also used; and finally, calculations were made with nonmonotonic operators of NOMOWA,
which has a negative value, and which exhibit non-monotonicity.
Keywords: Fuzzy logic, non-monotonic distances, color psychology, millennials.
1. Introduction
In recent years the study of generational groups has taken relevance, the millennial generation
stands out by its own, particularly for its buying behavior in addition to consumption in digital
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environment. It is an attractive market for sensory and digital marketing since they are young
people who are accustomed to giving their opinion and being listened, guided not by established
formality, but by natural behaviors and providing credit to useful information from the interaction
between them through social networks.
Research related to the generation of communication links and the use of specific colors will
influence the millennials when making decisions. In specific, the red color is influencing them,
becoming then, an important part of their everyday decisions. Companies around the world use
signals such as colors and shapes to convey a brand image and to increase the possibility of
consumer purchase (Hess & Melnyk, 2016).
This research paper is based on the measurement of perceptions about the color red and what it
communicates, linked to the characteristics that define the millennials. When reference is made to
a subjective "sensation" or "perception" that is not possible or cannot be measured, another
concept is used: the valuation, using the theory of fuzzy numbers (Kaufmann & Gil Aluja, 1986).
Through the literature review, first the mathematization of the colors is carried out and then the
mathematization of the words that define millennials utilizing the fuzzy logic. The mathematical
framework allows modeling the uncertainty of the cognitive human processes that can be treated
by a computer (González, 2011), then the:
1.Weighted Hamming Distance (WHD) has been used to show the most definitive coincidences
between the characteristics of the millennials and the colors that communicate the values that
distinguish them, in such a way that the researchers of this generational group have more
information that allows them to approach to this group of people in specific.
2. Subsequently, the Ordered Weighted Average Distance OWAD was used;
3. After the Non-Monotonic Weighted Hamming Distance- NON-MONOTONIC-WHD;
4. The weighted average non-monotonic ordered distance is calculated. NON-MONOTONIC
OWAD. All the above tools will allow to observe that the use of the weights adjusted to the
individual characteristics, means that the degree of uncertainty in measuring is less. Therefore,
the distance is also smaller (WHD and NON- NOMOTONIC WHD). On the other hand, when
the weights are only ordered, the degree of uncertainty is more significant. Therefore, the
distance also increases (OWAD and NON-MONOTONIC OWAD).
2. Preliminaries
2.1 Color psychology
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For centuries artists, philosophers, psychologists, and scientists have studied the effects of color,
developing many theories about the use of it. The number and variety of such approaches show
that universal rules cannot be applied: the perception of color depends on individual experiences.
To Goethe, it was really important to understand the human reactions to color, and his research is
a starting point of modern color psychology (Illusion Studio, 2016).
The study made by Kauppinen‐ Räisänen & Luomala, (2010), suggests that an essential function
played by colors is communication, and the evidence also shows the role of colors as a means of
communication. The color communication is related to the context, and there is a relationship
between the meaning of the packaging color and the type of product. Similarly, marketing
research suggests that consumers make product choices based on the meanings they associate
with colors and how the colors of the product fit their overall color preferences (Madden, Hewett,
& Roth, 2000).
2.2 Millennials
Millennials use consumption to define who they are and to distinguish themselves. In a research
made by Charters et al., (2011), it is evident that amongst millennial consumers the use of image,
color, and positioning vary from one country to another. On the other hand, a research made by
Credo, Lanier, Matherne, & Cox, (2016), shows that social and service-oriented activities are
increasingly important for young people.
In addition to a study made by Elliot & Barth, (2012), it was observed that in the design of wine
labels for millennial consumers, they want a more balanced mix between mind and heart (Harris
Interactive, 2001). This can explain their attempt to satisfy emotional needs through
consumption, often choosing brands of their choice in the same way they choose their friends
(Vrontis & Papasolomou, 2007).
Millennials are individualists, they do not want to be part of a mass of consumers, they are
selective, and they like personalized treatment. This includes products with a design, color, and
characteristics suitable for each buyer. In this line, colors often play a crucial role because they
are associated with a consumer culture or a consumer subculture. The notion of an association
between colors and cultures dates back to (Luckiesh, 1927), who proposed that race, customs and
the civilization type affect color preferences.
2.3 Fuzzy Logic implementation
The use of the Fuzzy model data analysis allows to have higher authenticity in the data collection,
maximizing the validity in the interpretation of results. This model reduces the uncertainty of the
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information as it adapts to the consumer's performance and potentiates efficiency in decision-
making (Casabayó & Borja, 2010).
The complexity of the problems and the inaccuracy of the situations have made it necessary to
introduce mathematical schemes that are more flexible and adapted to reality. In this sense, the
theory of fuzzy sets, has allowed the birth of some techniques that will facilitate the solution of
those problems in which uncertainty appears (Kaufmann & Gil Aluja, 1986).
