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A NEW FUZZY MODEL FOR EVALUATION OF KEY PERFORMANCE INDICATORS AND PROCESS QUALITY

Danijela Tadić, Miladin Stefanović, Slavko Arsovski, Snežana Nestić

Abstract. Improvement of key business processes is one of requests of standard ISO 9001:2008 and has a critical effect on the competitive advantage of any organization. In this paper key business processes, their objectives, key performance outcomes and key objective indicator for each identified objective are defined with respects to critical success factors. Modelling of the relative importance of purchasing key performance indicators and their values, as well as modelling of influence of specific objective on process quality will be presented in this paper using fuzzy sets. The algorithm for evaluation of KPIs and process quality is presented and illustrated by example of purchasing process in one service organization.

Keywords: process quality strategy, effectiveness, fuzzy set, fuzzy AHP, fuzzy logic

1. INTRODUCTION

Quality management includes all the activities that organizations use to direct, control, and coordinate quality. These activities include formulating a quality policy and setting quality objectives. They also include quality planning, quality control, quality assurance, and quality improvement. According to literature review (Deming, 1993 Juan, 1988, Crosby, 1984) it could be stated that achievement of quality goals leads to improvement of the competiveness, effectiveness and flexibility of an organization. This is a reason why considered problem has become a topic of research for both industry and academy in last decades. The quality goals and objectives could be considered as part of strategic goals and objectives. In other words the formulation of quality goals and quality strategy are based on the strategy development process and proposed in different researches (Kaplan, Norton, 2008). The quality goals are defined by top managers with respect to vision (how the organization wants to be perceived by the world), mission (what organization wants to be achieve) and values (prescribe its behavior, character and culture). In the further steps top managers define a goals and critical success factors (CSFs)- which the organization must accomplish to achieve the mission, by examination and categorization of the impact (Oakland, 2004). These CFS are sufficient for the mission to be achieved and to use for identification of the key business process in an organization. Business Process Management (BPM) defines objectives of key business processes with respects to CFSs which must be accompanied by measurable of key performance indicators (KPIs Improvement of key business processes could be achieved if objectives can be measured through key performance indicators (KPIs). KPIs, on the other hand, are measures that quantify management objectives, along with a target or threshold, and enable the measurement of strategic performance. In the literature, there are numerous process performance measurement methods (Neely et al, 1995). In these measurement systems values of variables are expresses by precise numbers.

Performance measurement systems are developed on different mathematical and logical frameworks. With respects to recommendation of ISO 9001:2008 that each enterprise should develop approach in improvement of processes the issue of definition of KPIs definition of their weights, importance and values, as well as their influence of the quality of specific process could be stated as important issue.

Considering the fact that enterprises exist in rapid changing environment, it is not easy to evaluate the variables with precise numbers. In this paper, authors developed a new approach for assessment of quality of specific process and weights and values of KPIs using fuzzy sets. It is assumed that decision makers of BPM

express their judgments far better by using linguistic expressions than by representing them in terms of precise numbers. Uncertainties in the relative importance and values of measures of objectives caused by lack of appropriate information and conflicting evidence (some of the information available is wrong, information of non-relevant features of the considered problem, etc) are described by linguistic expressions. There are numerous theories which claim to be the only proper tool to model linguistic expressions. According to Zimmermann (Zimmermann, 1997), fuzzy sets theory can be the most appropriate way for modelling linguistic expressions.

In this paper we will address following issues: modelling of the relative importance of purchasing key performance indicators and their values, as well as modelling of influence of specific objective on process quality. The algorithm based on fuzzy sets will be presented that will enable evaluation of each KPI, as well as their importance on specific objective and further evaluation of process according to realization of each objective.

The paper is organized in the following way. The section 2 describes the problem statement. Modelling of uncertainties are described in Section 3. A new fuzzy model based on fuzzy logic for evaluation operational strategy execution effectiveness is proposed in Section 4. In Section 5, a proposed model is illustrated by example with real-life data. Conclusions are presented in Section 6.

