i Development of an optimal spatial decision-making system using approximate reasoning Submitted by David Thomas Bailey BEng(Hons) QUT A thesis submitted in partial fulfilment of the requirements of the degree of DOCTOR OF PHILOSOPHY Research Centre for Built Environment and Engineering Research Energy and Resource Management Research Program Faculty of Built Environment and Engineering Queensland University of Technology Novemer 2005
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i
Development of an optimal spatial decision-making system using approximate reasoning
Submitted by
David Thomas Bailey
BEng(Hons) QUT
A thesis submitted in partial fulfilment
of the requirements of the degree of
DOCTOR OF PHILOSOPHY
Research Centre for Built Environment and Engineering Research
Energy and Resource Management Research Program
Faculty of Built Environment and Engineering
Queensland University of Technology
Novemer 2005
ii
TTAABBLLEE OOFF CCOONNTTEENNTTSS
TABLE OF CONTENTS II
LIST OF FIGURES VI
LIST OF TABLES VIII
LIST OF ABBREVIATIONS IX
ABSTRACT X
STATEMENT OF AUTHORSHIP XI
ACKNOWLEDGEMENTS XII
1 INTRODUCTION AND METHODOLOGY 1 1.1 INTRODUCTION 1 1.2 THE PROBLEM 2
1.2.1 Context and fundamental elements of infrastructure site selection 2 1.2.2 Background 3 1.2.3 Use of Approximate Reasoning 5 1.2.4 Case Study 6
FIGURE 8.3: CREATING A CONTINUOUS SUITABILITY MAP FOR COMMUNITY IMPACT ................................................................................152
FIGURE 8.4: CREATING A DISCRETE SUITABILITY MAP FOR ZONING ...........................................................................................................152
TABLE 2.2: TYPES OF ATTRIBUTES, A BRIEF DESCRIPTION, AND DESCRIBING AUTHORS................................................................................30
TABLE 4.1: DIMENSIONS OF A DSS ...........................................................64
TABLE 4.2: GIS SPATIAL ENTITIES IN VECTOR AND RASTER ........71
The first step in the development process was to generate a clear statement of the
problem and survey existing approaches to its solution. To maintain the focus on
a practical application, a focus group was assembled, consisting of planning and
infrastructure managers from industry, and academics from QUT. The meeting
led to a consensus on key statements about the aims, objectives, and scope of the
proposed Spatial Decision Support System (SDSS). Once the groundwork had
been laid, an extensive literature review, encompassing the techniques and
technology of spatial decision-making, was conducted. Planning and research
initially overlapped as feedback from the literature review provided the impetus
for a more detailed description of desired functionality.
This chapter provides key statements from problem diagnosis, and a preliminary
review of the decision science techniques and technology most commonly used
for location problems. A detailed discussion of Approximate Reasoning
techniques, and the technical aspects of SDSSs follow in chapters 3 and 4.
18Chapter 2 Problem Diagnosis and Preliminary Literature Review
2.2 Problem diagnosis
The initial meeting for problem diagnosis and needs assessment was based
around the discussion paper in Appendix C, and took contributions from
professionals involved in planning, infrastructure development and management,
and environmental management. Also present were QUT academics from the
fields of Geographical Information Systems, Software Design, Mathematics, and
Environmental Management. Key statements emerging from the meeting were
as follows:
• The system will support decision-makers in planning, infrastructure
development and management, and environmental management with site
selection decisions.
• The system should be able to accommodate qualitative variables such as
socio-economic and environmental impacts.
• The system should accommodate multiple criteria and multiple points of
view of the measurement and weighting of those criteria.
• Outputs from the system should be graphical where possible, preferably
in a mapping format.
• The modelling capabilities of the system should be transparent and easily
understandable.
• The system should aim to aid decision-makers, not replace them.
These basic statements of desired functionality were then used as the focus for a
state of the art literature review. The first stage of the review focused on the
existing techniques and technology involved in spatial decision-making.
Specifically, the review was conducted to answer the following questions:
1. What are the analytical techniques used in the solution of the type of
Infrastructure site selection problems encountered by decision-makers at
BAC, and planners in general?
2. What are the major limitations of these techniques?
19Chapter 2 Problem Diagnosis and Preliminary Literature Review
3. What technology platforms are used in the analysis of Infrastructure site
selection problems?
4. What are the most promising methods for advancing current techniques and
technologies?
The remainder of this chapter is drawn from the first stage of the review.
2.3 Introduction to location problems
Solving location problems is an everyday activity performed by individuals and
groups who use spatial information to make decisions about such things as where
to live, where to shop, and how to manage the environment and infrastructure
(Jankowski, Andrienko et al. 2001). The primary objective of these problems is
to identify the most desirable location for a facility or service (Maniezzo,
Mendes et al. 1998), such as locating a new airport, allocating law enforcement
resources, or buying a new home.
The choice between competing locations is made according to how well each
location satisfies a set of conditions. These conditions, commonly referred to as
evaluation criteria or simply criteria, will vary across space and are unique to
each location problem. They may encompass issues such as maximisation of
utility, minimisation of detrimental environmental and social impact, and ease of
accessibility (Nijkamp, Rietveld et al. 1990). The term ‘criteria’ is generic and is
used to convey the concepts of both objectives and attributes. The primary
objective may also be referred to as the goal, and is usually the top level of a
hierarchy of sub-objectives (Saaty and Kearns 1985). These sub-objectives are
operationalised by assigning measures to achieve them, called attributes
(Malczewski 1999). For example if the objective is to minimise environmental
damage when locating an industrial facility, an attribute chosen to represent this
objective may be the number of acres of bushland lost.
20Chapter 2 Problem Diagnosis and Preliminary Literature Review
When criteria are conflicting, it is inevitable that trade-offs will need to be made.
In order to optimise the trade-off process, it is essential to specify how relatively
important each criterion is. This is usually a subjective process whereby the
decision-maker assigns weights to each criterion according to his or her
preferences (Bogetoft and Pruzan 1997). However spatial decisions are often
made by groups of decision-makers, to satisfy the needs of multiple stakeholders.
Such situations are described as group decision-making, and in a group
environment where decision-makers are autonomous and heterogeneous it is
inevitable that conflicts will occur (Chu-Carrol and Carberry 2000). These
conflicts generally arise because of the diverse values of the groups or
individuals involved, which lead to different weighting of criteria, but conflicts
may also arise from the definition of criteria, or the decision-making process
(Bogetoft and Pruzan 1997).
A site selection decision is essentially a choice between alternative sites. Each
alternative will have a set of outcomes (consequences) in relation to the various
evaluation criteria, however the set of outcomes is seldom completely
deterministic, and some level of uncertainty usually enters the decision-making
process (Spradlin 1997). Sources of uncertainty are generally two fold. Firstly
there may be some uncertainty about the validity of the information upon which
the decision is to be based, such as the reliability of an expert opinion (Keeney
and Raiffa 1976). Secondly there may exist some unpredictability about future
events and the state of the future environment in which the decision outcome
dwells, such as the weather or economic outlook. Types of uncertainty are also
twofold, the first being stochastic, as described by a probability distribution of
the alternate states of attributes and outcomes, and the second is fuzziness
(imprecision in data), as described by fuzzy set theory (Bellman and Zadeh
1970).
2.3.1 Problem classifications
This research was driven by infrastructure site selection problems, which are
referred to here by the more generic term Group Multi-criteria Location
Problems (GMCLP’s). GMCLP’s are complex real world decision problems with
21Chapter 2 Problem Diagnosis and Preliminary Literature Review
the objective of finding an optimal site for a facility or service from multiple
alternatives, using multiple evaluation criteria and the opinions of multiple
stakeholders.
GMCLP’s belong to a general class of decision-making problems referred to as
multicriteria decision problems. Classification of these problems is summarised
in Figure 2.1. It is widely accepted that multicriteria decision problems can be
broken into two categories. Multiattribute decision-making (MADM) problems
involve a finite or relatively small number of discrete alternatives, whereas
multiobjective decision-making (MODM) problems have a relatively large or
infinite number of feasible alternatives (Jankowski 1995). MADM and MODM
have also been referred to as discrete and continuous decision problems (Hwang
and Yoon 1981), as MADM implies a discrete number of pre-specified
alternatives, whereas in MODM the alternatives are generated during the solution
process. It is important to note that if there exists a direct correspondence
between objectives and attributes, a MODM problem becomes a MADM
problem, as the objectives may be completely defined by a limited number of
attributes in this scenario.
Group decision-making, where more than one set of goals or preferences is
considered, is then distinguished from individual decision-making, where the
objectives are agreed. This distinction is made on the grounds of conflicting
objectives rather than number of decision-makers. The level of uncertainty
provides a third division between deterministic problems, where all relevant
information is known, and probabilistic or fuzzy problems, where there is some
uncertainty. In real world decision problems uncertainty is commonplace, and
deterministic problems are rare.
22Chapter 2 Problem Diagnosis and Preliminary Literature Review
Figure 2.1: Classification of Multicriteria Decision Problems
Modified from: (Malczewski 1999)
A Rigorous definition of GMCLP’s is suggested here and defines them as:
‘the selection of an optimal location from a large number of spatial alternatives
by a heterogeneous group of decision-makers using multiple evaluation criteria
under uncertainty.’
MMUULLTTIICCRRIITTEERRIIAA DDEECCIISSIIOONN
PPRROOBBLLEEMMSS
Multiattribute decision problems
Individual
Certain Uncertain
Probabilistic Fuzzy
GGMMCCLLPP’’ss
Group
Certain Uncertain
Probabilistic Fuzzy
Multiobjective decision problems
Individual Group
Certain Uncertain
Probabilistic Fuzzy
Certain Uncertain
Probabilistic Fuzzy
23Chapter 2 Problem Diagnosis and Preliminary Literature Review
They contain the following four key attributes:
1. A large number of spatial alternatives:
The alternatives under consideration are numerous enough to make manual
analysis impractical i.e. the problem is non-trivial
2. A heterogeneous group of decision-makers:
Multiple parties are involved in the decision process and there is no guaranteed
consensus among them
3. Multiple evaluation criteria with an explicit spatial component
The decision is based on multiple, conflicting criteria that vary across space
4. Uncertainty
The relationship between the available raw data and site suitability is subject to
some kind of uncertainty
The GMCLP discussed in Chapter 8 offers a practical example of the type of
location problem defined above. It involves locating a new industrial facility
somewhere on the 2700 ha Brisbane Airport site. Stakeholders include the
Brisbane Airport Corporation, The Commonwealth Government and Community
representatives. Decision-makers wish to satisfy six evaluation criteria, which
include issues such as environmental value and community impact, that are hard
to quantify and subject to disagreements among parties, as well as uncertainty in
measurement.
2.4 Decision science techniques
Decision science, also referred to as decision analysis, operations research,
systems engineering and management science, has a long history. Put simply it is
the application of scientific method to everyday decision-making. Decision
science seeks to apply logical reasoning to decision problems in a structured
way, thereby making the decision process explicit and repeatable. It also offers a
means to look inside a particular decision and make explicit how and why it was
24Chapter 2 Problem Diagnosis and Preliminary Literature Review
made. Decision science has found many applications in engineering, the military
and business management. Although there is evidence that formal decision-
making methods in military strategy date back thousands of years, the field of
decision science is commonly assumed to have originated during World War II,
when scientific methods were applied to strategy in antisubmarine warfare by
T.C. Koopmans.
There are a multitude of formal decision-making methods. However those that
have been applied to location problems are relatively few and fall into three
broad categories.
1. Map algebra methods
Map algebra includes standard spatial functions and simple overlay methods
that screen out sites based on Boolean operators or simple arithmetic.
2. Multicriteria evaluation methods
Multicriteria evaluation methods offer the ability to rate criterion outcomes on a graduated scale and choose the relative importance or weight of each criterion.
3. Artificial intelligence methods (soft computing or geocomputation)
These methods include neural networks, fuzzy systems and evolutionary algorithms. They are usually complex in nature and offer great potential for complex spatial problems.
The following Sections provide an overview of these three groups of methods,
particularly the widely applied family of multicriteria evaluation techniques. A
more detailed review of the Approximate Reasoning methods is provided in
Chapter 3.
2.4.1 Map algebra
Map algebra, or overlay analysis, is the most basic level of spatial analysis. It
involves the use of simple arithmetic, Boolean and relational operators to
combine input maps. Table 2.1 provides a sample of map algebra operations.