The theory of fuzzy sets is used to develop an evaluation procedure adjusted to reality. The
proposed approach makes it possible to treat impact dimensions as linguistic variables and, based
on them, formulate evaluative criteria in the form of fuzzy rules (García, Félix Benjamín, & Bello
Pérez, 2014).
2.4 Hamming Distance
The Hamming Distance is a useful technique to calculate the differences between two elements,
two sets, etc. For example, it can be useful in the fuzzy set theory to calculate the distances
between Fuzzy sets, Fuzzy value intervals, intuitionist fuzzy sets and interval intuitionist fuzzy
sets. The Hamming distance adapted from (Gil, 2012) can be described as follows:
Hamming between two fuzzy subsets and j:
Next:
To carry out this comparison, it is expected to use the so-called "Hamming relative distance." It is
obtained by dividing the absolute distance by the number of characteristics, qualities or
singularities, in this case, "n." It will be then:
D
˜
P
˜
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15
2.5 OWA Operators
OWA operators are tools that allow adding information. That is, from a series of data, a single
representative value of the information can be obtained. As an additional characteristic of the
OWA operators, it can be said that the elected value obtained is an added value according to
predetermined optimism/pessimism parameters (Merigó, 2008).
The ordered weighted average distance operator (OWAD) is used as a data analysis tool since it
provides a parametrized family of distance aggregation operators between the maximum distance
and the minimum distance and can be further extended using other types of ranges such as the
Euclidean distance, the Minkowski distance, and the quasi-arithmetic distance (Merigo & Gil-
Lafuente, 2012).
1
n| ai -bi |
i=1
n
åæ
èç
ö
ø÷
2.6 Non-monotonic OWA and OWAD operators
It can be defined as follows for two sets X = {x1, x2, …, xn} and Y = {y1, y2, …, yn}.
Definition 1. A non-monotonic OWAD operator of dimension n is a NOM-OWAD mapping: [0,
1]n [0, 1]n → [0, 1] that has an associated weighting vector W with 11 nj jw and wj [-1, 1]
so that:
NOM-OWAD (x1, y1, x2, y2, …, xn, yn) =
n
jjj Dw
1
,
Where Dj is the j value of the longest individual distance from | xi - yi |
It should be noted that the main difference with the NOM-OWAD is that the weighting vector wj:
can be less than 0. In definition 1 the study considers between -1 and 1. But it is also possible to
consider more general cases, heavy OWA (Yager, 1999) (Merigo & Gil-Lafuente, 2012), where
weights can move between -∞ and ∞.
3. Applications
This is a transactional qualitative research, with primary and secondary data obtained from the
analysis of books, scientific articles, and specialized marketing magazines. A selection of
literature was carried out that in an extensive and detailed way to describe the importance of
color, its general aspects, its symbolism, what it communicates, as well as the characteristics and
concepts associated to it.
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As a second stage, some scientific articles were reviewed about millennials and their
consumption habits. The articles consulted to define the characteristics that define millennials
were the following: Engagement and talent management of gen Y(Weyland, 2011); Generation Y
values and lifestyle segments, (Valentine & Powers, 2013); Millennials (Gen Y) consumer
behavior, their shopping preferences and perceptual maps associated with brand loyalty, (Ordun,
2015); Consumer expectation from online retailers in developing e-commerce market: An
investigation of developing online market in Bangladesh, (Rahman, 2015a); Optimizing digital
marketing for generation Y: An investigation of developing online market in Bangladesh,
(Rahman, 2015b); Hip to be cool: A gen Y view of counterfeit luxury products, (Francis &
Burgess, 2015); Discovering the millennials’ personal values orientation: A comparison to two
managerial populations, (Weber, 2015); Effects of consumer embarrassment on shopping basket
size and value: A study of the millennials consumer, (Satinover N., Raska, & Flint, 2015);
Adaptative use of social networking applications in contemporary organizations: Examining the
motivations of gen Y cohorts, (Shirish, Boughzala, & Srivastava, 2016); Online purchase
behavior of generation Y in Malaysia, (Muda, Mohd, & Hassan, 2016); Acceptance of online
mass customization by generation Y, (Junker, Walcher, & Blazek, 2016); Gen Y: A study on
social media use and outcomes, (Omar, 2016); Creativity and cognitive skills among millennials:
Thinking too much and creating too little, (Corgnet, Espín, & Hernán-González, 2016); Gen Y
customer loyalty in online shopping: An integrated model of trust, user experience and branding,
(Bilgihan, 2016) y Generation X vs Generation Y: A decade of online shopping, (Lissitsa & Kol,
2016).
Later a matrix of the millennials’ profile was elaborated; the words that describe their personality
were identified, where these words that characterize them are mathematically defined, generating
then a pattern. An scale was established where the numerical interval from 0 to 1, according to
the highest occurrences of each word in the articles consulted, as well as the intensity of the
description to each construct. Later, a table is developed to establish a relationship between the
words associated with the profile of the millennials and the degree of association of each of these
words with the color red.