2. LITERATURE REWIEV

Purchasing deals primarily with managing all aspects related to the inputs for an organization (i.e., purchased goods, materials, and services), while supply chain management deals with inputs, conversion, and outputs. As a result of implementation of SCM in manufacturing companies, the quality of the purchasing process is now playing a key role in management of the selection of an optimal supply process, which is strategically crucial (Erol, 2009). Having a high level of quality of the purchasing process is very important for all companies, especially for manufacturing companies where more than 65% financial resources is spent on the purchasing of resources. There are different aspects of ISO 9001’s implementation in terms of the relationships with three key supply chain (SC) management practices (internal processes, supplier relationships, and customer relationships). Prajogo et al. (2012) indicates that supplier and internal process management both have a positive effect on operational performance, while customer process management has no significant impact. The quality level of the purchasing process would, directly, affect the quality level of the supply chain (Wu and Wang, 2011). Therefore, improving the level of quality of the purchasing process must be significant (Sánchez-Rodríguez 2003, Sánchez-Rodríguez and Martínez-Lorente, 2004; Paulraj et al., 2006, Soroush (2012)).) for enhancing the quality level of the supply chain. Establishing target performance levels and then implementing metrics to track performance, relative to those targets, gives the data necessary to continually improve performances.

The relation between implementation of quality management systems such as ISO 9001 (ISO 9001:2008) and the quality of processes and outcomes is clear and has been identified in many researches. Obtaining a clear understanding of business process quality constitutes the most important prerequisite (Lohrmann and Manfred, 2013). Koc (2007) provides results showing that ISO 9000’s implementation makes a significant difference to a firm’s performance when comparing certified and non-certified firms. There are various ways in which a company can claim that its QMS meets the requirements of ISO 9001. These include certification and party assessment or even self-assessment. In assurance of quality, self - assessment has an important place. Rezaie et al. (2011) introduced a self - assessment system based on the fundamental principles and requirements of ISO 9004:2000 and provided a tool for assessment of organizational maturity and recognition of improvement points. A number of researches have also focused on the application of different approaches in the selection, ranking and assessment of parameters (including suppliers) or even management systems. For instance, Tsai and Choua (2009) proposed a novel hybrid model for selecting optimal management systems under resource constraints. Flegel and Brozova (2011) presented a fuzzy decision model for selection of an appropriate management system (ISO 9001 or ISO 14001). Feng (2004) presented a method of fuzzy integrated estimation of the effectiveness of a quality management system. An improved fuzzy model

for evaluation of the effectiveness of QMS was presented in Liu et al. (2008). Identifying quality improvement opportunities in a enterprises is not an easy task (Fore, 2011).

One of the first steps in improvement is identification and assessment of weak spots and self-assessment. The assessment model could identify impacts on the existing system as well as provide the result of introducing new standards Khir and Kai (2012). The assessment of the quality of processes provides a platform to compare and benchmark different purchasing processes and indicators, as well as define actions for their improvement. There are different solutions for QMS assessment and steering (MATLAB's GUI components and its Fuzzy Logic Toolbox (Lee et al., 2011) or the Pareto Analytical-Hierarchy Process (PAHP) and the Multichoice Goal Programming (MCGP) (Mahmoud et al., 2011)).

Psomas et al. (2013) developed an instrument that measures the effectiveness of the ISO 9001 Quality Management System (QMS), based on its components, meaning the ISO 9001 objectives. In that research ISO 9001 objectives and their indicators are identified from the literature, and the focus was on SMEs. The Performance measurement can be achieved through: Key Result Indicators – KRIs, Result Indicators - RIs, Performance Indicators – PIs and Key Performance Indicators - KPIs (Parmenter, 2010). KPIs are focused on aspects that are critical to the success of the company. Their purpose is to enable performance measurement and evaluation of processes and organization. They also indicate the quality of the processes, activities and the company. Proper selection of KPIs is essential for effective performance measurement because too many KPIs as well too complex KPIs can cause unnecessary waste of time and money.

Traditionally, the monitoring of a purchasing department's performance is primarily focused on cost analysis and the evaluation of suppliers rather than on internal service aspects Holschbach and Hofmann (2011), so some researches have focused on the internal service quality of purchasing departments (Large and König, 2009). Performance and quality measurement is an essential element of effective planning and control as well as decision making. The measurement results reveal the effects of strategies and potential opportunities (Bhagwat, 2007). It is clear that very important issues is measurement of the quality of specific process. Each process could be measured according their objectives and accompanied KPIs. It is very important to provide formal model for assessment the KPIs, their values as well as the influence of specific objectives on quality of process. This is important for companies because it provides a platform to find weak spots, and provides improvement actions, comparing different purchasing processes.