25Chapter 2 Problem Diagnosis and Preliminary Literature Review
82Chapter 5 Problem analysis and conceptual system design
The difficulty in solving group problems lies in how to fully accept and combine
differing assessments from each member of the group. Deriving an aggregated
criterion weighting alone is inadequate if criterion assessments vary, and
assessing each criterion is complicated by conflicting opinions about which
attributes best represent which objective. As aggregation procedures tend to
produce a single measure of suitability, there is also a need to keep conflicts
visible after an aggregation, so they may be fully explored.
5.2.2 Uncertainty
Uncertainty in spatial decision-making has traditionally been considered in terms
of the physical processes and variables that form the basis of imprecise datasets
upon which decisions are made. Keeney and Raiffa (1976) define two basic
sources of uncertainty, the first being uncertainty about the source data used to
make a decision, and the second is uncertainty about future events which may
effect the decision outcome. These two sources of uncertainty can be further
classified into two types of uncertainty, being either probabilistic or fuzzy
(Malczewski 1999). Probabilistic uncertainty is described by a probability
distribution and fuzziness by fuzzy set theory. However these distinctions may
mean little to a strategic decision-maker making subjective value judgements,
who has little or no training in mathematical analysis.
Uncertainty in site selection is often due to uncertainty in a value judgement that
may be hard to directly associate with a physical process. In an unstructured
problem such as site selection, human intuition is frequently the basis for
decision-making (Turban 1995). The uncertainty inherent in intuitive value
judgements is quantified in the minds of decision-makers, and may bear no
measurable relationship to the stochastic uncertainty in source data or future
events, although it may be partially or wholly based on these factors. This highly
elusive and difficult to represent type of uncertainty plays a major role in human
reasoning. It is proposed here that this type of uncertainty be defined by the term
‘decision-maker uncertainty’ as the intuitive reasoning of the decision-maker is
the physical process most responsible for it. Decision-maker uncertainty arises
when the decision-makers themselves provide the only measure of the
83Chapter 5 Problem analysis and conceptual system design
relationship between source data and suitability by making statements such as ‘A
location less than fifty metres from the main road would be good’. It is extremely
common in decision problems with qualitative variables, and has been largely
overlooked in the literature on site selection.
The distinction between decision-maker uncertainty and data uncertainty is
important as data uncertainty such as known inaccuracies in distance
measurement or temporal fluctuations in demand has often been represented
successfully through the use of stochastic modelling techniques (Murray 2003).
Decision-maker uncertainty is somewhat different in nature. In the mind of a
decision-maker if a suitability assessment is uncertain they might simply lower
their assessment to compensate. If asked for an estimate of their confidence in
the assessment they will most probably answer with a linguistic term such as
‘very certain’ or ‘uncertain’. Underneath this perceived level of uncertainty there
is also the inherent vagueness of the assessment itself. The simplest way to
provide a suitability assessment is via a set of linguistic terms such as ‘good’,
‘bad’, ‘very bad’, etc, but inherent in these terms is an element of linguistic
uncertainty.
One may therefore postulate that when dealing with subjective linguistic
suitability assessments from decision-makers the overall level of decision-maker
uncertainty comprises two elements. Firstly the uncertainty quantified by the
decision-maker, for which the term ‘quantitative uncertainty’ is suggested.
Secondly there is the imprecision of the suitability term used by the decision-
maker, which is defined as ‘linguistic uncertainty’ in the literature eg. (Zadeh
1975; Herrera and Herrera-Viedma 2000). In keeping with the requirement of
simplicity it is therefore necessary to devise a method to directly incorporate
these two elements into an analysis. The problem is how to turn an assessment
such as ‘I am certain that location A is good with respect to Criterion 1’ into a
mathematical quantity that can be manipulated by an analytical model, whilst
retaining its information value.
84Chapter 5 Problem analysis and conceptual system design
5.2.3 Simplicity
The need for simplicity in Spatial Decision Support Systems is paramount, as has
been noted by many authors eg. (Crossland, Wynne et al. 1995; Brail 2000; Lu,
Yu et al. 2001). There are two kinds of simplicity to consider here. Firstly the
semantics of the analytical method used should be simple enough for users to
easily interact with the system. Secondly the mathematics of the technique
should be simple enough to be implemented in an algorithm capable of analysing
millions of discrete alternatives in a realistic timeframe. These two requirements
are often conflicting, as simplifying user interaction generally requires more
effort behind the scenes.
Simplicity in use and interaction has often been noted as a requirement in
Decision Support Systems (Turban 1995), and one of the main objectives in DSS
design should be to increase willingness to use DSS as many studies reveal that
millions of dollars have been wasted on unused DSS’ (Lu, Yu et al. 2001). In
fact while spatial decision support systems have been proven to increase
decision-maker effectiveness (Crossland, Wynne et al. 1995), few applications
are actually in use to support decision-makers in siting decisions (Maniezzo,
Mendes et al. 1998), and highly capable analytical systems are often used as
simple visualisation tools, primarily due to difficulties in use and understanding
of the systems by strategic decision-makers (Klosterman 2000).
Most GIS have very limited inbuilt capabilities for the simple integration of
decision-maker preferences with spatial data, and the use of MCE within GIS
provides a platform for this integration (Malczewski 1999). However there are
many stages in the MCE process that are complex or cumbersome to implement.
Among these are criteria rating and standardisation, selection of an appropriate
aggregation procedure, and differentiating amongst alternatives with a similar
overall rating.
85Chapter 5 Problem analysis and conceptual system design
5.2.4 Control
A key requirement of any decision support methodology is to deliver a sense of
control of the decision-making process to the decision-makers themselves.
Methods that operate as a ‘black box’, where users have little understanding or
control over outputs are unlikely to be fully embraced by decision-makers and
interest groups (O'Sullivan and Unwin 2003). However delivering a sense of
control to decision-makers requires that they be able to ‘look inside’ the
analytical processes employed and choose among the various analysis options
available. The choices made at this level are crucial to the overall results
obtained, as it is a well-noted fact that different decision-making methods often
produce different results. The most dominant influence on outputs is exerted by
the choice of aggregation procedure (Carver 1991; Heywood, Oliver et al. 1995).
5.3 A conceptual framework
The conceptual framework presented in this section is a blueprint for a new
Spatial Decision Support System for infrastructure site selection, at a conceptual
level. It proposes key methods and concepts for the new system, whilst leaving
the details of algorithm design to Chapter 6, and construction of the actual
system to Chapter 7.
5.3.1 Why use Approximate Reasoning?
It is a core hypothesis of this research that AR is a suitable basis for an
infrastructure site selection algorithm. AR techniques offer two immediate
advantages over crisp (non-fuzzy) methods. Firstly they enable uncertainty to be
factored into an analysis, as is discussed in more detail in Section 5.3.3. Secondly
they simplify that analysis as is described in Section 5.3.4. The use of AR in
decision-making is also backed up by a vast amount of literature and practical
experience, as was touched on in Chapter 3. But perhaps the most potent
86Chapter 5 Problem analysis and conceptual system design
argument for AR can be made at a more conceptual level. The fundamental
advantage of AR in decision-making is that it is a bridging technology that
enables human beings to more effectively interact with an analytical model.
The advent of powerful modelling capabilities, made possible by the digital
computer, has brought about an enormous increase in our ability to precisely
simulate complex real world systems. Engineers and scientists value this
precision in data, however the human mind has a finite ability to resolve detail
and store information. It uses words as labels for imprecise bundles, also termed
fuzzy granules, as a means to cope with complex problems. This mismatch of
precision between human and computer produces a decrease in our ability to
make precise and significant statements about models, as they grow more
complex.
In general there may be distinguished three distinct entities related to modelling
the physical world:
1. The physical process to be modelled.
2. The abstract (usually mathematical) representation of that process, termed the
model.
3. Human understanding of both the physical process and the mathematical
model, which makes construction and application of the model possible.
AR enhances the bridge between mathematical models and the associated
physical reality by facilitating a better human understanding of the modelling
process. Fuzzy methods are capable of capturing the vagueness of linguistic
terms in statements of natural language. This in turn provides greater capability
to model systems through human commonsense (approximate) reasoning and
creates a more useful aid to decision-making (Klir and Yuan 1999).
87Chapter 5 Problem analysis and conceptual system design
5.3.2 Catering for multiple decision-makers
It is proposed here that to adequately deal with the inevitable conflicts that will
arise from a heterogeneous group of decision-makers requires three elements.
1. A criterion weighting approach that applies to attributes and not objectives.
2. A method to accept differences of opinion in both criteria weighting and
rating.
3. The ability to identify conflicts in the post aggregation data exploration phase
of the decision-making process.
The first step in overcoming the three hurdles facing a heterogeneous group is to
ask decision-makers to assess and weight attributes directly. In this way the
attributes can be weighted and assessed with respect to the objective foremost in
the mind of each decision-maker, thereby bypassing the conflict that may arise in
trying to reach a consensus on which attributes best represent each objective.
To allow the processing of differences of opinion in weighting and rating, each
alternatives criterion outcomes and criterion weights are weighted and combined
using a Relevance Matrix (RM). The format for a RM is shown in Figure 5.2.
R = ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
JKJ
K
RR
RR
..........
..........
1
111
M
Figure 5.2: Relevance matrix
Deriving the relevance matrix is ideally achieved via consensus, and should be
based on the competency of a decision-maker to make assessments relating to
each criterion. However it may also be derived via a non-weighted averaging of
each decision-maker’s assessments of the competencies of others in the group.
Each criterions relevance values are normalised so that a criterion does not gain
extra importance based on solely relevance values. The values defined in the
The relevance matrix describes the relevance of the kth decision-makers opinion with respect to attribute j. (values are scaled after input so each criterions relevance values sum to 1)
88Chapter 5 Problem analysis and conceptual system design
relevance matrix are then used in a double weighted MCE aggregation of fuzzy
suitability scores.
Double weighting has been used previously to add extra weight to lower criterion
outcomes in hybrid Ordered Weighted Averaging techniques (Jiang and Eastman
2000). It is proposed that a criterion assessment from each decision-maker is
weighted according to the decision-makers preference and relevance as shown in
Equation 5.1.
∑∑= =
××=J
j
K
kjkjkijki WR
1 1
OS | i = 1…I (5.1)
N.B. Fuzzy quantities are shown in bold type
Where:
iS is the suitability of alternative i.
ijkO is the criteria outcome for alternative i with relation to criterion j and
decision-maker k, including quantitative and linguistic uncertainty.
jkR is the relevance of decision-maker k’s opinion with respect to criterion j.
jkW is the weight assigned to criterion j by decision-maker k
The aggregation output should be a fuzzy number representative of each
alternative’s overall compensatory suitability and uncertainty.
The task now remains to extract conflicts in the post aggregation data exploration
phase. To accomplish this it is proposed to extract an extra parameter
representative of conflict. The complete set of parameters proposed is discussed
fully in Section 5.3.5.
89Chapter 5 Problem analysis and conceptual system design
5.3.3 Handling Uncertainty
Although the use of fuzzy numbers to model linguistic uncertainty is common,
there is no universal method to derive the fuzzy numbers, or adjust the fuzzy
number to include the extra dimension of the quantitative uncertainty level
placed on the linguistic assessment. The problem of matching a fuzzy number
with a linguistic label dates back to the genesis of the linguistic approach, and is
beyond the scope of this thesis. However the ability to adjust a fuzzy number in
line with a decision-maker uncertainty assessment is a simpler task.
Incorporating decision-maker uncertainty into an analysis in this way offers real
advantages, as this type of uncertainty assessment can always be obtained
regardless of the level of knowledge about source data.
Linguistic uncertainty has long been represented using fuzzy set theory. Usually
the fuzzy set is reduced to a parametric form such as a triangular or trapezoidal
fuzzy number. Figure 5.3 shows a triangular fuzzy number (TFN) which
represents a linguistic term in three parameters (a,b,c).
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a c
b
Suitability
μ 'OK'
Figure 5.3: The suitability term ‘OK’ as TFN(0.3,0.5,0.7)
90Chapter 5 Problem analysis and conceptual system design
A method is now needed to encapsulate the level of quantitative uncertainty
expressed when the term is used in the form ‘I am very certain that this
alternative is OK with respect to criterion 3’. This may be accomplished using
the relatively new concept of a type-2 fuzzy set and its footprint of uncertainty
(FOU). A type-1 fuzzy set has a crisp membership function where each point on
the universe of discourse (x-axis) has a crisp membership value μ on the y-axis.
A type-2 fuzzy set possesses a secondary membership function (2MF) drawn
along a third axis that describes the relationship between the universe of
discourse and the primary membership function (Mendell and John 2002). The
2MF exists within a footprint of uncertainty (FOU). An example of a FOU is
shown in Figure 5.4.