Table 1 shows the data using Weighted Hamming Distance (WHD) and the Ordered Weighted
Average Distance (OWAD).
Table 1. Hamming Distance, WHD, and OWAD to calculate distances.
Calculations Hamming Distance WHD OWAD
Characteristics HD W W*
Results
W Ŵ Ŵ* Results Ŵ
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W1 Hope 1 0.35 0.026 0.026 0.85 0.064 0.064
W2 Technology 1 0.65 0.049 0.049 0.65 0.049 0.049
W3 Freedom 1 0.30 0.022 0.022 0.65 0.049 0.044
W4 Innovation 0.9 0.21 0.016 0.014 0.55 0.042 0.037
W5 Balance 0.9 0.21 0.016 0.014 0.35 0.026 0.024
W6 Friendship 0.9 0.21 0.016 0.014 0.35 0.026 0.024
W7 Communication 0.9 0.55 0.041 0.037 0.30 0.023 0.018
W8 Perception (interaction) 0.8 0.21 0.016 0.013 0.25 0.019 0.015
W9 Education 0.8 0.21 0.016 0.013 0.25 0.019 0.015
W10 Cooperativism 0.8 0.21 0.016 0.013 0.21 0.016 0.013
W11 Dynamism - multitasking 0.8 0.25 0.019 0.015 0.21 0.016 0.011
W12 Strong intellect /intelligence 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W13 Connectivity 0.7 0.35 0.026 0.018 0.21 0.016 0.011
W14 Leadership 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W15 Emotional sensitivy 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W16 Attention 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W17 Ethics 0.7 0.21 0.016 0.011 0.21 0.016 0.011
W18 Egocentrism 0.7 0.35 0.026 0.018 0.21 0.016 0.010
W19 Trust 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W20 Human values 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W21 Entertain 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W22 Personal growth 0.6 0.21 0.016 0.009 0.21 0.016 0.010
W23 Changes 0.6 0.21 0.016 0.009 0.21 0.016 0.008
W24 Joy 0.5 0.21 0.016 0.008 0.21 0.016 0.008
W25 Impersonality 0.5 0.21 0.016 0.008 0.21 0.016 0.008
W26 Pleasure 0.5 0.25 0.019 0.009 0.21 0.016 0.006
W27 Beauty 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W28 Health 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W29 Depression 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W30 Protection 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W31 Positive energy 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W32 Easy 0.4 0.21 0.016 0.006 0.21 0.016 0.006
W33 Solvency 0.4 0.21 0.016 0.006 0.21 0.016 0.005
W34 Experience 0.3 0.65 0.049 0.015 0.21 0.016 0.005
W35 Stability 0.3 0.21 0.016 0.005 0.21 0.016 0.003
W36 Luxury/sophistication 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W37 Fidelity 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W38 Self-confidence 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W39 Activity / Anxiety 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W40 Love 0.2 0.21 0.016 0.003 0.21 0.016 0.003
W41 Coherence 0.2 0.21 0.016 0.003 0.21 0.016 0.002
W42 Passion 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W43 Power 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W44 Work /Physical activity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W45 Selectivity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W46 Maturity 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W47 Competitiveness 0.1 0.21 0.016 0.002 0.21 0.016 0.002
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W48 Consumption 0.1 0.85 0.064 0.006 0.21 0.016 0.002
W49 Commitment 0.1 0.21 0.016 0.002 0.21 0.016 0.002
W50 Nutrition /feeding 0.1 0.21 0.016 0.002 0.21 0.016 0.000
W51 Praticity 0 0.21 0.016 0.000 0.21 0.016 0.000
W52 Bored 0 0.21 0.016 0.000 0.21 0.016 0.016
TOTAL 0.475 13.37 1 0.494 13.23 1 0.556
Source: Original from the author.
Table 1 shows how the distances are different using each method, with Hamming distance the
value is 0.475, while using weighted Hamming Distance (OWA), the result is 0.494, and with
Distance (from Hamming) ordered weighted average (OWAD), the value is 0.556. When the
weights are ordered, the degree of uncertainty is more significant therefore the distance increases.
4. Non-monotonic applications
NOMOWA operators have negative weights and exhibit non-monotonicity. While monotonicity
is undoubtedly a useful property in aggregation, there are situations in which nonmonotonicity
may be helpful. A potential application of these non-monotonic operators of OWA is in the
multi-criterion aggregation domain guided by quantizer in which the guide quantifier is not
monotonic (Yager, 1999).
The author Ovchinnikov, (1998) introduced an extension of the OWA operators that allow the
possibility of having a non-monotonicity in the aggregation process.
