IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 409 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 SOLAR PV POWER PLANT LOCATION SELECTION USING A Z- FUZZY NUMBER BASED AHP İrem Otay Istanbul Okan University, Faculty of Engineering Industrial Engineering Department, 34959 Akfirat-Tuzla Istanbul, Turkey irem.otay@okan.edu.tr Cengiz Kahraman Istanbul Technical University, Faculty of Management Industrial Engineering Department, 34367 Maçka Istanbul, Turkey kahramanc@itu.edu.tr ABSTRACT One of the most used renewable energy systems to produce clean and sustainable energy are solar energy photovoltaic (PV) plants. The selection among solar energy PV plant location alternatives requires a multi-criteria decision making approach with several conflicting and linguistic criteria. The assessment process is generally done in a vague and imprecise environment. Fuzzy set theory is often very beneficial for evaluating the subjective judgments of decision makers. The Analytic Hierarchy Process is the most used multi-criteria decision making method in the world because of its simplicity and efficiency. In this paper, we select a location for a solar energy PV plant using a 4-level hierarchy. We consider several criteria and sub-criteria including initial cost, maintenance cost, slope and distance to highways. A Z-fuzzy number is a relatively new concept in fuzzy set theory that enables one to circumvent the limitations of ordinary fuzzy numbers. Z-fuzzy numbers can be viewed as a combination of crisp numbers, intervals, fuzzy numbers and random numbers because of their generality. They give a better representation than ordinary fuzzy numbers. This study solves the multi-criteria solar PV power plant location selection problem with a Z-fuzzy based AHP method. To check the applicability of the method proposed here, a real-life case study from Turkey is presented and solved. Keywords: Solar PV power plant; location selection; fuzzy AHP; Z-fuzzy number; multi- criteria; uncertainty 1. Introduction The location selection for a solar photovoltaic (PV) power plant is a common problem in a sustainable and renewable energy supply chain. A PV power plant is a PV system composed of a lot of PV cells that convert energy from light directly to electricity. The main steps in a solar PV project are as follows: i. Concept development and plant site mailto:irem.otay@okan.edu.tr mailto:kahramanc@itu.edu.tr https://www.sciencedirect.com/science/article/pii/S1364032117312844 http://www.wiki-zero.co/index.php?q=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvUGhvdG92b2x0YWljX3N5c3RlbQ IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 410 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 identification, ii. Pre-feasibility study, iii. Feasibility study, iv. Legal and financial issues and contracts. v. Engineering, construction and commercial operations. The location of a photovoltaic (PV) power plant is a critical issue because of its direct impact on the performance, economic, environmental and social aspects of the plant. In the literature, there are many valuable studies about the problem of power plant location. For instance, Khan and Rathi (2014) focused on the problem of site selection for a solar PV power plant in India that employed a Geographical Information System (GIS) to solve the problem. Samanlioglu and Ayağ (2017) used an integrated fuzzy approach by integrating the Analytic Hierarchy Process (AHP) and PROMETHEE II to locate a power plant in Turkey. Garni and Awasthi (2018) conducted a literature review of 50 papers on selecting locations for solar PV power plants. The results show that the Analytical Hierarchy Process and its extensions are the most commonly used methodology, followed by overlay tool analysis in a GIS environment. Ozdemir and Sahin (2018) studied the location selection for a solar PV power plant location using a Photovoltaic Geographical Information System (PVGIS) and AHP. As mentioned above, the first step in a solar PV project is identifying the site for a plant. This requires several criteria and alternatives to be considered under uncertainty. The uncertainty arises in assessing the alternatives with respect to the various criteria because linguistic assessments are preferred by decision makers (DM) to exact numerical evaluations. Linguistic assessments can best be treated by fuzzy set theory