2. PROBLEM STATEMENT

In this Section, problem statement of definition of efficiency of quality of process is given which is placed in the internal perspective of strategic map.

According to CSFs, strategic management defines key processes which could be decomposed on sub-processes. The sub-processes under each business process are presented by set indices P . For each sub-process of treated a key business process defines objective. In this paper, objective of a sub-processes of any key business process are formally presented by set indices I where i is index of objective and I is total number of objectives of considered business sub process. Each objective i, i=1,…,I is associated with number of KPIs which are presented by set J . The index j denotes KPI of

objective i and the total number of KPIs associated objective i, i=1,..,I is denoted as . The values of KPIs for objective i, have different type (benefit type and cost type) and their values could be presented in different units, for example monetary unit, time unit, percent, quantity, index, etc.

The relative importance of sub-processes under considered key business process are not equal and they are determined by BMP team. It is realistic to assume that relative importance of KPIs are not equal. They are assessed by each decision maker of BMP team. The relative importance of each pair of KPIs are stated by

fuzzy pair-wise comparison matrix. The elements of this matrix are triangular fuzzy numbers

The normalized weights vector of KPIs is denoted as

. The relative importance of objective, is calculated by using similar way.

The target of each identified process and KPOs targets can be determined by using different measurement methods (survey, interview method, evaluation of leadership team, internal and/or external benchmarking, etc). It can be stated that target of KPIs , objectives and process are denoted as

respectively. The target vales could be measured in percents, i.e. belong to interval [0-1].

The current values of KPIs are given by using different measurement procedure. The overall value of each

KPI is based on evaluation of BMP. BMP make decision with respect to target value and current value. In

decision making, decision makers, beside two values connected with each KPI, respect a KPI type. With

resects the fact that KPIs have measurement units, by using presented procedure for determining of overall

value of KPIs, they become non dimensional values which could be compared. The value of each KPI of

each objective are described by predefined linguistic expressions with respect its current and target values.

Process quality strategy effectiveness is determined by using proposed fuzzy algorithm. According to these

values BMP team makes decision about redesigning of quality strategy.

3. MODELLING OF KPIs RELATIVE IMPORTANCE AND VALUES FOR PURCHASING PROCESS

3.1 Basic definition of fuzzy sets

Fuzzy sets are represented by its membership function which the parameters are shape, granularity and location on the universe of discourse. The membership function shape of a fuzzy set can be obtained based on one’s experience, subjective belief of decision makers, intuition and contextual knowledge about the concept modeled (Zimmermann, 1978), uncertainty available on the treated linguistic variables (Berman, Trubatch 1997). However, subjectively in determining membership function has been considered as the weakest point in fuzzy sets theory. Among the commonly used fuzzy numbers, triangular fuzzy numbers offer a good compromise between descriptive power and computational simplicity. The triangular fuzzy numbers are applicable to the present study. Fuzzy sets of higher types and levels have not as yet played a significant role in applications of fuzzy sets theory (Klir, Yuan, 1995). Granularity is defined as number of fuzzy numbers assigned to the relative importance parameters, their values, and level of effectiveness Lootsma (Lootsma, 1997) suggested that only seven categories at most can be used. The domain of fuzzy sets can be defined on different measurement scales.

Some definitions of fuzzy sets in (Dubois, Prade, 1979, Klir Folger, 1988, Zimmermann, 2001) presented used notations and are reviewed.

Definition 1. Uncertainty implies that in a certain situation a person does not dispose about information which quantitatively and qualitatively is appropriate to describe, prescribe or predict deterministically and numerically a system, its behavior or other characteristic (Zimmeramnn, 2001).

Definition 2. Linguistic variables are variables whose values are not numbers but words or sentences in a natural or artificial language (Zadeh, 1975).

Definition 3. Fuzzy set is defined as a set of organized pairs:

(2.1)

where:

Fuzzy set is defined on the universe set X R. In general, set X can be either finite or infinite. is a

membership function of fuzzy set .

Definition 4. A fuzzy number is a convex normalized fuzzy set of the real line R such that: (1)if exist

such that and (2) is piecewise continuous.