The following is shown in Table 2. The distinctive feature of these operators that allow negative
weights to be used in the OWA weighting vector, the application of non-monotonic tools: Non-
monotonic weighted Hamming Distance (WHD) and the weighted average distance ordered non
monotonic (OWAD), applied to color red, where the weighting was made based on the literature
review of color psychology to relate the reactions that could be extreme by red.
Table 2. Application of non-monotonic tools WHD and non-monotonic OWAD
Non-Monotonic-WHD Non-Monotonic-OWAD
Characteristic Non-Mon-WHD Non-Mon-WHD*
Results Non- Mon -
OWAD
Non- Mon -
OWAD*
Results
Non-Mon-WHD Non- Mon -
OWAD
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W8 -0.3 -0.019 -0.015 0.9 0.057 0.046
W11 -0.2 -0.013 -0.01 0.8 0.051 0.035
W15 -0.1 -0.006 -0.004 0.5 0.032 0.022
W17 -0.4 -0.025 -0.018 0.45 0.029 0.02
W19 -0.3 -0.019 -0.011 0.4 0.025 0.015
W20 -0.3 -0.019 -0.011 0.4 0.025 0.015
W28 -0.4 -0.025 -0.01 0.2 0.013 0.005
W29 -0.5 -0.032 -0.013 0.2 0.013 0.005
W34 -0.1 -0.006 -0.002 0.1 0.006 0.002
W37 -0.1 -0.006 -0.001 0.1 0.006 0.001
W41 0 0 0 -0.1 -0.006 -0.001
W42 1 0.063 0.006 -0.1 -0.006 -0.001
W43 0.9 0.057 0.006 -0.1 -0.006 -0.001
W44 0.8 0.051 0.005 -0.2 -0.013 -0.001
W45 0.2 0.013 0.001 -0.2 -0.013 -0.001
W46 0.2 0.013 0.001 0.3 0.019 0.002
W47 0.4 0.025 0.003 -0.3 -0.019 -0.002
W48 0.1 0.006 0.001 -0.3 -0.019 -0.002
W49 0 0 0 -0.3 -0.019 -0.002
W50 -0.2 -0.013 -0.001 -0.4 -0.025 0
W51 0.3 0.019 0 -0.4 -0.025 0
W52 0 0 0 -0.5 -0.032 -0.032
TOTAL 15.78 1 0.501 15.78 1 0.811
Source: Original from the author.
5. Conclusions
This research allows to know the demands of the millennial generation, and to discover the
perception they have over certain products and services. By using the fuzzy logic, the Hamming
distance, the ordered weighted average (OWA), the ordered weighted average distance operator
(OWAD) and the nonmonotonic operators of NOMOWA, it has been possible to value the
millennial's perceptions. The millennial generation has an imprecise conduct. Therefore, the
behavioral phenomenon must be contextualized to a geographical place and specific conditions.
In this context, the theory of fuzzy sets allows reducing the uncertainty when communicating
with the millennials. Fuzzy logic does not increase the difficulty of traditional mathematics and is
closer to human thinking (Canós, 2013).
It is important to clarify that shorter distances are the ideal ones since they accurately show a
slight gap between the ideal and what is sought, before this it can be established that the red color
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is not exactly the one that generates more anchoring with the millennials according to the
mathematical results. However, the color red is linked to consumption, passion, practicality and
selectivity, elements that reveal to a large extent the tastes and preferences of this market
segment, as well as its link with the brands, generating a passionate defense of the brands that
define them. And with those that they identify with, as well as those which they do not respect.
The selectivity of millennials includes friends, brands and experiences. Millennials like
distinctive brands.
This research focuses on the mathematical evaluation of the words that define the millennial and
the communication through colors, distinguishing the importance of the use of psychology color
and the analysis of phenomena related to perception through fuzzy logic as well as new non-
monotonic combination tools WHD and OWAD. Since these combinations use negative weights
for very radical aggregation cases, this analysis represents an innovation in the study of color
theory.
Finally, this document can be strengthened with future research where other colors are analyzed
and their link with millennials, as well as the integration of new combination tools.
6. References
Bilgihan, A. (2016). Gen Y customer loyalty in online shopping: An integrated model of trust,
user experience and branding. Computers in Human Behavior, 61(November), 103–113.
Canós, L. (2013). Gestión de recursos humanos basada en la lógica borrosa. Rect@: Revista
Electrónica de Comunicaciones Y Trabajos de ASEPUMA, (6), 29–60.
Casabayó, M., & Borja, M. (2010). Fuzzy Marketing. Barcelona, España: Deusto.