0
0.2
0.4
0.6
0.8
1
Suitability
μ
Primary Term FOU
Figure 5.4: Footprint of uncertainty
In this case the FOU of the suitability term is defined by moving vertices a and c
of the primary TFN outwards to the boundary of [0,1]. This provides a means to
superimpose quantitative uncertainty on the primary TFN by varying the
expected value of the 2MF with the quantitative uncertainty assessment. In this
case primary vertices a and c are reallocated to a different point for different
quantitative uncertainty assessments as shown in Figure 5.5.
91Chapter 5 Problem analysis and conceptual system design
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Suitability
μ
Totally certain
Certain
Moderately certain
Uncertain
Totally uncertain
'OK'
Figure 5.5: How a quantitative uncertainty assessment affects the primary
MF
It is proposed that by using TFN’s and the type-2 concepts described above it is
possible to represent linguistic suitability and uncertainty assessments as a
simple, robust mathematical quantity, capable of being manipulated by an
analytical model whilst retaining the original information value. The scaled TFN
will provide the basic unit to be manipulated in the algorithm. All that remains is
to devise a mathematical method of deriving the new a and c values from the
original primary MF and a linguistic uncertainty assessment. The specifics are
left for Chapter 6.
5.3.4 Creating simplicity
Simplicity in use and interaction is largely a product of choosing an AR
technique. Decision-makers benefit from a universal linguistic suitability scale
that greatly simplifies criteria standardisation. AR enables the use of words as the
basis for interaction with the system, both in terms of input and feedback.
Another way to increase ease of use is to produce a fully integrated system,
utilising a standard GIS interface. GIS is a mature technology and the methods
standard GIS packages employ to view and interact with spatial information are
the result of an ongoing process of refinement dating back to the 1960s. Instead
92Chapter 5 Problem analysis and conceptual system design
of trying to reinvent the wheel and create an entirely new interface, it is more
efficient to create a set of tools to enhance existing GIS functionality where
necessary, whilst retaining the highly effective aspects of the standard interface.
This may be achieved by incorporating tools into a toolbar that integrates
seamlessly with existing functionality.
The mathematical simplicity required to enable the analysis of large numbers of
alternatives in real-time is provided by adhering to three constraints:
1. Utilising parameter-based fuzzy numbers, thereby avoiding the extra burden
of more complex membership functions.
2. Manipulation of the TFN’s by arithmetic operations, easily performed by GIS
software.
3. Use of a scoring function to de-fuzzify outputs, thereby avoiding the use of
pairwise comparisons to rank alternatives, as the number of calculations
required to do this becomes unwieldy with large numbers of alternatives.
Details of the fuzzy algorithm are given in Chapter 6.
5.3.5 Giving decision-makers control
It is proposed here that in order to successfully deliver control to decision-makers
an easily understandable method to choose between different aggregation
procedures is required. This may be achieved by generating four descriptive
parameters for each alternative that are indicative of the qualities sought by
differing aggregation procedures, and independent of the problem domain.
Decision-makers then decide which of these parameters are most important to the
problem at hand. The parameters are as follows:
1. Utility: Utility is a measure of an alternatives fulfilment of all evaluation
criteria in a compensatory way. It is calculated via a weighted summation of
all criterion outcomes. A good solution requires good utility.
2. Certainty: Certainty is a measure of how predictable the outcome for a
particular alternative is. A good solution is one with a high level of certainty.
93Chapter 5 Problem analysis and conceptual system design
3. Safety: Safety is a measure proportional to the lowest criterion outcomes.
Alternatives with poor outcomes on some criteria may rate well in terms of
utility but will be unsafe or ‘risky’. A good solution is a safe solution.
4. Consensus: Consensus requires that all parties agree on the various aspects
of an alternative. Alternatives that are rated similarly on all criteria by all
decision-makers in the group exhibit a high level of consensus. A good
solution requires consensus.
None of the four parameters are sufficient to guarantee a good solution in
isolation. However by weighting and combining them decision-makers take
control of the process, and find solutions that best satisfy the dynamics of each
problem. Moreover by breaking down each solution into easily understandable
quantities, the mystery of what happens during analysis is lessened in the eyes of
users.
The four parameters should constitute an integral part of the interactive data
exploration and visualisation phase of the decision-making process. Using a
graphical point and click interface, decision-makers should be able to explore
each alternative site by receiving linguistic feed back on the four parameters,
plus an overall aggregated rating derived from combining them.
5.4 Conclusions
It was proposed that limitations on current SDSSs are derived from an inability
to deal with multiple conflicting parties, an inability to handle uncertainty, a lack
of simplicity in use and interaction and not delivering enough control to decision-
makers. This chapter has provided a conceptual blueprint for algorithm design
and system construction by outlining the desired characteristics of the system. It
was found that the system should possess the following characteristics:
• The ability to accept inputs from a heterogeneous group of decision-
makers, independently weighting and rating multiple attributes.
94Chapter 5 Problem analysis and conceptual system design
• An approximate reasoning algorithm based on a fuzzy MCE aggregation
of parameter-based fuzzy numbers that encapsulate linguistic suitability
and uncertainty assessments.
• The algorithm should utilise arithmetic operators for aggregation and a
scoring function for de-fuzzification to minimise calculation time and
enable real-time interactivity.
• The system should be fully integrated into existing GIS software.
• Linguistic outputs should be a set of descriptive parameters that give
decision-makers the ability to choose the characteristics of a solution that
are most appropriate to their specific problem, thereby enabling them to
gain control over the properties maximised during aggregation.
Chapter 6 Algorithm design 95
Chapter 6
AALLGGOORRIITTHHMM DDEESSIIGGNN
6.1 Introduction
The previous chapter has highlighted several limitations on current approaches to
site selection, and provided a conceptual blueprint for mitigating those
limitations. Algorithm design consisted of the formal implementation of those
conceptual ideas that specifically relate to the decision-making model. The
implementation takes the form of a new Approximate Reasoning Algorithm for
Infrastructure Site Selection (ARAISS). While it is not the contention of this
research that it is possible to develop a perfect analytical model for the solution
of all Infrastructure Site Selection Problems, ARAISS implements several
concepts that offer an improvement over current methodologies.
The core capabilities of ARAISS are its use of approximate reasoning to handle
uncertainty, its multiple decision-maker capability, its simplicity, and the way it
hands over control to decision-makers. ARAISS is described in detail in Section
6.2, and the results from MATLAB testing of the algorithm are given in Section
6.3. Conclusions are then drawn.
6.2 ARAISS
One of the principal outcomes of this research is the ARAISS algorithm
described in this section. ARAISS is a new and unique approach to infrastructure
site selection, which is loosely based on fuzzy multiattribute utility theory
(Ribeiro 1996). ARAISS is specifically targeted to an audience of strategic
Chapter 6 Algorithm design 96
decision-makers locating a new facility. It was designed to accommodate
qualitative and quantitative variables, and offers a means to perform an initial
analysis based on the issues of foremost importance in the minds of stakeholders.
As such it is a generic Spatial Decision Support algorithm suitable for the first
stage of a site selection process. A more comprehensive follow up assessment
incorporating a more detailed analysis is envisaged as a means to further validate
recommendations made from the ARAISS process.
6.2.1 Framework
Figure 6.1 shows the general framework for ARAISS. It is a two-phase
procedure where the final location is sought via an iterative process of reducing
alternatives. In Phase 1, decision-makers first define the problem, and then a
constraint analysis is performed to exclude totally unfeasible alternatives. A set
of linguistic suitability terms to be used when rating the various criteria is then
defined. Each decision-maker then contributes their preferences for criterion
weighting and rating, and this information is combined with decision-maker
relevance values in an aggregation. The aggregation derives output parameters
for the Utility, Certainty, Safety and Consensus of each alternative.
Phase 2 involves exploration and reduction of alternatives. Decision-maker
preferences for minimum acceptable parameter values, and parameter weights
are sought. They provide a means to rate and rank alternatives in terms of their
overall suitability, and thereby reduce the number of alternatives under
consideration by consensus. The desired outcome of this process is the selection
of a site or sites, which conform to the strategic needs of all decision-makers.
Once the strategic analysis has been performed, it may be necessary to analyse
tactical and operational issues using a more specific modelling procedure, and to
consider micro-placement issues such as footprint and orientation before making
a comprehensive decision. This last non-strategic phase is beyond the scope of
this thesis.
Chapter 6 Algorithm design 97
Figure 6.1: ARAISS Framework
Define problem
Define decision-maker relevance values
Perform compensatory aggregation function
Identify feasible alternative sites for analysis
Choose Decision-makers
Identify Utility, Certainty, Safety and Consensus
Final site selection
Define and rate criteria (factors)
Start
Define linguistic terms
Tactical and operational assessment
Micro-placement
Identify constraints
Explore and reduce alternatives
Iterate
Phase 2
Perform adjusted aggregation
Define criterion weights
Review inputs
Phase 1
Chapter 6 Algorithm design 98
6.2.2 Notation
Notation and terminology for site selection analysis has been inconsistent in the
literature. For example compare the notation of Malczewski (1995) to that of
Eastman (1995). To avoid confusion the following notation is used consistently
throughout this thesis:
A = {A1,A2,……AI} The set of I feasible alternatives
C = {C1,C2,……CJ} The set of J criteria (factors)
D = {D1,D2,……DK} The set of K decision-makers
W = ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
JKJ
K
WW
WW
..........
..........
1
111
M
R = ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
JKJ
K
RR
RR
..........
..........
1
111
M
Ok =
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
JIkkJ
Ikk
OO
OO
..........
..........
1
111
M
The overall suitability of alternative i (Si) is some function of each decision-
makers preferences for criterion outcomes and weights, combined with their
relevance to each criterion.
6.2.3 Linguistic term sets
The natural language approach to decision analysis relies on a systematic use of
words to characterize the values of variables, probabilities, relations, and truth-
values of assertions. The central concept is that of a linguistic variable whose
values are words or sentences, which serve as the names of fuzzy subsets of a
universe of discourse. The linguistic approach represents a blend of quantitative
The matrix of criterion outcomes for alternative i and criterion j, based on decision-maker k’s suitability and uncertainty assessments.
The matrix of relevance values specifying the relevance of the kth decision-makers opinion with respect to criterion j. (values are scaled after input so each criterions relevance values sum to 1)
The matrix of criterion weights specifying the kth decision-makers opinion of the weighting of criterion j.
Chapter 6 Algorithm design 99
and qualitative analysis by using numbers to make the meaning of words more
precise (Zadeh 1976).
A linguistic variable is generally characterised by the quintuple (X, T(X), D, Y,
M) where:-
X is the name of the variable. (e.g. Age)
T(X) is the term set which gives x it’s linguistic values. (e.g. Young, Not
Young,…Old, etc)
D is the universe of discourse. (e.g 0-150)
Y is a syntactic rule which generates the terms in T(X).
M is a semantic rule which associates with each term, x, in T(X) its
meaning, M(X). The meaning is defined by a membership function μ(x)
that associates each member of D with a degree of compatibility in x,
within the interval [0,1].
ARAISS uses four term sets:
T(S) site suitability terms
T(W) terms for weighting of criteria and decision-maker relevance
T(U) terms describing the level of uncertainty
T(G) terms for generating new suitability terms in T(S)
Generation of linguistic term sets involves two primary considerations. The first
is the selection of a grammar, i.e. the cardinality of the term set and syntactic
labelling as defined by a syntactic rule. The second is how to define a semantic
for each term, which in this case will take the form of a triangular fuzzy number
(TFN) or crisp number, via a semantic rule.
On the issue of grammar the first consideration is cardinality i.e. the number of
terms in the set. The term set should be small enough to be manageable and not
Whilst it is unrealistic to plan for all possible data needs, the following themes
provided a sound basis for many site selection problems.
• Flora
• Fauna
• Habitat value
• Topography
• Land use and zoning
• Cultural heritage sites
Chapter 7 InfraPlanner 126
• Contaminated sites
• Airport facilities including all buildings, roads, taxiways and runways
• Environmentally sensitive areas such as waterways
• Nearby residential communities
The real value of data is made apparent when it is combined with expert
knowledge and processed into useful information. This is accomplished by a
decision-making model.
7.2.5 Model
The Approximate Reasoning Algorithm for Infrastructure Site Selection
(ARAISS) described in Chapter 6 provides the ability to combine raw data
themes in accordance with decision-maker knowledge. It is a generic multi-
criteria group decision-making model capable of application to a wide variety of
strategic site selection decisions. The model is accessed via a set of user forms
designed to aid the various stages of the decision-making process.
The model accepts two types of inputs:
1. Data: in the form of pre-processed raster layers indicative of the spatial
variation of a raw attribute value.