according to the literature. Each linguistic assessment is represented by a fuzzy number having a membership function that may be linear or nonlinear. Fuzzy set theory has been extended to several types since the original fuzzy set theory that emerged in 1965. Figure 1 summarizes the progress of fuzzy set theory from 1965 to today. The main aim of all the extensions is to provide a new point of view when defining the membership function. Membership functions of ordinary fuzzy sets are defined by a membership degree and a non-membership degree whose sum is exactly equal to 1. Membership functions of type-2 fuzzy sets are represented by three dimensional graphs with an upper function and a lower function. Membership functions of intuitionistic fuzzy sets are represented by a membership degree and a non-membership degree whose sum is at most equal to 1. If the sum is less than 1, the difference is called the hesitancy of the DM. Membership functions of Pythagorean fuzzy sets offer a larger domain to the DM since their squared sum is at most equal to 1. Membership functions of neutrosophic fuzzy sets are composed of truthiness, indeterminacy and falsity degrees whose sum might be between 0 and 3. Hesitant fuzzy sets are different from other fuzzy sets since they offer techniques for treating more than one possible membership degree for a certain X value. https://content.iospress.com/search?q=author%3A%28%22Aya%C4%9F,%20Zeki%22%29 IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 411 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Figure 1 Extensions of fuzzy sets Within the framework of ordinary fuzzy sets, Zadeh (2011) proposed the Z-fuzzy number which is an ordered pair of fuzzy numbers (A, B). The first component A represents the fuzzy restriction while the second component B is the reliability of the first component. Researchers claim Z-numbers perform better when describing human judgments and dealing with uncertainty than traditional fuzzy numbers since they can handle restraint and reliability functions (Deng & Chan, 2011). In this paper, we convert the linguistic assessments to Z-fuzzy numbers and evaluate the PV power plant location alternatives based on the AHP. To the best of our knowledge, this is the first study employing a Z- fuzzy number-based AHP method for solving the solar PV power plant location problem. The rest of the paper is organized as follows: Section 2 gives a literature review of fuzzy AHP; Section 3 explains Z-fuzzy numbers, including their arithmetic operations; Section 4 gives the proposed method Z-fuzzy AHP step-by-step; Section 5 is an application of the proposed method to a PV plant location problem; Section 6 presents the conclusions and directions for further research. 2. Fuzzy AHP in the literature Fuzzy extensions of AHP have been obtained by using fuzzy numbers. Recently, ordinary fuzzy numbers have been extended to several different types of fuzzy numbers such as intuitionistic fuzzy numbers, Pythagorean fuzzy numbers and type-2 fuzzy numbers. These extensions have allowed new fuzzy AHP extensions to be developed in the literature that are briefly summarized as follows. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 412 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 2.1 Ordinary Fuzzy AHP Ordinary fuzzy AHP methods have been proposed by various authors. The first one was introduced by Van Laarhoven and Pedrycz (1983). They used triangular fuzzy numbers and Lootsma’s logarithmic least squares method for deriving fuzzy weights and fuzzy performance scores of alternatives. Buckley (1985) used trapezoidal fuzzy numbers and derived fuzzy weights and fuzzy performance scores by using a geometric mean method. Boender et al. (1989) modified Van Laarhoven and Pedrycz’s (1983) method and proposed a more robust approach to the normalization of the local priorities. Chang (1996) proposed an extent analysis method for deriving priorities from comparison matrices whose elements are defined as triangular fuzzy numbers. The drawback of this method is that it is possible to obtain the value of zero for initial weights or local priorities for some elements of the decision structure (Wang et al., 2008). Such a computed zero local priority may cause some of the information to not be considered in the calculations (Li et al., 2008). Cheng (1997) proposed a fuzzy AHP method based on both probability and possibility measures in which performance scores are represented by membership functions and the aggregate weights are calculated by using entropy concepts. Mikhailov (2003) proposed a fuzzy extension of AHP which obtains crisp priorities based on an α-cut of fuzzy numbers by using a technique called fuzzy preference programming (FPP). The main drawback of this approach is that each comparison matrix must be constructed as an individual FPP model which increases the complexity of the solution (Yu & Cheng, 2007). 