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Lectures on Modelling and Simulation; A selection from AMSE # 2017-N°1; pp 23-34
Selection at the AMSE Conference Valencia/Spain, July 13-14, 2017
Linguistic Measures of Subjective and Objective Poverty
Maria Jose Fernandez
Universidad de Buenos Aires, CIMBAGE, IADCOM / CONICET
Av. Córdoba 2122, Ciudad de Buenos Aires, C1120AAQ, Argentina
[email protected]
Abstract
Last decades several studies of subjective welfare with a great diversity of approaches have
appeared. Some have focused on finding variables that determine it. Others stress the importance
on quantifying it. Some investigates the determinants that make some people declare high levels
of welfare and others do not. One of crucial social problems in the study of welfare is the
recognition, measurement and analysis of the causes of poverty.
It is necessary to complement the objective poverty analysis with subjective indicators of
welfare in order to assess the correspondence between the objective improvements and the
subjective perceptions.
In this paper, we propose an evaluation model of Economic Welfare which includes
subjective and objective poverty indicators with the use of mathematical tools for the treatment of
uncertainty, in particular, linguistic models.
Keywords
Linguistic models, poverty measures, objective poverty, subjective poverty.
1. Introduction
Welfare Economics can be defined as a branch of Economics that explains the satisfaction of the
agents and the mechanisms that generate their increase and decrease. Its study is part of
disciplines as diverse as psychology, politics, sociology, philosophy and economics.
Utilitarianism posed by Bentham [1] and Mill [2] laid the foundations from which modern
Economic Science began the study of welfare. Welfare is also an abstract concept with subjective
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connotations, but correlated with objective economic factors and individual welfare refers to each
person's perception of having covered their needs [3].
During recent years, subjective assessments of quality of life are considered when measuring
development. It is often said that subjective welfare is a necessary and sufficient condition for
human development. Subjective welfare refers to an assessment of the welfare of an individual
obtained through a survey. Subjective happiness or welfare is a global assessment of the quality
of life by each individual [4]. The employment of subjective welfare measures is based on the
basic assumption the governments needs to evaluate the improvements in the quality of life of
their citizens [5]. Traditionally, study, measurement and design of public policies have paid
attention to economic indicators. Recent studies highlighted the importance of incorporating
subjective indicators, such as care or perception of happiness [6]. During last decades several
studies of subjective welfare that present a great diversity in the type of approach that they realize
have appeared. Some have focused on finding the variables that determine welfare. Others stress
the importance on quantifying happiness, and finally a group investigates the determinants that
make some people declare high levels of welfare and others do not. Dimensions that agents
consider important regarding their welfare and quality of life are the benchmark in the study of
subjective welfare. The self-evaluation that the subjects make regarding the satisfaction and
happiness they perceive in relation to the different dimensions is taken into account [7]. Main
social problems in the study of welfare are the recognition, measurement and analysis of the
causes of poverty. It is also fundamental to be able to design effective measures to reduce it.
However, this concept presents significant difficulties when it’s intended to measuring it
accurately. Evaluation of economic welfare can be based on two types of indicators: objective-
quantitative indicators (poverty lines, unsatisfied basic needs, human development index,
anthropometric indicators, etc.) and subjective-qualitative indicators (based on surveys that reveal
perceptions of individuals or households) [8].
Subjective poverty approach defines as poor those who are not satisfied with their situation,
because it is considered excluded from the normal way of life, regardless of the economic
situation of the agent. Studying poverty from a subjective point of view means considering that
any person or family can give their judgment about the degree to which it satisfies their basic
needs. To determine whether a person or family considers themselves poor or not, two forms are
generally used. It is possible to ask directly about certain perceptions about their condition or
observe their behavior. Subjective poverty can be understood as the perception of poverty that
has a sector of the population that feels and defines itself as poor because they cannot access a set
of goods and services that they consider of great importance [9]. Recognizing what causes
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subjective poverty can be a good mechanism to improve public policies based on a better
understanding of the needs and expectations of the population and the redefinition of priorities
[10]. Measuring welfare is a frequent task, and there is a high consensus on the need to quantify
it, but there are some divergences as to which indicators use to reflect a society's welfare situation
and little information on how population evaluates what happens with their own welfare [11].
Subjective measurements are based on population surveys where they are asked to define their
situation, usually located at a point on a qualitative scale. In general, information of welfare level
of each person is obtained through simple questionnaires with simple and direct questions that
capture people's perception of their satisfaction with access to certain goods or services.
The existence of qualitative variables, inherent to human behavior, or elements of the external
environment of difficult objective quantification, makes it difficult for individuals to represent
with an exact numerical value the valuation of the different aspects related to the welfare to be
assessed. Under such circumstances, it is more appropriate to express their responses by means of
linguistic values rather than exact numerical values. This approach is based on fuzzy sets theory
and is called linguistic approach. It is applied when the variables involved are of a qualitative
nature [12, 13, 14]. It is possible to model in a more appropriate way a great number of real
situations, since they allow representing the information of the individuals, that it is not always
precise, in a more appropriate way. A linguistic variable differs from a numerical one in that its
values are not numbers, but words or sentences of the natural language, or of an artificial
language [12]. The use of the diffuse linguistic approach implies the need to operate with words
[15].