2. Knowledge: in the form of linguistic assessments from decision-makers.
The model outputs raster layers of the same resolution as input layers, attributed
and colour coded to match terms in the linguistic term set used in decision-maker
input. Two basic types of raster layers may be created.
1. Criterion Maps: Criterion Maps are the InfraPlanner equivalent of a
suitability map, with the added element of uncertainty. They are a raster map
identifying the spatial variation of the suitability and uncertainty of one
attribute, according to one decision-maker. Criterion Maps are created from a
data layer indicative of the spatial variation of the raw value of an attribute
Chapter 7 InfraPlanner 127
(eg. a zoning map) by associating the raw attribute value with the suitability
and uncertainty values provided by the decision-maker. Criterion Maps can
be either discrete (based on a categorical variable such as land ownership) or
continuous (based on a variable that covers a continuous range of values such
as proximity from a feature).
2. Decision maps: Decision Maps are created by combining criterion maps with
decision-maker preferences for criterion weights, decision-maker relevance,
and output parameter weights. Decision maps describe the spatial variation of
aggregated site parameters: Suitability, Uncertainty, Risk, and Conflict. The
output of an adjusted aggregation (whereby Suitability, Uncertainty, Risk,
and Conflict are weighted and combined) is also a type of decision map.
The specifics of how InfraPlanner accomplishes this are given in Section 7.4.
7.3 Development process
Development of the InfraPlanner system followed a simplified evolutionary
prototyping structure, conducted in close consultation with end users. The
process consisted of a logical sequence of activities, which was documented via a
logic model.
Logic modelling is a resource management tool used to document the underlying
reasons and goals behind a program of activities. In a logic model the program is
divided into six elements.
1. Resources are the raw materials available
2. Activities make use of the available resources
3. Outputs are the tangible results of an activity
4. Customers are those who receive the outputs
5. Outcomes (Short, medium, or long term) are the reason for undertaking the
activities
6. External influences are those influences that are beyond the scope and control
of the program
Chapter 7 InfraPlanner 128
The logic model detailing the sequence of events involved in the InfraPlanner
development process was shown in Figure 1.2. The main activities in the model
are described in Sections 7.3.1 – 7.3.5.
7.3.1 Planning
The planning phase of system development was conducted in conjunction with
end users from BAC. A needs assessment and problem diagnosis was conducted
to define the goals of the system, and to determine the types of decisions the
system would provide assistance with. Goals defined in the planning phase
included:
• The system should support decision-makers with facilities placement
decisions within the Brisbane Airport grounds
• The system should be able to accommodate qualitative variables such as
socio-economic and environmental impacts
• The system should accommodate multiple criteria and points of view
• Outputs from the system should be graphical where possible, preferably in a
mapping format
• The modelling capabilities of the system should be transparent and easily
understandable
These basic statements of desired functionality were then used as the focus for a
state of the art literature review.
Chapter 7 InfraPlanner 129
7.3.2 Research
The research phase consisted of a state of the art review of published literature on
the techniques and technology involved in spatial decision-making. Specifically,
the review was conducted to answer the following research questions:
1. What are the analytical techniques used in the solution of multicriteria
location problems?
2. What are the major limitations of these techniques?
3. What technology platforms are used in the analysis of spatial problems and
what are their major characteristics?
4. What are the most promising methods for advancing current techniques and
technologies?
The review clearly showed that Multi-criteria evaluation (MCE) is the most
suitable analytical technique for the solution of multicriteria location problems.
However several shortcomings were noted. Most important of these are the
inability to deal with uncertainty, inability to deal with a group environment, and
the perception by decision-makers that current methods are not user friendly. The
universally accepted technology platform for the analysis of location problems
was found to be a GIS, coupled or fully integrated with decision-making models.
Advanced Artificial Intelligence and soft computing techniques offered an ability
to overcome some of the shortcomings of MCE, but it was necessary to deploy
them in a user friendly way in order to avoid the perception of a ‘black box’
scenario.
7.3.3 Analysis and design
The primary objective of the design phase was to produce a clear conceptual
system design specification based on outputs from the planning and research
phases, and to provide input from technology experts. This phase produced two
major outputs.
Chapter 7 InfraPlanner 130
1. A new fuzzy model for the type of location problems encountered by
decision-makers at Brisbane Airport and strategic decision-makers in
general. The model is described in Chapter 2.
2. A design specification for the prototype system to implement the new
model. The key objectives contained in the design specification are
summarised in Section 7.2, and the working system is fully described in
Section 7.4.
7.3.4 Construction
Construction covered the technical implementation of the design. In the case of
InfraPlanner construction consisted of integrating the new fuzzy decision-making
model into the selected GIS package. Technology selection was a vital aspect of
the design process as the capabilities of the chosen GIS package have a
significant impact on functionality, compatibility and development time. The
three key aspects considered when choosing among the many commercially
available systems were:
1. Level of raster analysis functionality
2. Customisation capabilities
3. File format compatibility
ArcGIS was eventually chosen, as it possessed comprehensive raster analysis
functionality, offered an inbuilt Visual Basic for Applications (VBA)
customisation environment, and was compatible with the existing MicroStation
CAD software employed by Brisbane Airport.
ArcGIS customisation is based around the manipulation of a set of
programmatically controllable software objects collectively referred to as
ArcObjects. ArcObjects offered access to the objects that make up ArcGIS
software at a high enough level of granularity to be a flexible and effective
development tool. Construction mainly focused on development of the set of user
forms described in Section 7.4. The forms offer an intuitive visual way to
Chapter 7 InfraPlanner 131
implement the algorithm described in Chapter 6. Source code is provided in the
Appendix.
7.3.5 Implementation
Implementation consisted of testing and evaluation of the system. InfraPlanner
was tested and evaluated using a real world site selection problem faced by the
Brisbane Airport. Brisbane Airport planners, regulators, and external consultants
were involved in the validation problem, which involved the location of a new
recycling facility on the Airport site. The validation problem is fully described in
Chapter 8.
7.4 The InfraPlanner prototype
InfraPlanner consists of a set of tools designed to implement ARAISS in a GIS
environment. The tools are accessed in ArcMap via the InfraPlanner Toolbar
shown in Figure 7.1.
Figure 7.1: The InfraPlanner toolbar
Tools available from the InfraPlanner Toolbar are structured as follows:
Project Tools:
Select project: A user form to select a stored decision project
Create new project: A user form to create a new decision project
View project Information: A user form listing current project options
Create Maps:
Chapter 7 InfraPlanner 132
Criterion map: User forms to create discrete or continuous
suitability maps from a raster map
Decision maps: A user form to bring suitability maps together in an
aggregation and create output parameter maps
Format Map:
Tools to format existing raster maps with numeric attribute values into a
suitability, utility, risk, uncertainty or conflict map. The transformation is purely
visual not analytical, and is not discussed further here.
Explore Maps:
A point and click tool to be used to interactively explore selected locations and
all their outcomes, or to perform an adjusted aggregation.
InfraPlanner tools are used to follow the general framework of ARAISS, as
shown in Figure 7.2. Specific tools are described in the following Sections.
Chapter 7 InfraPlanner 133
Figure 7.2: How InfraPlanner tools fit into the decision-making framework
Define problem
Define decision-maker relevance values
Perform compensatory aggregation function
Identify feasible alternative sites for analysis
Choose Decision-makers
Identify Utility, Certainty, Safety and Consensus
Final site selection
Define and rate criteria (factors)
Start
Define linguistic terms
Tactical and operational assessment
Micro-placement
Identify constraints
Explore and reduce alternatives
Iterate
Perform adjusted aggregation
Define criterion weights
Review inputs
Chapter 7 InfraPlanner 134
7.4.1 Project tools
The project tools are used to specify and view the type of decision, decision-
makers involved, criteria, and the linguistic term set used for input and feedback.
Setting the project information is shown in Figure 7.3.
Figure 7.3: Setting project information
Chapter 7 InfraPlanner 135
Inherent in the input of project information is choosing a linguistic suitability
term set to be used for decision-maker input and feedback. InfraPlanner creates
new term sets by using Equation 6.1 to add new terms to a set of primary
suitability terms as shown in Figure 7.4. The user first chooses the primary term
set to build on and then uses the ‘Create Term Set’ user form to follow the
process described in Section 6.2.3.
Figure 7.4: Creating a new term set
7.4.2 Creating maps
InfraPlanner provides the ability to create several types of maps used in the
decision-making process. In most cases some pre-processing is required to
provide the system with suitably classified raster input maps. Pre-processing is
performed using standard Map Algebra techniques, such as those described in
Chapter 7 InfraPlanner 136
Chapter 2. Pre-processing usually consists of converting a vector map to raster
format, or performing a proximity function to create a raster map indicative of
distance from some feature. Boolean constraint maps are also created using
standard map algebra techniques.
7.4.2.1 Suitability Maps
Suitability maps are either based on discrete (categorical) variables such as
regional zoning, or a variable that takes a continuous range of values, such as
elevation. Discrete suitability maps are created using the form shown in Figure
7.5. Users specify a source theme containing the pre-processed baseline data for
the suitability map and classify the categories it contains using linguistic
suitability and uncertainty assessments.
Figure 7.5: The discrete criterion map user form
Users interact with the discrete criterion map user form as shown in Figure 7.6.
Chapter 7 InfraPlanner 137
Figure 7.6: Creating a discrete criterion map.
Name the new Criterion Map to be created
Load the Discrete Criterion Map form from the InfraPlanner Toolbar
Input a description of the map
Select a source theme from the pre-screened list of discrete source maps
Choose the attribute field within the map to linguistically classify.
Rate each attribute category in terms of suitability and uncertainty
Click the ‘Create’ button to create the new map
The new criterion map is created and displayed
Chapter 7 InfraPlanner 138
Continuous criterion maps are created using the form shown in Figure 7.7. Users
specify points along the domain of the source variable and rate them with
linguistic suitability and uncertainty values. Points whose values lie between the
rated points are classified according to equations 6.6 – 6.9, which is essentially a
linear extrapolation of the centre point, and support of the TFN.
Figure 7.7: The continuous criterion map user form
Users interact with the continuous criterion map user form as shown in Figure
7.8.
Chapter 7 InfraPlanner 139
Figure 7.8: Creating a continuous criterion map
Name the new Criterion Map to be created
Load the Continuous Criterion Map form from the InfraPlanner
Toolbar
Input a description of the map
Select a source theme from the pre-screened list of continuous source maps
Rate a minimum of 3 points in terms of suitability and uncertainty
Click the ‘Create’ button to create the new map
The new criterion map is created and displayed
Chapter 7 InfraPlanner 140
7.4.2.2 Decision Maps
The term ‘Decision Maps’ is a generic term used within InfraPlanner to describe
the four aggregated parameter maps (Suitability, Uncertainty, Risk and Conflict).
Using the ‘Create Decision Maps’ user form, users associate a previously created
criterion map with each criterion and decision-maker in the chosen decision
project. They also input the decision-maker relevance and criterion weighting for
each criterion in the decision project, with respect to each decision-maker. The
output parameter maps are created by an aggregation of the criterion maps, using
equations 6.15 – 6.22. The ‘Create Decision Maps’ user form is shown in figure
7.9, and user interaction is illustrated in Figure 7.10.
Figure 7.9: The decision maps user form
Chapter 7 InfraPlanner 141
Figure 7.10: Creating decision maps
Name the new Decision Maps to be created.
Load the Decision Map user form from the InfraPlanner
Toolbar
Choose a constraint map to limit the area under consideration
Enter the Decision-maker relevance value for the displayed decision-maker
Click the ‘Add‘ button when the inputs are correct to cycle to the next set of inputs and repeat the previous step.
Click the ‘Create’ button when all inputs have been entered to create the new maps
The new parameter maps are created and
displayed
Enter the weight of the displayed criterion according to the displayed decision-maker.
Choose the previously created criterion map that represents the displayed criterion according to the displayed decision-maker.
Chapter 7 InfraPlanner 142
7.4.3 Exploring maps
Map exploration is facilitated using a point and click tool that allows users to
examine any feasible alternative site in all its dimensions. An interactive report is
displayed which provides information on the four output parameters plus
individual criterion outcomes and provides an opportunity to set the weighting
parameters for an adjusted aggregation. Map exploration is shown in Figure 7.11.
Figure 7.11: Map exploration
Chapter 7 InfraPlanner 143
7.5 Validating InfraPlanner
Validation of the working prototype was conducted in three ways. The first and
most valuable means of validation was the case study presented in Chapter 8.