2.2 Type-2 fuzzy AHP The concept of a type-2 fuzzy set was introduced by Zadeh (1975) as an extension to an ordinary fuzzy set called a type-1 fuzzy set. Kahraman et al. (2014) developed an interval type-2 (IT2) fuzzy AHP method together with a new ranking method for type-2 fuzzy sets and then applied the method to supplier selection. Kilic and Kaya (2015) proposed a new evaluation model for investment projects for development agencies operating in Turkey to address the ambiguities and relativities in real world scenarios by using type-2 fuzzy sets and crisp sets simultaneously. Abdullah and Najib (2014a) proposed a new fuzzy AHP characterized by IT2 FS for linguistic variables. It was different from the typical FAHP which directly utilized trapezoidal type-1 fuzzy numbers. This method introduced IT2 FS to enhance judgments in the fuzzy decision-making environment. This new model included linguistic variables in IT2 FS and a rank-value method for normalizing upper and lower memberships of IT2 FS. 2.3 Intuitionistic fuzzy AHP Atanassov (1986)’s intuitionistic fuzzy sets (IFSs) include the membership value as well as the non-membership value for describing any x in X such that the sum of membership and non-membership is at most equal to 1. Sadiq and Tesfamariam (2009) applied the concept of IFS to AHP which is called IF-AHP to handle both vagueness and ambiguity related uncertainties in the environmental decision making process. Abdullah et al. (2009) applied IFS to the AHP method called IF-AHP to quantify vagueness uncertainties in AHP using IFS for the decision-making problem. The authors constructed several linear programming models to generate optimal weights for attributes. Wang et al. (2011) proposed an IF-AHP method in which the decision information was represented by intuitionistic fuzzy values. The method synthesizes the eigenvectors of the intuitionistic fuzzy comparison matrix in which all the decision information is intuitionistic fuzzy. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 413 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Zhang et al. (2011) discussed the approximation of IFS to fuzzy sets based on the relationships between IFS and fuzzy sets. They also showed that the intuitionistic fuzzy complementary judgement matrix approximates the fuzzy complementary judgement matrix and proved that the consistency adjustments of both are equal. Based on these results, the authors proposed an AHP method based on an intuitionistic judgment matrix. Feng et al. (2012) proposed a Dempster Shafer – AHP (DS-AHP) method combined with intuitionistic fuzzy information. The expected utility was used to transform a decision matrix having intuitionistic fuzzy information obtained from the assessments and then a non-linear optimization model was used to combine the attributes. Wu et al. (2013) proposed an interval valued intuitionistic fuzzy AHP (IVIF-AHP) method for MCDM problems developing a score function for interval valued intuitionistic fuzzy numbers (IVIFNs) and introducing some new concepts such as antisymmetric interval matrix, the transfer interval matrix and the approximate optimal transfer matrix. Kaur (2014) proposed a triangular intuitionistic fuzzy number based (TIFN) approach for the vendor selection problem using AHP. Xu and Liao (2014) proposed a new way to check the consistency of the intuitionistic preference relation and then introduced an automatic procedure to repair the most inconsistent one. Abdullah and Najib (2014a) proposed a new preference scale in the framework of the interval-valued intuitionistic fuzzy AHP (IVIF-AHP). The comparison matrix judgment was expressed in IVIFNs with degree of hesitation. Abdullah and Najib (2014b) proposed a new method of intuitionistic fuzzy AHP (IF-AHP) to deal with uncertainty in decision-making. The new IF-AHP was applied