It is necessary to complement the analysis of the population living conditions with the subjective
indicators of welfare in order to assess the correspondence between the objective improvements
and the subjective perceptions that the agents perform on them. Given that the type of questions
used to define a subjective welfare indicators are qualitative in nature, the use of a linguistic
model that operates with words directly will allow aggregating opinions of the individuals
adequately without losing information. The proposed approach will let to capture the nuances and
degrees of welfare present in human perceptions, whereas the classical models allow only binary
contrasts between positive and negative perceptions, not including the variations of intensities
between them. Application of linguistic models to evaluate the population's perceptions of their
welfare makes it possible to analyse individuals’ life quality under the use of linguistic variables
belonging to the habitual language. In addition, it will allow studying and processing individual
and aggregated opinions operating with words directly without losing information nor rigorous.
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This paper is structured as follows. In first place, a Linguistic Combined Model for Economic
Welfare is presented. A Welfare Linguistic Subjective Indicator and a Linguistic Poverty Line are
combined to measure a household multidimensional poverty. Next section develops an example
and finally some conclusions are presented.
2. Linguistic Combined Model of Economic Welfare Evaluation
Poverty is a multidimensional reality that is not usually completely measured because of its
nature. Population’s living conditions are characterized by subjective and objective aspects. Thus,
poverty measures sometimes are in the need to combine subjective and objective features.
Since subjective well-being indicators are built through surveys that reveal the individual's
perception in certain areas considered using qualitative scales, is very relevant the use
of linguistic variables in their formulation [16]. Then, since poverty is a matter of degrees, a
linguistic poverty line is used to evaluate objective welfare of each household [17].
First, households' perceptions in five chosen areas will be collected using a multiple choice
survey (Appendix). With the information obtained, ILBE index will be calculated for each
household [16]. Then, the fuzzy poverty line will be calculated for that household [17]. Finally,
the subjective evaluation of the household will be contrasted with the degree of poverty for
identifying different situations on multidimensional poverty.
2.1. Welfare Linguistic Subjective Indicator
Welfare Linguistic Subjective Indicator (ILBE) takes into account five areas of welfare: 1. health,
2. education, 3. housing, 4. income and 5.employment [16]. Economic welfare is determined by
their perception about these aspects. These perceptions are taken from direct surveys of heads of
households. The questionnaire induces households to assess their access to the five areas
considered using linguistic labels. The assessment of each area will provide a component of ILBE
and aggregation enable an indicator for each household.
According to the domain of the variables involved, it is assumed the use of one of the following
sets of linguistic terms, in order to the head of household express their views on each question
made:
excellentgood,very good, mean,bad, bad,very dreadful, 65432101 sssssssS
poor}non poor,non almost
poor,somewhat poor,notorpoornor poor,rather poor, very poor,absolutely {
65
432102
ss
sssssS
important} absolutely important, very important,pretty
careless, important, little t,uninportanrather t,unimportan {
654
32103
sss
ssssS
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With the information obtained in surveys the indicator value for a family is obtained. This value
is calculated for each area of satisfaction for the selected household. The assessment of the degree
of satisfaction of each home for each area that integrates the ILBEh is obtained by
using the aggregation operator of linguistic information with the information gathered from
surveys (Appendix).
- Health Area: Evaluation will be based on household responses to questions 1 (access to
healthcare) and 2 (access to medicines and vaccination): heqq sssEAA 21
,1.
Where 11
Ssq is the response of question 1, 12Ssq is the response of question 2 and is the
evaluation of the health area of this household.
- Education Area: Evaluation will be based on household responses to questions 3 (conformity
to the educational level of the head) and 4 (access to the education system): edqq sssEAA 43
, .
Where 13
Ssq is the response of question 3, 14
Ssq is the response of question 4 and is the
evaluation of the education área of this household.
- Housing Area: Evaluation will be based on household responses to questions 5 (housing
conditions) and 6 (neighborhood general conditions): hoqq sssEAA 65
, .
Where 15
Ssq is the response of question 5, 16
Ssq is the response of question 6 and is the
evaluation of the housing área of this household.
- Income Area: Evaluation will be based on household responses to questions 7 (income) and 8
(household income need not to feel poor): iqq sssEAA 87
, .
Where 11
Ssq is the response of question 7, 11
Ssq is the response of question 8 and is the
evaluation of the income área of this household.
- Employment Area: Evaluation will be based on household responses to questions 9 (number of
hours worked) and 10 (working conditions): emqq sssEAA 109
, .
Where 11
Ssq is the response of question 9, 110
Ssq is the response of question 10 and is the
evaluation of the employment área of this household.
Since not all areas that compose the indicator are equally important for all households, the survey
includes a question which asks the degree of importance assigned to each family to each of them
(Question 13, appendix) corresponding to a linguistic label in the set 3S .