Results showed that users found InfraPlanner simple to use and understand, and
selected sites that they deemed acceptable. Secondly a peer reviewed paper was
presented at ANZIIS 2003 as shown in Appendix A. Lastly a focus group was
created at ANZIIS 2003, consisting of five researchers and academics from the
fields of AI and soft computing. A combination of discussion paper and
questionnaire was created for the group, and is reproduced in Appendix E. The
focus group was given the discussion paper after the presentation of the
conference paper, and asked for their feedback on the algorithm and the
methodology used to create it. The group exercise quickly took the form of a
vigorous discussion, in which feedback was positive, with all present agreeing
that both the development process and the model derived from it was valid. Some
researchers noted that the use of a software design flowchart would be a good
way to represent the model, as they found the logic model used difficult to
follow. Other specific comments included:
• Documentation of the model should be in a commonly accepted, and easily
understandable format
• Users need to be able to understand the impacts of preferences given during
the data input phase
• Use of fuzzy numbers to represent words is valid, but needs more work in
terms a rigorous and repeatable way of defining the membership function
• Users should understand how the model works
• The concept of weighting inputs based on relevance of opinion was valid but
a rigorous way of generating the relevance matrix was needed
7.6 Discussion
InfraPlanner is a working prototype of a generic SDSS for GMCLP’s of a
strategic nature. The system demonstrates that approximate reasoning techniques
are suitable for use in SDSSs, although designing and building the InfraPlanner
Chapter 7 InfraPlanner 144
Spatial Decision Support System proved to be extremely challenging.
Constructing a DSS is generally considered to be a complex, time consuming
task, requiring a group of skilled individuals, and this was proven in practice.
There are many small issues that are not generic enough to be mentioned in
publications on SDSSs but nonetheless proved problematic. Among these were
choosing a GIS package from the myriad of options available, and dealing with
the organisational changes that occurred during the development process.
Chapter 8 A case study using InfraPlanner 145
Chapter 8
AA CCAASSEE SSTTUUDDYY UUSSIINNGG IINNFFRRAAPPLLAANNNNEERR
8.1 Introduction
Validation of any proposed algorithm requires a practical implementation to test
assumptions made during the design process. In many cases there exists a set or
sets of standard real world data and solutions upon which to compare the
accuracy of a given algorithm. In the case of site selection decisions under the
types of uncertainty discussed in Chapter 5, there appears to be no standard
dataset that incorporates all the variables used as inputs to the InfraPlanner
algorithm. Specifically there is no dataset that includes subjective uncertainty
assessments from multiple decision-makers, and preferences for decision-maker
relevance, or the priorities placed on the four output parameters; Utility,
Certainty, Consensus, and Safety. To overcome this data shortage problem an
experiment was conducted using a real world site selection decision at Brisbane
Airport, where the desired inputs and outputs could be generated and commented
upon by decision-makers themselves.
Inputs were generated for three stakeholder groups using actual decision-makers
or representatives chosen by the experimenter for their knowledge of the
situation. The problem used was real, and the objective was to choose the best
location for a recycling facility on the 2700 ha Brisbane Airport site. This chapter
details the problem and all inputs, the process used to implement InfraPlanner in
deriving solutions, the results generated, and a discussion of their relevance.
Chapter 8 A case study using InfraPlanner 146
8.2 The problem
The problem worked through here concerns the location of a new recycling
facility on the Brisbane Airport grounds. The Airport occupies 2700ha of land,
located 13km North East of the Queensland State Capital, Brisbane, and
adjoining Moreton Bay. The site is flat and low lying, occupying part of the
original Brisbane river delta, which has undergone extensive changes since the
1830s, with most of the original network of tidal waterways being replaced with
constructed drains. Much of the vegetation on the site has been planted in the last
15 years, and was chosen to reduce the attraction of birds. There are, however,
some environmentally sensitive areas to consider when locating new
developments, as well as issues associated with airport facilities, Government
legislation and the effects of airport operations on local communities. Figure 8.1
shows the general layout of the Brisbane Airport site.
The facility to be located inputs masonry from demolished buildings and, via
crushing and grinding, turns out various grades of landfill material. The main
impacts of such an operation on its immediate vicinity are noise and dust
emissions. There are three separate groups with an interest in the outcome. The
Brisbane Airport Corporation (BAC), as represented by their Infrastructure
Planning Manager. The Commonwealth Government, as represented by an
independent contractor responsible for ensuring regulatory compliance, and a
local residential community adjoining the Airport, whose inputs were provided
by an Airport representative with knowledge of their concerns. The groups differ
considerably in their priorities and suitability assessments, creating a rich
decision-making environment.
Chapter 8 A case study using InfraPlanner 147
Figure 8.1: Brisbane Airport Layout
Chapter 8 A case study using InfraPlanner 148
8.3 Procedure
The experiment was structured to follow the decision-making framework shown
in Figure 6.1, with the first steps involving problem definition and definition of a
linguistic term set. The linguistic terms used are shown in Table 8.1.
Table 8.1: Linguistic terms
Suitability (as a TFN) Weighting Uncertainty Term generation
Totally unsuitable
(0,0,0) Irrelevant 0
Very Certain 0 Zero 0
Bad (0,.2,.4) Unimportant .3 Certain 1 Very Small .1 Indifferent (.3,.5,.7) Moderately
Important .5 Moderately
Certain 2 Small .3
Good (.6,.8,1) Important .7 Uncertain 3 Medium
.5
Perfect (1,1,1) Very Important
.9 Very Uncertain
4 Large .7
Probably Good*
(.51,.71,.91) Critical 1* Very Large .9
• The suitability term ‘probably good’ was included as a ‘large’ increase on ‘indifferent’ at the request of decision-makers..
With the problem defined as ‘selecting the best site for the recycling facility’, the
next step was to identify the constraints (Boolean criteria) that would limit the
sites under consideration. During an initial consultation a set of five constraints
was derived:
1. Airport Boundary: The site must lie within the existing airport
boundary to avoid the cost of land acquisition.
2. Existing Buildings: Sites already occupied should be excluded to avoid
the loss of existing facilities.
3. Road access: The site must be within 200m of selected access
roads to avoid the cost of building new access.
4. Zoning: The site must lie in a zone designated ‘General
Industry’ or ‘Light Industry’ as defined by the
BAC 1998 Master Plan to comply with
Government planning requirements.
Chapter 8 A case study using InfraPlanner 149
5. Conservation: The site must not occupy an area of high
conservation value, thereby preserving the
sensitive areas on the Airport grounds.
The map of unconstrained alternatives (available sites) was derived using map
algebra techniques, and is shown in Figure 8.2.
Chapter 8 A case study using InfraPlanner 150
Figure 8.2: Unconstrained Alternatives
Chapter 8 A case study using InfraPlanner 151
The next step in the process involved the definition and linguistic assessment of
criteria that vary on a suitability scale from ‘Totally Unsuitable’ to ‘Perfect’.
Decision-makers directly defined six criteria as important to the site selection
process. They are described in Table 8.2:
Table 8.2: Criteria definition
Criterion
Name
Type Description
Environmental value
Continuous As all areas of high conservation value are excluded, this criterion defines on a continuous scale how the distance from sensitive areas affects suitability
Zoning Discrete The facility may be placed in either a ‘General Industry’ or ‘Light Industry’ zone, and this criterion describes how that decision affects suitability.
Tenant Amenity Continuous Defines how the distance from sensitive tenants affects suitability
Community Impact
Continuous Defines how distance from the closest residential community affects suitability
Landfill Discrete It would be desirable to locate the facility close to areas which are more in need of the fill material generated by the facility.
Traffic Impact Discrete To regulate traffic flow and trucking noise, the use of some access roads is more desirable than others.
These criteria are represented as a set of suitability maps, created using
InfraPlanner interfaces to convert linguistic inputs from each decision-maker to a
spatially explicit format, as shown in Figures 8.3 and 8.4.
Chapter 8 A case study using InfraPlanner 152
Figure 8.3: Creating a continuous suitability map for community impact
Figure 8.4: Creating a discrete suitability map for zoning
Chapter 8 A case study using InfraPlanner 153
Each decision-maker will generate a map for each criterion for which their
opinion is deemed to be sufficiently relevant to include, and which they feel to be
relevant to the decision environment. Thus a decision-maker may opt out of
generating a map on the grounds of lack of expertise or if they feel that a
particular criterion should have no effect upon overall suitability. The inputs
required to generate the maps take the form of sentences, from which the relevant
information is input to the suitability map generation interface. Inputs were as
follows:
BAC Inputs:
Environmental value is ‘important’: It is ‘moderately certain’ that sites
of moderate conservation value are ‘good’ whilst it is ‘very certain’ that
all others are ‘perfect’.
Zoning is ‘very important’: It is ‘very certain’ that general industry zones
are ‘perfect’ whilst it is ‘moderately certain’ that light industry zones are
‘good’.
Tenant Amenity is ‘important’: It is ‘very certain’ that sites less than
50m from sensitive tenants are ‘totally unsuitable’. It is ‘moderately
certain’ that sites 100m from sensitive tenants are ‘good’. It is ‘certain’
that sites 500m from sensitive tenants are ‘perfect’.
Community Impact is ‘important’: It is ‘very certain’ that sites less than
500m from Pinkenba are ‘totally unsuitable’. It is ‘uncertain’ that sites
1000m from Pinkenba are ‘good’. It is ‘very uncertain’ that sites 2000m
from Pinkenba are ‘perfect’, and ‘certain’ that sites 4000m from Pinkenba
are ‘perfect’.
Landfill is ‘moderately important’: It is ‘very certain’ that sites on
Lomandra Dr are ‘perfect’. It is ‘moderately certain’ that sites on Randle
Rd, Sugarmill Rd and Viola Pl are ‘good’. It is ‘moderately certain’ that
sites on Airport Dr are ‘indifferent’.
Chapter 8 A case study using InfraPlanner 154
Traffic impact is ‘important’: It is ‘very certain’ that sites on Airport
Drive are ‘bad’. It is ‘moderately certain’ that sites on Lomandra Drive
and Viola Pl are ‘good’. It is ‘certain’ that sites on Randle Road and
Sugarmill Rd are ‘perfect’.
Community Inputs:
Environmental value is ‘very important’: It is ‘moderately certain’ that
sites of moderate conservation value are ‘probably good’ whilst it is
‘certain’ that all others are ‘perfect’.
Zoning is ‘irrelevant’:
Tenant Amenity is ‘irrelevant’:
Community Impact is ‘critical’: It is ‘very certain’ that sites less than
2000m from Pinkenba are ‘totally unsuitable’. It is ‘uncertain’ that sites
3000m from Pinkenba are ‘good’. It is ‘certain’ that sites 4000m from
Pinkenba are ‘perfect’.
Landfill is ‘irrelevant’:
Traffic impact is ‘important’: It is ‘very certain’ that sites on Airport
Drive are ‘perfect’. It is ‘certain’ that sites on Lomandra Drive and Viola
Pl are ‘bad’. It is ‘very certain’ that sites on Randle Road and Sugarmill
Rd are ‘bad’.
Government Inputs:
Environmental value is ‘important’: It is ‘moderately certain’ that sites
of moderate conservation value are ‘good’ whilst it is ‘very certain’ that
all others are ‘perfect’.
Chapter 8 A case study using InfraPlanner 155
Zoning is ‘very important’: It is ‘very certain’ that general industry zones
are ‘perfect’ whilst it is ‘moderately certain’ that light industry zones are
‘good’.
Tenant Amenity is ‘important’: It is ‘very certain’ that sites less than
50m from sensitive tenants are ‘totally unsuitable’. It is ‘moderately
certain’ that sites 100m from sensitive tenants are ‘good’. It is ‘certain’
that sites 500m from sensitive tenants are ‘perfect’.
Community Impact is ‘important’: It is ‘very certain’ that sites less than
500m from Pinkenba are ‘totally unsuitable’. It is ‘uncertain’ that sites
1000m from Pinkenba are ‘good’. It is ‘very uncertain’ that sites 2000m
from Pinkenba are ‘perfect’, and ‘certain’ that sites 4000m from Pinkenba
are ‘perfect’.
Landfill is ‘moderately important’: It is ‘very certain’ that sites on
Lomandra Dr are ‘perfect’. It is ‘moderately certain’ that sites on Randle
Rd, Sugarmill Rd and Viola Pl are ‘good’. It is ‘moderately certain’ that
sites on Airport Dr are ‘indifferent’.
Traffic impact is ‘important’: It is ‘very certain’ that sites on Airport
Drive are ‘bad’. It is ‘moderately certain’ that sites on Lomandra Drive
and Viola Pl are ‘good’. It is ‘certain’ that sites on Randle Road and
Sugarmill Rd are ‘perfect’.
As illustrative examples, the suitability maps created by BAC and the residential
community representative for Traffic Impact and Community Impact are shown
in Figures 8.5, 8.6, 8.7 and 8.8.