to establish a preference in the sustainable energy planning decision-making problem. Dutta and Guha (2015) proposed a preference programming based weight determination method of IF-AHP in which decision makers expressed their pair-wise comparisons by using generalized triangular intuitionistic fuzzy numbers. Keshavarzfard and Makui (2015) presented an intuitionistic fuzzy Multiple Attribute Decision Making (MADM) approach for modelling and solving AHP problems with a small amount of relationships among various criteria. IF-AHP was used to evaluate the weighting for each criterion and then intuitionistic fuzzy DEMATEL method was applied to establish contextual relationships among the criteria. Onar et al. (2015) proposed an interval valued intuitionistic fuzzy AHP (IVIF-AHP) approach to measure the overall performance of wind energy alternatives. 2.4 Hesitant fuzzy AHP Hesitant fuzzy sets (HFS) are useful for dealing with situations where decision makers are hesitant to provide their preferences about objects, preferring to offer a margin of error. HFSs permit the membership degree of an element to be a set which is represented as several possible values between 0 and 1. Tuysuz and Simsek (2017) developed a hesitant fuzzy linguistic term sets based AHP approach and applied it to the performance comparison of cargo firms. Kahraman et al. (2017) developed a hesitant fuzzy linguistic AHP and applied it to Business-to-Customer marketplace prioritization. Oztaysi et al. (2015) developed a hesitant fuzzy AHP method involving multi-expert’s linguistic evaluations aggregated by ordered weighted averaging (OWA) operator. 2.5 Pythagorean fuzzy AHP Yager (2013) introduced a Pythagorean fuzzy set (PFS) characterized by a membership degree and a non-membership degree satisfying the condition that the square sum of its membership degree and non-membership degree is equal to or less than 1 which is a http://0-www.scopus.com.divit.library.itu.edu.tr/authid/detail.url?authorId=55580964700&eid=2-s2.0-84893082409 IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 414 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 generalization of IFS. Ilbahar et al. (2018) developed a novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP and fuzzy inference system. 2.6 Neutrosophic AHP The neutrosophic sets developed by Smarandache (1998) extend the concept of Intuitionistic Fuzzy Sets (IFSs) that were introduced by Atanassov (1983) for a new point of view to uncertainty, impreciseness, inconsistency and vagueness. Smarandache (1998) introduced the degree of indeterminacy/neutrality as a new and independent component of fuzzy sets and defined a neutrosophic set composed of three components: truth membership, indeterminacy membership, and falsity membership. Radwan et al. (2016) developed a novel hybrid neutrosophic AHP approach in learning management systems in decision making to handle indeterminacy of information. Abdel-Basset et al. (2017) integrated AHP into a Delphi framework under a neutrosophic environment and introduced a new technique for checking consistency and calculating the consensus degree of an expert’s opinions. 3. Preliminaries: Z-fuzzy numbers Zadeh (1975) defined a Z-number associated with an uncertain variable Z as an ordered pair of fuzzy numbers (A, B) where A is a fuzzy subset of the domain X of the variable Z and B is a fuzzy subset of the unit interval. The concept of a Z-number is intended to provide a basis for computation with numbers which are not totally reliable. A Z-number can be used to represent information about an uncertain variable of the type where A represents a value of the variable and B represents an idea of certainty or probability. There are a limited number of studies on Z-fuzzy numbers. Biswas (2012) observed the drawback of the existing fuzzy numbers, studied Z-fuzzy numbers and presented fundamental arithmetic operations for Z-fuzzy numbers. Abu Bakar and Gegov (2014) conducted a study ranking Z-numbers by proposing a multi–layer decision making methodology. Biswas (2016) discussed whether or not the fuzzy set theory was appropriate for large size problems with a number of universes and a lot of elements in these universes. In the study, the researcher also focused on Z-fuzzy numbers and their mathematical operations. Definition 1. A Z-number is an ordered pair of fuzzy numbers denoted as Z = (Ã, R̃). The first component Ã, a restriction on the values, is a real-valued uncertain variable 𝑋. The second component �̃� is a measure of reliability for the first component, described in Figure 2. When 𝑎2𝑒𝑞𝑢𝑎𝑙𝑠𝑎3, a trapezoidal fuzzy number becomes a triangular fuzzy number. http://www.sciencedirect.com/science/article/pii/S0925753517312316 http://www.sciencedirect.com/science/article/pii/S0925753517312316 http://www.sciencedirect.com/science/article/pii/S0925753517312316 IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 415 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Figure 2 A simple Z-fuzzy number Definition 2. Let a fuzzy set A be defined on a universe X be given as: A = {〈x, μA(x)〉 |xϵX} where μA: X → [0,1] is the membership function A. The membership value μA(x) describes the degree of belonging of x ∈ X in 𝐴. The Fuzzy Expectation of a fuzzy set is denoted as: 𝐸𝐴(𝑥) = ∫ 𝑥𝜇𝐴(𝑥) 𝑑𝑥𝑥 (1) which is not the same as the meaning of the Expectation of Probability Space. It can be considered to be the information strength supporting the fuzzy set 𝐴. Definition 3: Converting a Z-number to a regular fuzzy number Consider a Z-number 𝑍 = (𝐴,̃ �̃�) described by Figure 2. The left is the part of restriction, and the right is the part of reliability. Let �̃� = {〈𝑥, 𝜇�̃�(𝑥)〉|𝜇(𝑥) ∈ [0,1]} and �̃� = {〈𝑥, 𝜇�̃�(𝑥)〉|𝜇(𝑥) ∈ [0,1]}, 𝜇�̃�(𝑥) is a trapezoidal membership function, and 𝜇�̃�(𝑥) is a triangular membership function. 1. Convert the second part (reliability) into a crisp number using Equation 2. 𝛼 = ∫ 𝑥𝜇�̃�(𝑥) 𝑑𝑥 ∫ 𝜇�̃�(𝑥) 𝑑𝑥 (2) where ∫ denotes an algebraic integration. Alternatively, Equation 3 can be used for this defuzzification: 𝛼 = 𝑎1+2∗(𝑎2+𝑎3)+𝑎4 6 (3) 2. Add the weight of the second part (reliability) to the first part (restriction). The weighted Z-number can be denoted as �̃�𝛼 = {〈𝑥, 𝜇�̃�𝛼(𝑥)〉|𝜇�̃�𝛼(𝑥) = 𝛼𝜇�̃�(𝑥), 𝜇(𝑥) ∈ [0,1]} 𝑎4 𝑎3 𝑎2 𝑎1 �̃� 𝑍 = �̃�, �̃� 1 0 𝜇�̃�(𝑥) 𝑥 𝑏3 𝑏2 𝑏1 �̃� 1 0 𝜇�̃�(𝑥) 𝑥 IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 416 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 3. Convert the irregular fuzzy number (weighted restriction) to a regular fuzzy number. The ordinary fuzzy set can be denoted as �̃�′ = {〈𝑥, 𝜇�̃�′(𝑥)〉|𝜇�̃�′(𝑥) = 𝜇�̃� ( 𝑥 √𝛼 ) , 𝜇(𝑥) ∈ [0,1]}. �̃�′ has the same Fuzzy Expectation with �̃�𝛼, and they are equal with respect to Fuzzy Expectation, which can be denoted by Figure 3. Figure 3 Ordinary fuzzy number transformed from Z-number 4. If the restriction function and reliability function are defined as in Figure 4 (their heights may be any value between 0 and 1), the calculations are modified as follows: Let �̃�𝛿 = {〈𝑥, (𝜇�̃�(𝑥); 𝛿)〉|𝜇(𝑥) ∈ [0,1]} and �̃�𝛽 = {〈𝑥, (𝜇�̃�(𝑥); 𝛽)〉|𝜇(𝑥) ∈ [0,1]}; 𝝁 �̃� 𝜹(𝒙) is a trapezoidal membership function and 𝝁 �̃� 𝜷 (𝒙) is a triangular membership function. When 𝑎2 = 𝑎3, a trapezoidal membership function becomes a triangular membership function. Figure 4 A simple Z̃δ,β number, �̃�𝛿,𝛽 = �̃�𝛿, �̃�𝛽 In this case, restriction and reliability functions are defined as in Equations 4-5, respectively. The reliability membership function in Equation 4 is substituted into the defuzzification formula (Equation 2 or Equation 3) so that Equation 6 is obtained. 𝑎4 𝑎3 𝑎2 𝑎1 �̃�𝛿 δ 0 𝜇�̃�(𝑥) 𝑥 √𝛼𝑎4 √𝛼𝑎3 √𝛼𝑎2 √𝛼𝑎1 �̃�′ 1 0 𝜇(𝑥) 𝑥 𝑏3 𝑏2 𝑏1 �̃�𝛽 β 0 𝜇�̃�(𝑥) 𝑥 IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 417 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 𝜇�̃� 𝛿(𝑥) = { 𝑥−𝑎1 𝑎2−𝑎1 𝛿 , 𝑖𝑓𝑎1 ≤ 𝑥 ≤ 𝑎2 𝛿, 𝑖𝑓𝑎2 ≤ 𝑥 ≤ 𝑎3 𝑎4−𝑥 𝑎4−𝑎3 𝛿, 𝑖𝑓𝑎3 ≤ 𝑥 ≤ 𝑎4 0, 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (4) 𝜇 �̃� 𝛽 (𝑥) = { 𝑥−𝑏1 𝑏2−𝑏1 𝛽 , 𝑖𝑓𝑏1 ≤ 𝑥 ≤ 𝑏2 𝑏3−𝑥 𝑏3−𝑏2 𝛽 , 𝑖𝑓𝑏2 ≤ 𝑥 ≤ 𝑏3 0, 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (5) Thus, we have √𝛼 = √ ∫ 𝑥𝝁 �̃� 𝜷 (𝒙) 𝑑𝑥 ∫ 𝝁 �̃� 𝜷 (𝒙) 𝑑𝑥 (6) Then, the weighted �̃�𝛿,𝛽 number can be denoted as in Equation 6. �̃�𝛿,𝛽 𝛼 = {〈𝑥, 𝝁�̃�𝜶 𝜹 (𝒙)〉|𝝁 �̃�𝜶 𝜹 (𝒙) = ∫𝑥𝝁 �̃� 𝜷 (𝒙)𝑑𝑥 ∫ 𝝁 �̃� 𝜷 (𝒙)𝑑𝑥 𝝁 �̃� 𝜹(𝒙), 𝜇(𝑥) ∈ [0,1]} (7) The ordinary fuzzy number converted from Z-fuzzy number can be given as in Equation 8. �̃�𝛿,𝛽 ′ = {〈𝑥, 𝝁�̃�′ 𝜹 (𝒙)〉|𝝁�̃�′ 𝜹 (𝒙) = 𝝁 �̃� 𝜹 (𝒙 ∫ 𝝁 �̃� 𝜷 (𝒙) 𝑑𝑥 ∫ 𝑥𝝁 �̃� 𝜷 (𝒙) 𝑑𝑥 ) , 𝜇(𝑥) ∈ [0,1]} (8) 4. Z- fuzzy number based AHP In this method we integrate z-fuzzy numbers with AHP. The advantage of this integration is to incorporate vagueness in the evaluations and reliabilities to these evaluations into the AHP. The steps of the proposed Z-fuzzy number based-AHP are presented in the following: Step 1. Define the multi-criteria decision making problem and design a hierarchical structure of the problem. Step 2. Use the scale of linguistic restriction function given in Table 1 and the scale of reliability function presented in Table 2. These are the scales that have been proposed by the authors. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 418 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Table 1 Triangular Z-fuzzy restriction scale Linguistic Terms Restriction function Equally Better (E) (1,1,1;1) Slightly Better (SLB) (1,1,3;1) Moderately Better (MB) (1,3,5;1) Strongly Better (STB) (3,5,7;1) Very Strongly Better (VSTB) (5,7,9;1) Certainly Better (CB) (7,9,10;1) Absolutely Better (AB) (9,10,10;1) Table 2 Reliability scale with its corresponding triangular Z-fuzzy numbers Linguistic Reliability Triangular Z-fuzzy reliability function Absolutely Reliable (AR) (0.8,0.9,1;1) Strongly Reliable (SR) (0.7,0.8,0.9;1) Very Highly Reliable (VHR) (0.6,0.7,0.8;1) Highly Reliable (HR) (0.5,0.6,0.7;1) Fairly Reliable (FR) (0.4,0.5,0.6;1) Weakly Reliable (WR) (0.3,0.4,0.5;1) Very Weakly Reliable (VWR) (0.2,0.3,0.4;1) Strongly Unreliable (SU) (0.1,0.2,0.3;1) Absolutely Unreliable (AU) (0,0.1,0.2;1) Decision makers may assign different values for the given linguistic terms and correspondingly different fuzzy restriction functions in Table 1 if s/he wants to assign intermediate values. Step 3. Construct the pairwise comparison matrices and fill them in with their corresponding Z-fuzzy numbers using the linguistic scales in Tables 1 and 2. Step 4. Transform Z-fuzzy numbers to their corresponding equivalent ordinary fuzzy numbers. Step 5. Check the consistency of each fuzzy pairwise comparison matrix. Assume  ijaA ~ ~  is a fuzzy positive pairwise comparison matrix and  ijaA  is its defuzzified positive pairwise comparison matrix. If the result of the comparisons of  ijaA  is consistent; then, it can imply that the result of the comparisons of  ijaA ~ ~  is also consistent. In the IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 419 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 consistency measurement, reliability functions are ignored since they cause a consistent pairwise comparison matrix to become an inconsistent one when they are converted to regular fuzzy numbers. Step 6. Apply Buckley’s ordinary fuzzy AHP method (Buckley, 1985). The steps of this method are summarized as follows: Step 6.1. Calculate the geometric mean for each parameter of ija ~ in the n dimensional pairwise comparison matrix of criteria. Thus, 𝑛 × 𝑛 matrix is converted to an 𝑛 × 1 matrix. This is the step that converts Z-fuzzy numbers to regular fuzzy numbers. Step 6.2. Sum the values of each parameter in the column then normalize the values in the 𝑛 × 1 matrix. Step 6.3. Apply the fuzzy division operation to get the normalized weights vector. Step 6.4. Defuzzify the normalized weights vector using the center of gravity method given by Equation 2. Step 6.5. Normalize the weights so their sum is equal to 1. Step 6.6. Apply Steps (6.1-6.5) for the rest of the pairwise comparison matrices of sub-criteria and alternatives. Step 6.7. Combine all the weight vectors, to obtain the global weights and determine the best alternative as in the classical AHP. 5. Application In this section, a real life problem of a newly founded facility is solved using the proposed Z-AHP method. A brief problem definition is presented, followed by the results of the proposed method as illustrated with a figure and tables. 5.1 Problem definition In 2015, the Renewable Energy General Directorate reported by the Solar Energy Map (SEM) of Turkey highlighted that “the total annual insolation time is 2.737 hours, and the total solar energy derived per year is 1.527 kwh/m2 per year” (https://www.rvo.nl/sites/default/files/2015/10/Renewable%20Energy %20Turkey.pdf). The research has shown that capacity additions for renewable energy sources in Turkey have increased remarkably especially in recent years. The report of Shura (2018) noted that in 2017 there was a net renewable energy capacity of 3.2 GW versus 1.5 GW for non-renewables. The report also said that the PV capacity of 1.79 GW added in 2017 was more than three times what was added in 2016 (Shura, 2018). According to the Republic of Turkey Ministry of Energy and Natural Resources, by