If 3Ss
jh
is the linguistic label that shows the importance allocated by the household h the area
j
1 EAA: extended arithmetic mean [16].
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( 5,...,1j ); the weighting, hjw , correspondent must verify that 1,0jhw
5
1
1j
jhw , and is
obtained by applying
5
1j
jjjh hhw nh ...,,1 .
Having assessed the components of the index and obtained their respective weights, the ILBEh is
obtained by the use of aggregation operator of linguistic
information hemihoedhehh ssssssEWAAILBE ,,,, 2.
If it is wanted to express the degree of aggregate welfare of each household by a term of the set
1S , the sub index of the virtual label hs is approximated to an integer
value through the usual rounding operation (round h ) and it is got a linguistic original label.
Questions 11 and 12 will be used to compare the consistency of the households’ responses,
211Ssq and
112Ssq .
2.2. Objective Poverty Evaluation
It is needed to classify the household according to their income, because it is important to
analyze how poor households perceive their welfare as how they do the non-poor ones. For
classifying the household, we will employ the Fuzzy Poverty Lines and the Poverty Degrees
developed by Fernandez [17]. In this model, poverty is considered as a matter of degree.
First, a Fuzzy Basic Food Basket (CBAF) is determined to calculate the Indigence Line to the
Equivalent Adult. To assess the CBAF for an adult fuzzy triangular numbers are expressed by its
confidence intervals and are operated with them [18]. Given nCCC ,...,1 , its cardinal is
nC monthly valuation of CBAF is given by:
n
i
ii
CBAF PQV1
/ niRPQ ii ,...,1, .
Being each n component of the basket, the quantity of component i of the basket, the
price of that good [17]. Then, a fuzzy scale is constructed to determine the units of equivalent
adults of each household, obtained from a fuzzy energy needs table [17]. Being hU the units of
equivalent adults of h-th household and CBAFV the valuation of CBAF for an equivalent adult unit,
the valuation of the CBAF for the h-th household is: CBAF
hh
CBAF VUV .
In order to obtain the fuzzy poverty line, it is indispensable to establish the fuzzy inverse of
Engel's coefficient e~ 3. Fuzzy poverty line for the equivalent adult will be determined
by: eVLP CBAFf~. .
2 EWAA: weighted arithmetic mean [16]. 3 Fuzzy inverse Engel's coefficient relates food expenditures with non-food ones using triangular fuzzy numbers [17].
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Being fLP the fuzzy poverty line for the equivalent adult and hU the units of equivalent adults
of h-th household, the valuation of the Poverty Line for the h-th household is: f
hh
f LPULP .
Once calculatedh
fLP , household's monthly effective total income is compared and it is
determined whether it is completely poor, not poor, or whether it is in the gray area. For
classifying households within the gray zone, it is possible to associate the degree of belonging to
the set of poor households with a set of labels. It is possible to construct a set of labels to classify
households with respect to the concept of poverty (Table 1 and Figure 1).
The use of this approach allows capturing the different degrees present when valuing a measure
that represents welfare that is intended to measure. The use of fuzzy sets theory helps to
understand the phenomenon dimensions more comprehensively.
2.3. Joint Poverty Analysis
In order to analyze the determinants of the non-poor / feeling poor and the poor / non feeling poor
families, households will be separated into four groups.
The objective poorness or non-poorness will be assessed with the fuzzy poverty lines method. A
household will be considered poor with a qualification lower than “High” (Left branch and
) and will be considered non poor in any other situation.
The subjective feeling of poverty will be determined with ILBE index. Once is approximated
to a label of the set , it will be considered feeling poor households those who gets a valuation
lower than “bad” ( , and ), and feeling non poor in any other situation.
Households will be categorized into 4 groups.
Group 1. Poor / Feeling Poor.
Objective Poverty degree: “High”, “Very High” and
“Absolute”
ILBE: “Bad”, “Very Bad” and “Dreadful”.
Group 2. Poor / Non feeling poor.
Objective Poverty degree: “High”, “Very High” and
“Absolute”
ILBE: “Mean”, “Good”, “Very Good” and “Excellent”.
Group 3. Non poor / Feeling poor. Group 4. Non poor / Non feeling poor.
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Objective Poverty degree: “Medium”, “Low”, “Very
Low” and “Null”
ILBE: “Bad”, “Very Bad” and “Dreadful”.
Objective Poverty degree: “Medium”, “Low”, “Very
Low” and “Null”
ILBE: “Mean”, “Good”, “Very Good” and “Excellent”.
Special attention will be paid to Group 2 and 4 in order to make deeper analysis of the
determinants of perceptions of poverty.
3. Application
A household will be evaluated in order to classify it into one of the four groups outlined above.