Chapter 8 A case study using InfraPlanner 156
Figure 8.5: BAC Traffic Impact Suitability Map
Chapter 8 A case study using InfraPlanner 157
Figure 8.6: BAC Community Impact Suitability Map
Chapter 8 A case study using InfraPlanner 158
Figure 8.7: Traffic Impact Suitability Map for the Residential Community
Chapter 8 A case study using InfraPlanner 159
Figure 8.8: Community Impact Suitability Map for the Residential
Community
Chapter 8 A case study using InfraPlanner 160
It was then necessary to perform an aggregation using the criterion weightings,
relevance weights, and suitability maps previously created. Inputs are
summarised in Tables 8.3 and 8.4. The interface used is shown in Figure 8.9.
Table 8.3: Criterion weighting
Criterion Weights
BAC Pinkenba Commonwealth
Environmental
Important
Very
Important Important
Zoning Very Important Irrelevant Very Important
Tenant amenity Important Irrelevant Important
Pinkenba Important Critical Important
Landfill Moderately
Important Irrelevant
Moderately
Important
Traffic
Important Important
Moderately
Important
Chapter 8 A case study using InfraPlanner 161
Table 8.4: Decision-maker Relevance values
Criterion DM Relevance
BAC Pinkenba Commonwealth
Environmental Important
Moderately
Important Important
Zoning
Very
Important Irrelevant Very Important
Tenant amenity Important Irrelevant Important
Pinkenba Important
Very
Important Important
Landfill Important Irrelevant
Moderately
Important
Traffic Important Important
Moderately
Important
Chapter 8 A case study using InfraPlanner 162
Figure 8.9: Performing an aggregation
Chapter 8 A case study using InfraPlanner 163
8.4 Results
After all data was input the InfraPlanner aggregation interface was used to create
the following four maps:
1. A compensatory double-weighted aggregation (Utility)
2. Conflict assessment (Consensus)
3. Risk assessment (Safety)
4. Uncertainty assessment (Certainty)
The four parameter maps are shown in Figures 8.10 – 8.13.
Chapter 8 A case study using InfraPlanner 164
Figure 8.10: Utility
Chapter 8 A case study using InfraPlanner 165
Figure 8.11: Uncertainty
Chapter 8 A case study using InfraPlanner 166
Figure 8.12: Risk
Chapter 8 A case study using InfraPlanner 167
Figure 8.13: Conflict
Chapter 8 A case study using InfraPlanner 168
An adjusted aggregation based on decision-maker preferences for the importance
of minimizing conflicts risks and uncertainty, or maximizing compensatory
suitability was then performed to enable an adjusted overall suitability estimate
to be derived. To perform an adjusted aggregation it is necessary to weight the
four output parameters, and the following weightings were used to derive the
map shown in Figure 8.14:
Utility is ‘Very Important’
Risk is ‘Very Important’
Conflict is ‘Important’
Uncertainty is ‘Unimportant’
Using the output maps and some further analysis it was possible to identify the
sites of interest (in this case based on individual cells) as shown in Figure 8.15.
Examining the sites exposes the main difficulties behind the site selection task.
Decision-makers disagreed on the best site for the facility and there was also a
difference between the site with the best utility and the site with the best safety.
The sites identified as having the best consensus and certainty, were not viable
solutions in this case as decision-makers agreed with certainty that these sites
were unsuitable. This illustrated that the parameters are not suitable for use in
isolation and must be combined effectively to generate valid solutions. The
adjusted aggregation leaned towards the site with a good combination of all
factors.
Using the interactive exploration interface it was then possible to examine each
alternative comprehensively, and narrow down possible solutions by setting
minimum thresholds for any parameter. The interface offers the ability to view
the decision area as a regular map or use any of the derived raster maps. Clicking
on a particular location produces a natural language analysis in real time as
shown in Figure 8.16.
Chapter 8 A case study using InfraPlanner 169
Figure 8.14: Adjusted aggregation
Chapter 8 A case study using InfraPlanner 170
Figure 8.15: Sites of interest
Chapter 8 A case study using InfraPlanner 171
Figure 8.16: Alternative exploration
Unfortunately no location was completely satisfactory to all, and the primary
benefit gained from the system was the clear identification of the source of
conflict, which has become the subject of negotiation between parties.
8.5 Discussion
The nature of the site selection problem presented here is typical of many real
world situations. A fundamental problem in designing systems to solve such
problems is that there is often no universally accepted solution to find, and it is
not always possible to derive the best compromise from initial assessments. Most
GIS based decision-making methods assume that crisp numerical suitability
assessments can be processed according to a pre-determined algorithm to derive
a solution. However the complex nature of many site selection decisions make
such assumptions unrealistic. It was noted during the selection process that
decision-makers were reluctant to place their faith in a derived solution without
fully understanding how that solution was obtained. This creates a significant
Chapter 8 A case study using InfraPlanner 172
hurdle for system designers whose aim is to replicate, and by default replace, the
decision-making process.
Using a pre-determined optimisation algorithm is standard procedure in many
areas of problem solving, and works particularly well when the exact utility of a
solution can be precisely measured and used as feedback to improve
performance. However the exact utility of a solution in site selection is seldom
known. Multiple, conflicting criteria, and the added human element of
conflicting opinions of measurement and importance create an ill-structured
problem that is often dynamic, in that assessments may change as the solution
space is examined. It is also relevant to note that problem-solving strategies vary
from person to person, making the group situation a particularly dynamic
environment.
InfraPlanner was designed as an intelligent spatial decision support system to
provide decision-makers with relevant, understandable processed information,
whilst leaving them in control of the decision-making process. To this end it was
noted that decision-makers expressed satisfaction with outputs, as they enabled
the group to find the core elements behind their conflicting assessments. In a real
world situation, where political issues can dominate operational concerns, it is
often most beneficial to identify these core areas as they may be traded off for
concessions outside the sphere of the site selection task.
Giving decision-makers the ability to generate a variety of solutions that
maximized aggregated suitability or minimized risk, conflict and uncertainty
provided an easily understandable way for decision-makers to take more control
of the analysis, rather than accepting imposed heuristics. Moreover, whilst the
system makes computationally deriving a solution from input data possible, its
major strength was the high information value of outputs. The experiment
confirmed that a focus on a meaningful, interactive exploration of alternative
outcomes, as opposed to attempting to derive a solution from initial inputs, is a
valid way to support decision-makers in their task. Further specific feedback was
limited due to data privacy issues.
Chapter 8 A case study using InfraPlanner 173
There are some important limitations of the current ‘InfraPlanner’ system:
Firstly, the method used is limited to analysing problems with a single objective,
which makes it unsuitable for situations where multiple facilities are to be
located simultaneously or multiple land uses considered. Secondly, the use of
single cells as alternatives does not accurately represent the true size and spatial
configuration of a proposed development, which has been surprisingly seldom
noted (Brookes 1997). Lastly, utilizing linguistic terms for data input may
unnecessarily limit the accuracy of results in those cases where hard quantitative
data is available.
Another difficulty noted in the group situation was in the definition of criteria.
As an example, some decision-makers noted overlap in their perception of
community impact versus environmental impact. Some authors have described
multicriteria decisions, particularly those with multiple objectives, in terms of a
hierarchical structure, whereby some criteria encompass others, eg (Saaty 1980).
In a group situation this provides another area for disagreement and/or
misunderstanding.
The experience gained from the example at Brisbane Airport proved the validity
of an approximate reasoning approach to group site selection problems under
uncertainty. The InfraPlanner system enabled decision-makers to express their
assessments linguistically and receive meaningful linguistic feedback, whilst
taking more control of the process than other methods allow, and satisfaction
with outputs was expressed. The results also indicated a definite benefit from
utilizing a multi-decision-maker framework, as consensus was unattainable. An
emphasis on providing meaningful processed information, rather than offering a
heuristically derived solution was also found to be beneficial.
Chapter 8 A case study using InfraPlanner 174
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175Chapter 9 Conclusions
Chapter 9
CCOONNCCLLUUSSIIOONNSS
9.1 Introduction
This research has focused on the use of Approximate Reasoning to improve the
techniques and technology of spatial decision support in Infrastructure Site
Selection. A new Approximate Reasoning Algorithm for Infrastructure Site
Selection (ARAISS) was developed and implemented in a new Spatial Decision
Support System (InfraPlanner). The algorithm was then tested and validated in a
real world site selection problem at Australia’s Brisbane Airport.
This concluding chapter presents a final overview of the research presented in
this thesis. The activities conducted during the research program are summarised,
and the conclusions drawn are highlighted. Directions for future research are
suggested before finishing with a set of concluding remarks.
9.2 Summary of Results
The project was a combination of theory-focused research consisting of the
theoretical development of a new fuzzy site selection algorithm (ARAISS) and
design-focused research consisting of the practical application of the theory in a
new SDSS (InfraPlanner). Results are summarised in the following sections.
9.2.1 Answer to the Research Question
As stated in Chapter 1, the fundamental question behind this research was:
176Chapter 9 Conclusions
“Can Approximate Reasoning (AR) be integrated into a GIS based SDSS to
mitigate current difficulties with SDSSs utilised for Infrastructure Site
Selection?”
Results from hypothetical trial problems and a real world case study have clearly
shown that it is both possible and beneficial to integrate approximate reasoning
into a GIS based SDSS. As detailed in the following sections, ARAISS
performed well in both simulated and actual problems, in providing valid
solutions and supplementary information in a format that was easy for decision-
makers to use and understand.
9.2.2 Achievement of the Research Aims
The aim of this research was to create new knowledge at the intersection of
Physical Planning, Decision Science, Soft Computing, Decision Support and
Expert Systems, Geographical Information Systems, and Software Design.
This research has contributed to knowledge by showing that the integration of
AR and SDSSs is possible and putting forth one practical way to achieve it. A
new AR algorithm for site selection in GIS was devised, tested and implemented
in a real world case study. Both the algorithm and the outcomes of the case study
were separately peer reviewed and published at international conferences as
shown in Appendix A.
9.2.3 Achievement of the Research Objectives
Two specific research objectives were defined for this research:
1. Develop a practical infrastructure site selection algorithm based on an
Approximate Reasoning ‘linguistic’ approach.
2. Develop a new spatial decision support system based on the algorithm
developed in objective 1.
177Chapter 9 Conclusions
Objective 1 resulted in the creation of an Approximate Reasoning Algorithm for
Infrastructure Site Selection (ARAISS). ARAISS implements several concepts
that offer an improvement over current methodologies. The core capabilities of
ARAISS are its use of approximate reasoning to handle uncertainty, its multiple
decision-maker capability, its simplicity, and the way it hands over control to
decision-makers.
Objective 2 resulted in the creation of the InfraPlanner Spatial Decision Support
System. InfraPlanner is a prototype Spatial Decision Support System (SDSS)
designed to aid decision-makers with Group Multicriteria Location Problems. It
was created in ArcView GIS and is based on ARAISS.
9.3 Research Overview
The research was conducted in four phases as illustrated below:
1. Planning and Research:
• Needs assessment, problem diagnosis & definition of system
objectives.
• Review relevant literature and gather other information.
2. Analysis & Design:
• Conceptual design of the InfraPlanner system.
• Development of the decision-making algorithm.
3. Construction:
• Coding and debugging of the InfraPlanner prototype.
4. Implementation and Feedback:
• Testing and evaluation of InfraPlanner in a real world validation
problem.
• Critical assessment of the prototype and suggestions for future
improvements to the system.
178Chapter 9 Conclusions
The activities conducted and conclusions drawn from each of the phases are
summarised in the following sections.
9.3.1 Planning and research
Planning and research consisted of a set of increasingly targeted critical literature
reviews. The initial review found that Multicriteria Evaluation (MCE) was
currently the dominant analytical technique used in the solution of infrastructure
site selection problems. Several shortcomings were noted with current MCE
techniques, and most important of these were the inability to deal with
uncertainty, inability to deal with a group environment, and the perception by
decision-makers that current methods are not user friendly.
The universally accepted technology platform for the analysis of location
problems was found to be a Geographical Information System (GIS), coupled or
fully integrated with decision-making models. Advanced artificial intelligence
(AI) and soft computing techniques offered an ability to overcome some of the
shortcomings of MCE, but it was necessary to deploy them in a user friendly way
in order to avoid the perception of a ‘black box’ system. A ‘black box’ system
occurs when users have little or no understanding or control of an analysis
beyond the input of data and knowledge, and it was found that systems based on
current advanced AI techniques often fall within this category.