Definition 5. Fuzzy number on R is to be a triangular fuzzy number if its membership function R

is equal to

(2.2)

Where , l and u stand for the lower and upper value of the support of X respectively, and m for the modal value. The triangular fuzzy number can be denoted by (l, m, u). The support of X is the set of elements

. When l=m=u, it is a non-fuzzy number by convention.

Definition 6. The operations of fuzzy numbers are based on the theorem set by Dubois and Prade (Dubois,

Prade, 1980). Let two fuzzy numbers and . The membership

functions of these fuzzy numbers are subjective from zero to one and * is a continuous binary operation.

Then is a fuzzy number which is denoted , such as . Values in domain of fuzzy number ,

can be calculated as z=x*y and .

Definition 7. Defuzzifacation is an operation which determines the scalar or the crisp value that is the best representative of a fuzzy set.

3.2 Modelling of the relative importance of purchasing key performance indicators

All KPIs are usually not of the same relative importance. It can be assumed that, their importance are unchangeable during the considered period of time. We think that the judgment of each pair of treated KPIs best suits human-decision nature (by analogy with AHP method). In other words, the relative importance of KPIs of each objective i is stated by pair-wise comparison matrix. The elements of these matrix are judgemental by decision makers of BPM which use predefined linguistic expressions. BMP team make

decision by consensus. They are modelled by and described by triangular fuzzy numbers,

. The domains of defined triangular fuzzy numbers are

defined on standard scale measures [1-5]. The value 1 means that relative importance of KPI j and KPI of objective i, have equal the relative importance. The value 5 means that relative importance of KPI j over KPI of objective i, has most important.

These triangular fuzzy numbers which are given in the following way:

low importance-

moderate importance-

high importance-

If high relative importance of KPI over KPI j of objective i, holds, then pair-

wise comparison scale can be represented by the fuzzy number .

Weights vector of the considered KPIs of objective i, is calculated by applying the method in

(Chang, 1996). The normalized weights vector .

is a non-fuzzy number and this gives the priority weights of one KPO over the other under objective i,

.

3.3 Modelling of purchasing key performance indicator values

In general, the KPIs of each objective can be different benefit type or cost-type and they have different measurement units, for instance percent, days, etc. Each KPI are associated two values: target value and current value.

BPM uses predefined linguistic expressions for describing KPI values. These linguistic expressions are modelled by triangular fuzzy numbers, whose domains belong to the common scale [0-1]. The value 0 denotes very low value of KPI. The value 1 indicates a very high value of KPI. The triangular fuzzy numbers for modelling the KPO values are:

very low value-

low value-

medium value-

high value-

very high value-

3.4 Modelling of importance of specific objective on purchasing process quality

In this paper, influence of specific objective on process quality is modelled by one of five predefined linguistic terms. These linguistic expressions are modelled by triangular fuzzy numbers which domains belong to interval [0-1]. The value 1 denotes total lack of gap between objective value and its target. The value 0 indices a very high value gap between objective value and its target. Granularity of these triangular fuzzy numbers is performed by respect to opinions of decision makers.

The triangular fuzzy numbers for modelling imporantance of specific objective on process quality:

no important -

low importance-

medium importance-

very important -

highly importnat-

4. THE PROPOSHED ALGORITHM FOR ASSESMENT OF KPIs AND PURCHASING PROCESS QUALITY

For the BPM carrying outs the analysis, the following tasks are important: (1) to estimate how much each KPI of treated objective could contribute to closing the value gap, and (2) to evaluate effectiveness of process quality strategy used for redesign of strategy.

The Algorithm of proposed fuzzy model is presented as follows:

Step 1. Input pair-wise fuzzy comparison matrix of the relative importance of KPI for each objective i:

By using extent analysis which is proposed in (Chang, 1996), weights vector of KPIs at the objective level, is

calculated.

Step 4. Calculate weighted normalized KPI values for each objective i, :

,

The membership function values of the fuzzy number are calculated by using fuzzy operation dilatation

(Zimmermann, 2001, Dubois, Prade, 1980).

Step 5. Define the objective weight i:

Step 6. The overall weighted value of objective i is given:

Step7. Calculate representative scalar fuzzy number by method of maximal possibility (Dubois, Prade,

1980).

=defuzz

Step 8. Determine value gap of objective i:

The process quality effectiveness in observed objective i, i=1,...I can be defined according to the rule of fuzzy logic (Zimmerman, 2001, Klir, Folger, 1988):

IF the value gap , THAN strategy efficiency is described by linguistic expression where

.