In first place, it will be calculated the Fuzzy poverty line for that family, and then it will be
compared with its income. For that period, the amount needed to buy the Fuzzy Basic Food
Basket for the equivalent adult will be an approximate triangular fuzzy number:
82.2031,62.1766,50.1501CBAFV [17, 19]. Fuzzy inverse of Engel's coefficient will be
50.2,41.2,30.2~ e , and the poverty line for the equivalent adult will be an approximate
triangular fuzzy number 55.5079,4.4257,45.3453~. eVLP CBAFf.
Household is structured as follows: Head of household, a female 35 years old, her son 18 years
old and her mother 61 years old. This household represents 59.2,44.2,17.2hU units of
equivalent adults. The fuzzy poverty line will be calculated and approximated to a triangular
fuzzy number 03.1315605.1038898.7493 ,,LPULP f
hh
f [17, 19].
The family declares to the interviewer that its monthly effective total income is $9500. Thus, its
income belongs to the poverty set in a 0.69 degree; household presents a high level of objective
poverty.
In a second phase, the household answer the subjective survey. The responses where:
Question Valuation Associated Linguistic Label
1 Good 141Sssq
2 Good 142Sssq 421
, sssEAAs qqhe
3 Mean 133Sssq
4 Good 144Sssq 5.343
, sssEAAs qqed
5 Bad 125Sssq
6 Bad 126Sssq 265
, sssEAAs qqho
7 Very bad 117Sssq
8 Bad 128Sssq 5.187
, sssEAAs qqi
9 Mean 139Sssq
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10 Mean 1310Sssq 3109
, sssEAAs qqem
11 Rather
poor 2211
Sssq
12 Bad 1212Sssq
Question 13: 1. Health Very important 351Sss
25.01 w
2. Education Very important 352Sss 25.02 w
3. Housing Careless 333Sss 15.03 w
4. Income Pretty Important 344Sss 20.04 w
5. Employment Careless 335Sss 15.05 w
1392.2,,,, SssssssssEWAAILBE hemihoedhehh → presents a mean feeling of poverty.
When classifying into one of the groups, this household belongs to Group 2 “Poor / Non feeling
poor”. Further analysis will be needed to understand why this family doesn’t perceive poverty or
maybe it weigh mostly access to certain goods or services than its own income.
4. Conclusions
Subjective welfare measures are a complementary tool of objective indicators. It is important to
understand the connection between objective and subjective improvements.
The proposed approach allows showing different groups considering objective and subjective
poverty. This disaggregated analysis will help the analysts to understand the determinants of
poverty perceptions in relation to objective well-being.
The implementation of linguistic models will help to understand the degrees inherent in the
analysis of human welfare.
In future researches it will be interesting to go deeper into the structure of the survey, the
determinants of welfare perceptions versus the objective situation of poverty, and it will be
possible to make contributions regarding the construction of a single index combining both
approaches.
Acknowledgement
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The authors thanks to the Secretaría de Ciencia y Técnica of the Universidad de Buenos Aires
(UBACyT Project 2016 20020150100090BA), to the Facultad de Ciencias Económicas of that
University where the Project belongs to and to the Consejo Nacional de Investigaciones
Científicas y Técnicas (CONICET).
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Appendix. Survey form
1. You consider that your access to health care is:
Dreadful – very bad – bad – mean – good- very good – excellent.
2. You consider that your access to medication and vaccination, if needed, is:
Dreadful – very bad – bad – mean – good- very good – excellent.
3. You consider your education level is:
Dreadful – very bad – bad – mean – good- very good – excellent.
4. You consider that access to the education system is:
Dreadful – very bad – bad – mean – good- very good – excellent.
5. You consider that your housing conditions are:
Dreadful – very bad – bad – mean – good- very good – excellent
6. You think that the general conditions of their neighborhood (asphalt, lighting, sewers,etc.) are:
Dreadful – very bad – bad – mean – good- very good – excellent
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7. You think your income is:
Dreadful – very bad – bad – mean – good- very good – excellent
8. How much extra home income your household need not to feel poor?
Income amount Linguistic
label
Income
amount
Linguistic
label
More than double Dreadful 40 – 50%
more Good
double Very bad 10 -30 %
more Very good
80 – 90% more Bad nothing excellent
60 – 70% more Mean
9. Considering the number of the amount of hours that you work, you find it:
Dreadful – very bad – bad – mean – good- very good – excellent
10. You think that your working conditions are:
Dreadful – very bad – bad – mean – good- very good – excellent
11. Do you feel poor?
Absolutely poor – very poor – rather poor – nor poor or not poor – somewhat poor – almost non
poor – non poor.
12. How do you evaluate your level of economic welfare?
Dreadful – very bad – bad – mean – good- very good – excellent
13. Indicate the importance of each area for your welfare.
area Absolut.
important
Very
important
Pretty
important Careless
Little
important
Rather
unimportant Unimportant
1. health
2. Education
3. Housing
4. Income
5. Employment