Approximate reasoning methods based on the use of fuzzy sets, were then
investigated. It was found that most fuzzy methods used in spatial problems
process crisp values obtained from simplifying fuzzy membership functions, and
not the functions themselves, thereby losing the information value of a fuzzy
quantity. A fuzzy number possesses both a mean value and a spread (support)
that may be used to indicate the uncertainty of an answer, however it was found
that there was currently no robust way for decision-makers to input their level of
confidence in applying a particular linguistic label.
The inflexibility of a fuzzy inference system once the rules were generated, and
the extra processing power required for fuzzy pairwise comparison methods left
179Chapter 9 Conclusions
fuzzy MCE as the most appropriate approach to facility site selection. A method
was needed to incorporate approximate reasoning in an MCE analysis suitable
for site selection problems.
The planning and research phase concluded with a review of current software
systems used to solve site selection problems. The umbrella term used for these
systems is Spatial Decision Support Systems (SDSSs). SDSSs are a type of
Decision Support System (DSS) that integrates GIS technology with decision-
making models to aid in the solution of spatial problems. It was found that the
ideal SDSS would be both flexible and user friendly, be fully integrated within a
single GIS software package, provide real-time graphical interactivity and cater
for group decision-making.
The literature consistently noted that the major hurdle facing developers was how
to make systems that are simple and easy to use. There was found to be a general
tendency towards ‘shallow use’ of SDSSs by real world planners and decision-
makers, which was largely the result of real or perceived difficulty in using such
systems. There was also found to be a void of systems capable of accepting
uncertainty assessments directly from decision-makers.
9.3.2 Analysis and design
It was noted during the analysis stage that limitations on current SDSSs are
derived from an inability to deal with multiple conflicting parties, an inability to
handle uncertainty, a lack of simplicity in use and interaction and not delivering
enough control to decision-makers. A conceptual blueprint for the design of a
new algorithm and its implementation in a SDSS was created, and it was
proposed that the new system should possess the following characteristics:
• The ability to accept inputs from a heterogeneous group of decision-makers,
independently weighting and rating multiple attributes.
180Chapter 9 Conclusions
• An approximate reasoning algorithm based on a fuzzy MCE aggregation of
parameter-based fuzzy numbers that encapsulate linguistic suitability and
uncertainty assessments.
• The algorithm should utilise arithmetic operators for aggregation and a
scoring function for de-fuzzification to minimise calculation time and enable
real-time interactivity.
• The system should be fully integrated into existing GIS software.
• Linguistic outputs should be a set of descriptive parameters that give
decision-makers the ability to choose the characteristics of a solution that are
most appropriate to their specific problem, thereby enabling them to gain
control over the properties maximised during aggregation.
The ARAISS site selection algorithm was designed to achieve the goals outlined
during conceptual design. The algorithm works by extracting four parameters
inherent in each alternative that indicate levels of Utility, Safety, Consensus, and
Certainty. Weighting of the four parameters enables decision-makers to decide
which aspects of the solution are most important to their specific problem, and
thereby delivers a real means of control over algorithm performance. The
algorithm performed as expected in example problems, delivering sound results
in a five alternative, three decision-maker problem with simulated inputs.
9.3.3 Construction
InfraPlanner was created as a working prototype of a generic SDSS for site
selection problems of a strategic nature. The system demonstrated that
approximate reasoning techniques are suitable for use in SDSSs, although
designing and building the InfraPlanner Spatial Decision Support System proved
to be extremely challenging. Constructing a DSS is generally considered to be a
complex, time consuming task, requiring a group of skilled individuals, and this
was proven in practice. There are many small issues that are not generic enough
to be mentioned in publications on SDSSs but nonetheless proved problematic.
Among these were choosing a GIS package from the myriad of options available,
181Chapter 9 Conclusions
and dealing with the organisational changes that occurred during the
development process.
9.3.4 Implementation and feedback
An experiment was conducted using a real world site selection decision at
Brisbane Airport, where the desired inputs and outputs could be generated and
commented upon by actual decision-makers. Inputs were generated for three
stakeholder groups using actual decision-makers or representatives chosen by the
experimenter for their knowledge of the situation. The problem used was real,
and the objective was to choose the best location for a recycling facility on the
2700 ha Brisbane Airport site.
The experiment confirmed that a focus on a meaningful, interactive exploration
of alternative outcomes, as opposed to attempting to derive a solution from initial
inputs, is a valid way to support decision-makers in their task. The results
generated by the system were found to be sound, and corresponded well with the
real sites preferred by the decision-making group. Decision-makers found the
method easy to use and the outputs were perceived as helpful.
It is important to note that ARAISS was designed to analyse qualitative site
selection problems with a single objective, and may need to be augmented to
cater for at least three other common types of site selection problems. Firstly in
situations where multiple facilities are to be located simultaneously or multiple
land uses considered. Secondly where the use of single cells as alternatives does
not effectively represent the spatial configuration of a proposed development.
Thirdly where using linguistic terms for data input does not offer the best means
of information input, for example where hard quantitative data is available.
9.4 Validation
A fundamental problem in designing an algorithm to solve infrastructure site
selection problems is that there is often no perfect solution to find, and it is not
182Chapter 9 Conclusions
always possible to derive the best compromise from initial assessments. Using a
pre-determined optimization algorithm is standard procedure in many areas of
problem solving, and works particularly well when the exact utility of a solution
can be precisely measured and used as feedback to improve performance.
However the exact utility of a solution in site selection is seldom known.
Multiple, conflicting criteria, and the added human element of conflicting
opinions of measurement and importance create an ill-structured problem that is
often dynamic, in that assessments may change as the solution space is
examined. It is also relevant to note that problem-solving strategies vary from
person to person, making the group situation particularly dynamic. In such a
climate the traditional model of testing a new algorithm against others using
standard test data and set benchmarks becomes obsolete.
In the case of ARAISS a second major hurdle is the absence of a standard dataset
with which to generate results and compare those results to known solutions.
Datasets used in other published work on multi-criteria site selection either lacks
multiple decision-maker inputs, or uncertainty data. In fact due to the unique
approach of ARAISS, which requires decision-makers to weight output
parameters not generated by other methods, validation is challenging from the
outset.
In the absence of an existing dataset with all the necessary inputs and outputs to
test ARAISS and InfraPlanner, there were three practical means of validation
applicable to this research:
1. Using custom made sample datasets based on hypothetical problems to
evaluate the success of the algorithm.
2. Using a real problem to gain feedback on the suitability of results
produced by ARAISS, and the benefits gained by using InfraPlanner.
3. Peer review of the ARAISS model and the process used to develop it.
Use of the first method was described Section 6.3, which gives the results of
simulation exercises conducted using MATLAB. Several MATLAB simulations
were conducted to test the common sense validity of the algorithm. The problems
183Chapter 9 Conclusions
were all based on three decision-makers rating five alternatives with respect to
three criteria. Results showed that ARAISS performed as expected, producing
commonsense results and successfully extracting the four output parameters of
Utility, Certainty, Risk and Conflict.
Chapter 8 describes the use of Infra Planner in a real site selection problem at
Australia’s Brisbane Airport. The problem was based on six criteria with inputs
coming from three separate decision-maker groups. Once again sound results
were produced, with the algorithm selecting the same site as had been previously
earmarked. Decision-makers found it easy to provide their preferences
linguistically, and the output information provided by InfraPlanner was found to
be useful and easily interpretable.
Peer review was facilitated first and foremost by publication of the ARAISS
algorithm and its implementation in InfraPlanner as shown in Appendix A, and
secondly via a focus group conducted at the ANZIIS 2003 conference. Feedback
was positive, with all present agreeing that both the development process and the
model derived from it was valid. Some researchers noted that the use of a
software design flowchart would also be a good way to represent the model, as
they found the logic model used difficult to follow.
9.5 Key Findings
The following summary points are presented here as the key findings of this
research.
1. The key limitations of existing MCE techniques used for site selection were
found to be:
a) An inability to handle uncertainty.
b) An inability to handle a group decision-making environment.
c) Real or perceived difficulty of use, and a limited sense of control.
184Chapter 9 Conclusions
2. It was found that approximate reasoning could be used to mitigate these
difficulties in the following ways:
a) Uncertainty in spatial decision-making may be modelled using fuzzy
numbers to quantify linguistic suitability assessments. The fuzzy numbers
may be scaled for varying levels of uncertainty using the concept of type-
2 fuzzy sets.
b) Inputs from a heterogeneous group may be brought together by the use of
a relevance matrix, which is a device to weight a decision-makers ability
to judge a particular criterion.
c) The use of linguistic inputs and outputs, coupled with an emphasis on
providing useful information rather than direct solutions was found to
provide a simple way to interact with a SDSS, that delivered a greater
sense of control. In particular the identification of the overall utility,
uncertainty, risk, and conflict inherent in each solution provides greater
information value than a single numerical score.
9.6 Directions for future research
Expanding on the working prototype opens up several possibilities, and further
work is recommended to expand ARAISS and InfraPlanner to be capable of
handling multiple facility problems, and explicitly include the size and spatial
configuration of the required land parcels. Potential also exists to include existing
philosophies that have proven effective in this type of problem such as factor
analysis, approaches based on the triple bottom line, the use of key performance
indicators, and data envelopment analysis.
Genetic algorithms also offer a promising method to explore feasible alternatives
without resorting to the massive number of calculations required to fully examine
the solution space of such problems. Research on other artificial intelligence
techniques such as neural networks should produce benefits in complex spatial
decisions.
185Chapter 9 Conclusions
At a practical level, this new functionality may be added to InfraPlanner in three
basic ways:
1. By enhancement of the suitability map generation capability to include
extra parameters
2. By enhancement of the aggregation capability to process extra
information
3. By enhancement of the interactive feedback capability to display and
optimise based on the extra data required in the approaches outlined
above
There also exist several fundamental difficulties with multi-criteria decision-
making not addressed in this thesis, that offer promising direction for future
work. These include:
• Selection of criteria and criterion overlap
• Development of more accurate means of semantically representing decision-
maker preferences
• Methods for generating consensus in a group environment
• Methods for choosing a suitable decision-maker group
• Methods to quickly process raw data into the format necessary for use in a
SDSS
9.7 Concluding remarks
This research has produced a new fuzzy algorithm for the selection of sites for
large-scale infrastructure, and implemented it in a new Spatial Decision Support
System. The algorithm performed well in both hypothetical and real site selection
problems, however hard empirical validation is difficult to perform when there is
no completely accurate way to rate solutions to complex site selection tasks.
186Chapter 9 Conclusions
The construction of the algorithm, based on type-2 fuzzy set concepts, proved
practical, and produced results consistent with those chosen by real world
planners and decision-makers. Calculation times were sufficiently short to enable
seamless integration into a real-time GIS based analysis, and the format of inputs
and outputs proved simple and easy for users to understand.
Further validation of the methods developed in this research is recommended, as
are the integration of artificial intelligence techniques and other decision-making
philosophies. The confluence of Physical Planning, Decision Science, Fuzzy
Logic, Soft Computing, Decision Support and Expert Systems, Geographical
Information Systems, and Software Design should prove to be fertile ground for
innovation for many years to come.
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Appendix A Publications 199
Appendix A
PPUUBBLLIICCAATTIIOONNSS
Appendix A Publications 200
Appendix A Publications 201
The following peer reviewed original publications were the direct result of the
research presented in this thesis. They are reprinted here in Appendix A.
1. Bailey, D., A. Goonetilleke, and M. Deriche. A decision support system for site selection of large-scale infrastructure facilities using natural language. in Operations Research into the 21st Century. 2003. Noosa, Australia: The Australian Society for Operations Research (ASOR).
2. Bailey, D., A. Goonetilleke, and D. Campbell. Information analysis and dissemination for site selection decisions using a fuzzy algorithm in GIS. in Information and Knowledge Sharing. 2003. Scottsdale, Arizona: ACTA Press.
3. Bailey, D., D. Campbell, and A. Goonetilleke. An experiment with approximate reasoning using 'InfraPlanner'. in ANZIIS 2003. 2003. Sydney: Queensland University of Technology.
halla
These articles are not available online. Please consult the hardcopy thesis available from the QUT Library
Appendix A Publications 202
Appendix B The Brisbane Airport Environment 203
Appendix B
TTHHEE BBRRIISSBBAANNEE AAIIRRPPOORRTT
EENNVVIIRROONNMMEENNTT
Appendix B The Brisbane Airport Environment 204
Appendix B The Brisbane Airport Environment 205
Brisbane Airport occupies a site of 2700 ha, located 13km north east of the
Brisbane CBD, adjoining Moreton bay. The flat and low lying site occupies part
of the original Brisbane river delta, which has undergone extensive changes since
the 1830s, with most of the original network of tidal waterways being replaced
with constructed drains. Much of the vegetation on the site has been planted in
the last 15 years, and was chosen to reduce the attraction of birds.