Step 9. Calculate weighted value of treated process

Step 10. Determine value gap for process p:

The process quality effectiveness in observed key process p, p=1,...P can be defined according to the rule of fuzzy logic (Zimmerman, 2001, Klir, Folger, 1988):

IF the value gap , THAN strategy efficiency is described by linguistic expression where

.

5. ILUSTRATTIVE EXAMPLE – EVALUATION OF PURCHASING PROCESS

The proposed model is tested on the real-life data which are obtained from service organization from central Serbia. The selected process I purchasing process which is divided into seven sub-processes: define purchasing requirements, purchasing planning, suppliers of evaluation, contracting, verification of the purchasing, reclamation to supplier, and contract implementation monitoring.

The purchasing process is not very precise so, therefore, the decomposition of the purchasing process varies from company to company. In some companies, more attention is paid to planning of the purchasing, in others the selection of supplier, and in some companies’ attention is on both. Every company finds the most suitable way, which depends on its size, structure, types of activities and development of communication.

In view of the growing supply of reference models (such as CIMOSA, GRAI-GIM and PERA, and others), in various domains and in different formats, the potential benefits to organizations using them (Spiegel and Caulliraux, 2012), and the different approaches in the decomposition of the purchasing process, (Johnson and Chia-Yen, 2012) we selected a solution that could be suitable for small and medium sized manufacturing companies.

Many authors have presented a similar model of the purchasing process. In this paper the purchasing process is decomposed by using Structural system analysis (SSA) which is one of the process approach methods. The purchasing process is decomposed to the levels that are necessary for effective management of quality and process.

In this paper the 7 most common purchasing sub-processes in the manufacturing companies are selected based on the author’s research and experience at the Center for Quality, Faculty of Engineering in Kragujevac (Fig.1.):

Definition of purchasing requirements,

Purchasing planning,

Suppliers’ evaluation,

Contracting,

The purchasing goods verification,

Reclamation to supplier and

Contract implementation monitoring.

The target and current value of defined KPI are presented in Table 1.

Table 1 Objectives, KPIs of identified objectives of purchasing process, target and measured KPI values

Objectives of specific sub -processes

KPI DescriptionTarget Measure

d dataThe normalized value

Filling of purchasing requirements

(i=1)

Accuracy (j=1)

Denied requests’ percentage based on accuracy

0% 45%

Time (j=2)

Average time required to provide purchasing decisions, calculated from the date of receipt of the request requirements

5 days 20 days

Level of purchasing planning (i=2)

Percentage of purchasing plan realization (j=3)

Total purchasing contracts’ value in purchasing plan/Purchasing planning value

100% 80%

Percentage of realization (j=4)

Contract realization value/Value of contract realization

100% 75%

Completeness (j=5)

Purchasing percentage value that requires a change in the approved purchasing plan

< 5% 6%

Inventories level (j=6)

Inventories value purchased in the reporting period/Inventories value purchased in the previous reporting period (x100)

≤ 85% 110%

Level of suppliers evaluation (i=3)

Deadline (j=1)

Delayed deliveries percentage(0-1)% 4%

Quality verification (j=2)

Deliveries’ percentage with the inconsistencies established for the qualitative acceptance

1% 0%

Supplier approval status (j=3)

Consequences of nonconformities 3% (0-1)%

Level of contracting effect (i=4)

Time (j=1)

Average time required for the contract provision, calculated from the date of providing purchasing decision

<3 days 13 days

Completeness (j=2)

Percentage of changed tender documents after the announcement

0% 2%

Procedure correctness (j=3)

Percentage of accepted complaints of potential suppliers

0% 1%

Partnership (j=4)

Comparison of real prices and catalogue prices

100% 97%

Level of verification of the purchasing goods (i=5)

Success (j=1)Inconsistencies percentage of detected external control

0% 1%

Level of reclamation to supplier (i=6)

Success (j=1)

Successful reclamation percentage of the total complaints number after the identified nonconformities in exploitation

100% 90%

Level of contract implementation monitoring (i=7)

Success (j=1)Contracts percentage realized on time

100% 75%

The relative importance of the purchasing sub-process is given by pair-wise comparison matrix:

By applying procedure which is proposed in (Chang, 1996), the weights vector of purchasing sub-processes is calculated. It can be assumed that the objective weights are equal of the purchasing sub-processes weights and they are:

The relative importance of KPIs under each identified objective is given by pair-wise comparison matrix. The weights of KPIs are calculated by fuzzy extended analysis (Chang, 1996).