The major infrastructure currently on the Airport site as shown in Figure 8.1
consists of:
• 3560m long main runway (01/19) and associated taxiways
• 1760m long cross runway (14/32) and associated taxiways
• Domestic terminal building and apron
• International terminal building and apron
• General aviation buildings and apron
• Old international terminal building and apron
• Several Maintenance and support facilities
• Two major freight facilities plus several smaller facilities
• Three major catering facilities
• Private and rental vehicle parking areas
• Administration offices and control facilities
• Refuelling facilities and depot
• Lighting to runways, taxiways, aprons roads and car parks
Ten habitats have been classified on the site, as shown in the table below:
Monoculture of casuarina glauca, originally providing a relatively poor habitat, but well-established areas infested with weeds and may become attractive.
Low
Appendix B The Brisbane Airport Environment 206
Open Grassland
Closely mown grass surrounding the airports core facilities, which provides a poor habitat.
Low
Remnant Mangrove Communities (general)
Avicennia marina, the grey mangrove, is the dominant species. These are native mangrove communities, which are in good condition, provide a complex and diverse habitat, and contribute to the productivity of adjoining fisheries.
A,E,I,C,W,R,J,Q,F,N
High
Serpentine creek mouth mangrove community
A closed scrub community of Ceriops taga,l which is uncommon within the bay. It is contiguous with the luggage point to jubilee creek mangroves and provides a significant habitat for mammals, reptiles, amphibians and avifauna.
A,E,I,C,W,R,J,Q,F,N
Very high
Channel Mangrove Communities
Numerous drainage channels have been colonised by, or planted with grey or river mangroves.
A,E,I,W,R,J,Q,F,N
Moderate
Remnant Saltmarsh Communities
These communities fringe areas of remnant mangrove, and also occur in freshwater wetland sedges adjacent to Kedron Brook Floodway. The saltcouch Sporobolous virginicus) dominates, although patches of samphire are common.
A,E,I,W,R,J,Q,F,N
High
Freshwater Wetlands and Sedge Communities
These communities are recently colonised in poorly drained and inadequately filled former sandmining areas. The dominant species is Phragmites australis, although much diversity is supported by wetland areas in general.
A,E,I,W,R,J,Q,F,N
High
Coastal Dunes and Foreshore
May form important habitats for migratory (and other) birds.
A,E,I,C,W,R,J,Q,F,N
Moderate
Remnant and Engineered Creeks and Channels
It is likely that Serpentine and Jackson creeks support significant communities of flathead, whiting and bream. Engineered creeks and channels are likely to serve as significant nursery grounds for many species that subsequently migrate to the open waters of Moreton Bay, as well as invertebrates.
A,E,I,W,R,J,Q,F,N
Moderate
Remnant Bushland
A small (5ha) isolated bushland site at Pinkenba
A,I,Q Low
Abbreviations for statutory considerations:
Appendix B The Brisbane Airport Environment 207
A - Airports act 1996 and the Airports (Environment Protection) Regulations E - Endangered Species Protection Act 1992 I - Environmental Protection (Impact Proposals) Act 1974 C - Coastal Protection and Management Act 1995 W - Wetlands Policy of the Commonwealth of Australia 1997 R - Ramsar Convention J - JAMBA & CAMBA treaties Q - QLD Environmental Protection Act 1994 F - Fisheries Act 1994 N - Nature Conservation Act 1994 The airport is also generally bounded to the east, north and west by ecologically
significant habitats. At least thirteen rare, endangered or vulnerable fauna species
may be associated with the sites tidal or swampy areas as shown in the table
below.
Scientific Name Common Name Conservation Status Siting Commonwealth State
Birds
Esacus neglectus beach thick knee - V P Anas castanea chestnut teal - R O Numenius Madagascariensis eastern curlew - R O Sterna albifrons little tern E V O Ephippiorhynchus asiaticus jabiru - R P Rostratula benghalensis painted snipe - R P Dryolimnas pectoralis Lewin’s rail - R P Insects
Acrodipsas illidgei Illidge’s blue butterfly - E P
Marine Reptiles
Caretta caretta loggerhead turtle E E M Chelonia mydas green turtle V V M
Marine Mammals
Dugong dugon dugong - V M Sousa chinensis ndo-Pacific humpback - R M Dolphin
Terrestrial Mammals
Xeromys myoides alse water rat V R P Commonwealth: Commonwealth Endangered Species Protection Act 1992
E Endangered: in danger of extinction, and survival is unlikely if threats continue V Vulnerable: likely to become Endangered in the near future if threats continue R Rare: not considered Endangered or Vulnerable and may be abundant in restricted areas O Observed on site P Possibly on site M Marine animal probably occurring near site
The foreshore, intertidal and freshwater wetlands of the airport site may also
support a number of bird species protected by international treaty. These birds
are generally associated with the Moreton Bay area, which is arguably the most
important feeding ground for migratory waders along the east Australian coast
(Driscoll 1992).
The most significant communities on, and adjacent to the site are all associated
with wetland habitats: both intertidal (mangrove and saltmarsh) and freshwater.
Each of these habitats could be detrimentally affected by a range of activities
including:
Reclamation
Changes to the drainage patterns and hydrology of the site
Alteration to tidal inundation patterns of the site and flushing of the waterways
Increase in sediment loads
Dredging and maintenance of the channels
Discharge of contaminated water or fuel/chemical spillage
Increase in the nutrient levels of the water
Disturbance of acid sulphate soils and the consequent acidification of the water
Feral animals
Control of mosquito and biting midges
Proliferation of exotic weeds
Increases in noise and activity levels
In general, the effects include the following:
Increases in noise and activity could detrimentally affect bird life
Appendix B The Brisbane Airport Environment 209
Fragmentation and development could lead to the further introduction and
proliferation of exotic weeds and feral animals
Decreases in water quality are likely to affect populations of turtle, dugong and
dolphins in the area
RUST PPK, in their 1996 review also states that air pollution may pose
significant environmental concerns, in the areas immediately surrounding the
airport. This is not addressed in the AES, as the Airports (Environmental
Protection) Regulations do not apply to pollution generated by an aircraft. It is
dealt with under Commonwealth legislation namely the Air Services Act 1995
and Air Navigation (Aircraft Engine Emissions) Regulations. The affects of
aircraft noise on the environment may also be considerable.
The area upon which the Brisbane Airport is situated is claimed as the traditional
country of the Turrbal corporation, which has indicated that there were special
places within the vicinity of the airport site, including an unrecorded bora ring
destroyed during runway construction.
Since European settlement, a range of land-uses and events occurred on the area
now known as Brisbane Airport, most of which have left little trace. The only
physical items listed on the register of the National estate lie outside the airport
boundary, however significant archaeological sites connected with the convict
era and the WWII history of Brisbane, may exist within the site.
Appendix B The Brisbane Airport Environment 210
211Appendix C MATLAB Code
Appendix C
MMAATTLLAABB CCOODDEE
212Appendix C MATLAB Code
213Appendix C MATLAB Code
The following MATLAB code was used to perform a simulation of the ARAISS
algorithm on a three decision-maker, three criteria, five alternative problem. Code for the
main functions only has been included. Full code is available upon request.
Tripleanalyse.M (Main Loop)
% performs a fuzzy analysis and normalisation on the 3
datasets & termset & relevance mtx in the workspace
decode;
aggregateandnormalise;
rankoutputs;
showmatches;
plotoutputs;
clear;
Decode.M
% decodes the 3 coded decision matrices (dm1 2 & 3) using
the suitability & uncertainty termsets in the workspace
saves the resulting 3d fuzzy matrices
% NEED TO ADJUST THE WAY WEIGHTS ARE INPUT AS SOME ARE NOW
>= 1
load termset termset;
load dm1 dm1;
load dm2 dm2;
load dm3 dm3;
load rm rm;
[rows,cols] = size(dm1);
%weightsum is for use in critical weight
dm1weightsum = 0.0;
dm2weightsum = 0.0;
214Appendix C MATLAB Code
dm3weightsum = 0.0;
for i = 1:cols
dm1weightsum = dm1weightsum + dm1(rows, i);
dm2weightsum = dm2weightsum + dm2(rows, i);
dm3weightsum = dm3weightsum + dm3(rows, i);
end
fuzzydm1 = zeros(rows,cols,4);
for i = 1:rows
for j = 1:cols
for k = 1:4
if i < rows
fuzzydm1(i,j,k) = termset(dm1(i,j),k);
elseif dm1(i,j) < 1
fuzzydm1(i,j,k) = dm1(i,j);
else
fuzzydm1(i,j,k) = 2 * cols *
(dm1weightsum) + .1; %critical
dm1critscore = fuzzydm1(i,j,k)
end
end
end
end
fuzzydm2 = zeros(rows,cols,4);
for i = 1:rows
for j = 1:cols
215Appendix C MATLAB Code
for k = 1:4
if i < rows
fuzzydm2(i,j,k) = termset(dm2(i,j),k);
elseif dm2(i,j) < 1
fuzzydm2(i,j,k) = dm2(i,j);
else
fuzzydm2(i,j,k) = 2 * cols *
(dm2weightsum) + .1; %critical
dm2critscore = fuzzydm2(i,j,k)
end
end
end
end
fuzzydm3 = zeros(rows,cols,4);
for i = 1:rows
for j = 1:cols
for k = 1:4
if i < rows
fuzzydm3(i,j,k) = termset(dm3(i,j),k);
elseif dm3(i,j) < 1
fuzzydm3(i,j,k) = dm3(i,j);
else
fuzzydm3(i,j,k) = 2 * cols *
(dm3weightsum) + .1; %critical
dm3critscore = fuzzydm3(i,j,k)
end
216Appendix C MATLAB Code
end
end
end
[rows,cols] = size(rm);
fuzzyrm = zeros(rows,cols,4);
%normalise the crit rm values
rmcrit = zeros(1,cols);
rmsum = zeros(1,cols);
for i = 1:rows
for j = 1:cols
if rm(i,j) == 1
rmcrit(j) = 1
rmsum(j) = rm(1,j) + rm(2,j) + rm(3,j);
end
end
end
for j = 1:cols
if rmcrit(j) == 1
for i = 1:rows
if rm(i,j) < 1
rm(i,j) = rm(i,j) / (2 * rows * (rmsum(j))
+ .1)
end
end
end
end
217Appendix C MATLAB Code
for i = 1:rows
for j = 1:cols
for k = 1:4
fuzzyrm(i,j,k) = rm(i,j);
end
end
end
% now scale the fuzzy dm matrices for uncertainty
load dm1uncert dm1uncert;
load dm2uncert dm2uncert;
load dm3uncert dm3uncert;
for i = 1:rows-1 % no need to scale weights
for j = 1:cols
fuzzydm1(i,j,:) =
uncertscale(fuzzydm1(i,j,:),dm1uncert(i,j));
fuzzydm2(i,j,:) =
uncertscale(fuzzydm2(i,j,:),dm2uncert(i,j));
fuzzydm3(i,j,:) =
uncertscale(fuzzydm3(i,j,:),dm3uncert(i,j));
end
end
% Normalise weights with critical component - uncertainty
not a factor in weight
dm1weightsum = 0.0;
dm2weightsum = 0.0;
218Appendix C MATLAB Code
dm3weightsum = 0.0;
[rows,cols] = size(dm1);
dm1crit = 0.0;
dm2crit = 0.0;
dm3crit = 0.0;
for i = 1:cols
if dm1(rows, i) == 1
dm1crit = 1
end
end
for i = 1:cols
if dm2(rows, i) == 1
dm2crit = 1
end
end
for i = 1:cols
if dm3(rows, i) == 1
dm3crit = 1
dm3(rows, i)
end
end
if dm1crit == 1
for i = 1:cols
219Appendix C MATLAB Code
for j = 1:4
fuzzydm1(rows, i, j) = fuzzydm1(rows, i, j)/
dm1critscore;
end
end
end
if dm2crit == 1
for i = 1:cols
for j = 1:4
fuzzydm2(rows, i, j) = fuzzydm2(rows, i, j)/
dm2critscore;
end
end
end
if dm3crit == 1
for i = 1:cols
for j = 1:4
fuzzydm3(rows, i, j) = fuzzydm2(rows, i, j)/
dm3critscore;
end
end
end
save fuzzyrm fuzzyrm;
save fuzzydm1 fuzzydm1;
save fuzzydm2 fuzzydm2;
220Appendix C MATLAB Code
save fuzzydm3 fuzzydm3;
Aggregateandnormalise.M
function f = aggregateandnormalise()
% aggregates & normalises the 3 decisionmatrices stored in
the workspace to obtain alternative ratings (last row of