The relative importance of KPIs of filling of purchasing requirements (i=1):

The relative importance of KPIs of level of purchasing planning (i=2):

The relative importance of KPIs of level of suppliers evaluation (i=3):

The relative importance of KPIs of level of contracting effect (i=4):

The relative importance of KPI for the rest objectives are: .

The weighted values of KPIs of level of contracting effect (i=4) is presented in Fig. 1.

Fig. 1 The weighted KPIs values of level of contracting effect

The weighted value of level of contracting effect (i=4) is presented in Fig. 2

Fig. 2 The weighted value of of level of contracting effect

The weighted values of each identified objective of purchasing process are calculated by applying Algorithm (from Step 1 to Step 6).

By using Algorithm (Step 7 to Step 8) the weighted values of purchasing process objectives, the gap values for each objective and effeteness of quality strategy are calculated and presented in Table 2.

Table 2 The weighted objective values, gap values and quality strategy effectiveness

for the first period

The quality effectiveness

i=1 0.3361 0.6 0.5602 medium importance

i=2 0.4206 0.8 0.5257 medium importance

i=3 0.4264 0.9 0.4737 medium importance

i=4 0.4935 0.8 0.6169 medium importance

i=5 0.7 0.8 0.875 very important

i=6 0.9281 1 0.9281 highly important

i=7 0.5744 0.8 0.7180 medium importance

By using IF-THAN rules of fuzzy logic, we can determine quality effectiveness for each identified objective of purchasing process.

,

For specific illustrative example it is possible to conclude that sub-process i=4 (Level of contracting effect) is the most influential on quality of purchasing process. In the other words using the presented algorithm it is possible to conclude to which extent specific sub-process could contribute to the quality of process (in this case purchasing process).

The weighted value of purchasing process is given by using express (Step 9 of the proposed Algorithm), so that . Let us the target value of considered process is 0.72. The value gap for purchasing process is given by Algorithm (Step 9):

IF the value gap , THAN process quality effectiveness is described by linguistic expression

According to given results it could be concluded that process quality effectiveness of purchasing process can be described as very high (for this specific illustrative example).

6. CONCLUSION

Improvement of key business processes is one of requests of standard ISO 9001:2008 has a critical effect on the competitive advantage of any organization. Key business processes, their objectives, key performance outcomes and key performance indicator present very important success factors. It is important to have in mind that KPIs should be measured in order to provide platform for analysis of specific objectives, benchmarking and improvement. In this paper the approach for modelling of the relative importance of purchasing key performance indicators and their values, modelling of influence of specific objective on purchasing process quality as well as evaluation of quality of process as whole is presented.

In this paper, it was assumed that: (a) the relative importance of key performance indicator of each objective are determined and described by linguistic expressions; the fuzzy extent approach for the synthetic extent values of the pairwise comparison for handling fuzzy Analytic Hierarchical Process (AHP) is used to calculate the weight vector of key performance outcomes under each objective, (b) the values of key performance objectives are evaluated by Business Process Management which uses linguistic expressions. The all linguistic expressions are modelled by triangular fuzzy numbers. The proposed fuzzy model is arranged in two interference system. In the first of interference steps, the value gap of treated key business process is calculated using the proposed fuzzy model. In the second interference step, the process quality effectiveness is determined on the basis of the value of gap, using the fuzzy logic IF-THEN rules. It is shown that the proposed fuzzy model is highly suitable as a decision making tool for making decisions about the process quality effectiveness of key business processes in any organizations.

Contributions of this paper are also the following: (1) it handles uncertainty in relative importance and values of measures of objectives using fuzzy sets, and (2) it proposes fuzzy model for evaluation of process quality based on fuzzy logic rules.

The proposed algorithm is tested using real-life data from service organization from central Serbia. This procedure should be useful for the systematic application of process quality evaluation for all identified key business processes in enterprise. All the changes, as those in the number of objectives, number of KPIs or their relative importance and fuzzy number membership functions shape can be easily incorporated into the model. The proposed fuzzy method for determining the process quality is the first step in improving of key processes.

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