the end of June 2018 the total PV solar power plant installed capacity will be 4,723 MW comprised of a total of 4,703 MW unlicensed and 23 MW licensed plants (http://www.enerji.gov.tr/en-US/Pages/Solar). Thus, Turkey will have one of the largest solar PV markets in Europe (Shura, 2018). This study aims to solve the location selection problem of a private company for one of its newly installed PV energy production facilities in the southwest part of Turkey. Based IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 420 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 on the meetings held with investors and managers, the possible alternative locations are marked in Figure 5 (http://www.pv-financing.eu/wp-content/uploads/2017/06/PV- Financing-webinar-IT-ES-TR-business-models-slides-170517.pdf), are Antalya, İçel and Muğla. Figure 5 Solar map of Turkey showing the alternative locations for the facility (http://www.pv-financing.eu/wp-content/uploads/2017/06/PV-Financing- webinar-IT-ES-TR-business-models-slides-170517.pdf) After a detailed literature review and a meeting with the management, a 4-level hierarchy was designed that is illustrated in Figure 6. As seen from the figure, there are seven main criteria: geological & topographic factors, political & legal factors, technical factors, economical factors, environmental factors, location-related factors, and social factors with a total of 18 sub-criteria such as slope, legislation and social support. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 421 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Figure 6 Hierarchical structure of the problem Once the hierarchical structure of the problem was ready, linguistic judgments were obtained from the decision makers, who are three experts from the Energy Institute of Istanbul Technical University. Table 3 presents the pairwise comparison matrix of the criteria based on the linguistic restriction and reliability values on which the decision makers arrived at consensus, while Table 4 illustrates the pairwise comparison matrix of the criteria with corresponding values from Tables 1 and 2. Table 3 Pairwise comparison matrix of the criteria Criteria C1 C2 C3 C4 C5 C6 C7 C1 E, E SLB, VHR 1/CB, HR 1/VSTB, FR 1/MB, SR 1/STB, VHR MB, SR C2 1/SLB, VHR E, E 1/AB, SR 1/CB, AR 1/MB, SR 1/STB, FR SLB, HR C3 CB, HR AB, SR E, E 1/SLB, VHR STB, SR SLB, SR CB, SR C4 VSTB, FR CB, AR SLB, VHR E, E VSTB, SR MB, VHR AB, AR C5 MB, SR MB, SR 1/STB, SR 1/VSTB, SR E, E 1/MB, SR STB, VHR C6 STB, VHR STB, FR 1/SLB, SR 1/MB, VHR MB, SR E, E VSTB, AR C7 1/MB, SR 1/SLB, HR 1/CB, SR 1/AB, AR 1/STB, VHR 1/VSTB, AR E, E C3:Technical factors Goal: Selecting the best appropriate location for Solar PV Power Plant C1:Geological & topographic factors C2:Political & legal factors C4:Economical factors C5:Environmental factors C6:Location related factors C7:Social factors C11: Slope C12: Aspect C13: Longitute- latitude C21: Legislation s C22: Political stability C31: Technological development C32: Technological flexibility C41: Initial Cost (Land& material cost ) C42: Construction cost C43: Operation cost C53: Fauna & Flora C51: Land Use C52: Agrological capacity C61: Distance to urban areas C62: Distance to main roads C63: Distance to historical sites C71: Social support C72: Job availability Antalya İçel Muğla IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 422 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Table 4 Pairwise comparison matrix with corresponding triangular Z-fuzzy restriction and reliability scales Criteria C1 C2 C3 C4 C5 C6 C7 C1 ((1,1,1;1), (1,1,1;1)) ((1,1,3;1), (0.6,0.7,0.8;1)) ((0.1,0.11,0.14;1), (0.5,0.6,0.7;1)) ((0.11,0.14,0.2;1), (0.4,0.5,0.6;1)) ((0.2,0.33,1;1), (0.7,0.8,0.9;1)) ((0.14,0.2,0.33;1), (0.6,0.7,0.8;1)) ((1,3,5;1), (0.7,0.8,0.9;1)) C2 ((0.33,1,1;1), (0.6,0.7,0.8;1)) ((1,1,1;1), (1,1,1;1)) ((0.1,0.1,0.11;1), (0.7,0.8,0.9;1)) ((0.1,0.11,0.14;1), (0.8,0.9,1;1)) ((0.2,0.33,1;1), (0.7,0.8,0.9;1)) ((0.14,0.2,0.33;1), (0.4,0.5,0.6;1)) ((1,1,3;1), (0.5,0.6,0.7;1)) C3 ((7,9,10;1), (0.5,0.6,0.7;1)) ((9,10,10;1), (0.7,0.8,0.9;1)) ((1,1,1;1), (1,1,1;1)) ((0.33,1,1;1), (0.6,0.7,0.8;1)) ((3,5,7;1), (0.7,0.8,0.9;1)) ((1,1,3;1), (0.7,0.8,0.9;1)) ((7,9,10;1), (0.7,0.8,0.9;1)) C4 ((5,7,9;1), (0.4,0.5,0.6;1)) ((7,9,10;1), (0.8,0.9,1;1)) ((1,1,3;1), (0.6,0.7,0.8;1)) ((1,1,1;1), (1,1,1;1)) ((5,7,9;1), (0.7,0.8,0.9;1)) ((1,3,5;1), (0.6,0.7,0.8;1)) ((9,10,10;1), (0.8,0.9,1;1)) C5 ((1,3,5;1), (0.7,0.8,0.9;1)) ((1,3,5;1), (0.7,0.8,0.9;1)) ((0.14,0.2,0.33;1), (0.7,0.8,0.9;1)) ((0.11,0.14,0.2;1), (0.7,0.8,0.9;1)) ((1,1,1;1), (1,1,1;1)) ((0.2,0.33,1;1), (0.7,0.8,0.9;1)) ((3,5,7;1), (0.6,0.7,0.8;1)) C6 ((3,5,7;1), (0.6,0.7,0.8;1)) ((3,5,7;1), (0.4,0.5,0.6;1)) ((0.33,1,1;1), (0.7,0.8,0.9;1)) ((0.2,0.33,1;1), (0.6,0.7,0.8;1)) ((1,3,5;1), (0.7,0.8,0.9;1)) ((1,1,1;1), (1,1,1;1)) ((5,7,9;1), (0.8,0.9,1;1)) C7 ((0.2,0.33,1;1), (0.7,0.8,0.9;1)) ((0.33,1,1;1), (0.5,0.6,0.7;1)) ((0.1,0.11,0.14;1), (0.7,0.8,0.9;1)) ((0.1,0.1,0.11;1), (0.8,0.9,1;1)) ((0.14,0.2,0.33;1), (0.6,0.7,0.8;1)) ((0.11,0.14,0.2;1), (0.8,0.9,1;1)) ((1,1,1;1), (1,1,1;1)) When only the restriction functions are considered in the calculation of the consistency ratio for the matrix, we obtained 0.083 which is lower than the desirable 0.1. After the Z- fuzzy numbers have been converted to their corresponding equivalent ordinary fuzzy numbers, Table 4 is transformed into Table 5. Table 5 now represents the pairwise comparison matrix of the criteria using ordinary fuzzy numbers. Table 5 Z-fuzzy numbers converted to ordinary fuzzy numbers C1 C2 C3 C4 C5 C6 C7 C1 (1,1,1;1) (0.84,0.84,2.51;1) (0.08,0.09,0.11;1) (0.08,0.10,0.14;1) (0.18,0.30,0.89;1) (0.12,0.17,0.28;1) (0.89,2.68,4.47;1) C2 (0.28,0.84,0.84;1) (1,1,1;1) (0.09,0.09,0.10;1) (0.09,0.11,0.14;1) (0.18,0.30,0.89;1) (0.10,0.14,0.24;1) (0.77,0.77,2.32;1) C3 (5.42,6.97,7.75;1) (8.05,8.94,8.94;1) (1,1,1;1) (0.28,0.84,0.84;1) (2.68,4.47,6.26;1) (0.89,0.89,2.68;1) (6.26,8.05,8.94;1) C4 (3.54,4.95,6.36;1) (6.64,8.54,9.49;1) (0.84,0.84,2.51;1) (1,1,1;1) (4.47,6.26,8.05;1) (0.84,2.51,4.18;1) (8.54,9.49,9.49;1) C5 (0.89,2.68,4.47;1) (0.89,2.68,4.47;1) (0.13,0.18,0.30;1) (0.10,0.13,0.18;1) (1,1,1;1) (0.18,0.30,0.89;1) (2.51,4.18,5.86;1) C6 (2.51,4.18,5.86;1) (2.12,3.54,4.95;1) (0.30,0.89,0.89;1) (0.17,0.28,0.84;1) (0.89,2.68,4.47;1) (1,1,1;1) (4.74,6.64,8.54;1) C7 (0.18,0.30,0.89;1) (0.26,0.77,0.77;1) (0.09,0.10,0.13;1) (0.09,0.09,0.11;1) (0.12,0.17,0.28;1) (0.11,0.14,0.19;1) (1,1,1;1) After that, Buckley’s ordinary fuzzy AHP method is applied to find the weights of the criteria. By following the steps of the methodology in Section 4, the fuzzy weights of the criteria are calculated. The values are defuzzified using the center of gravity method and the defuzzified values are normalized. In this study, because of the space constraints, only the calculations for the main criteria are shown. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 423 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Table 6 Weights of main criteria Criteria Fuzzy weights Normalized fuzzy weights Defuzified weights Normalized crisp weights C1 (0.27, 0.37, 0.64) (0.02, 0.04, 0.09) 0.05 0.04 C2 (0.23, 0.31, 0.48) (0.02, 0.03, 0.07) 0.04 0.03 C3 (2.10, 2.89, 3.66) (0.15, 0.29, 0.54) 0.32 0.28 C4 (2.51, 3.40, 4.67) (0.18, 0.35, 0.69) 0.39 0.35 C5 (0.46, 0.80, 1.28) (0.03, 0.08, 0.19) 0.10 0.09 C6 (1.02, 1.82, 2.61) (0.07, 0.18, 0.39) 0.21 0.18 C7 (0.18, 0.24, 0.34) (0.01, 0.02, 0.05) 0.03 0.02 Table 6 demonstrates the results of the fuzzy, defuzzified and normalized crisp weights of the criteria. According to the results, the most important criterion is C4 Economical factors with a weight of 0.35. It is followed by the criterion C3 Technical factors with a weight of 0.28. The least important criteria are C7 Social factors and C2 Political and legal factors. After repeating the steps of the proposed procedure, the calculations for the pairwise comparison matrices of sub-criteria with respect to each main criterion are obtained and the results are illustrated in Table 7. Table 7 Pairwise comparison matrices of sub-criteria wrt C1 C11 C12 C1 3 weight s C11 E.E E.SR 0.145 C12 E.E 0.142 C13 STB.A R STB.S R E.E 0.713 CR=0.05 wrt C2 C21 C22 weights C21 E. E 0.453 C22 SLB. HR E. E 0.547 CR=0.00 wrt C3 C31 C32 weights C31 E.E E. VHR 0.50 C32 E. E 0.50 CR=.00 wrt C4 C41 C42 C43 weights C41 E. E E. SR 0.321 C42 E. E 0.312 C43 E. VHR SLB. AR E. E 0.367 CR=0.08 wrt C5 C51 C52 C53 weights C51 E. E STB. AR STB. SR 0.713 C52 E. E E. SR 0.145 C53 E. E 0.142 C=0.05 wrt C6 C61 C62 C63 weights C61 E. E E. AR STB. SR 0.458 C62 E. E STB. VHR 0.448 C63 E. E 0.094 CR=0.05 wrt C7 C71 C72 weights C71 E. E MB. SR 0.652 C72 E. E 0.348 CR=0.00 Table 8 contains the linguistic pairwise comparison matrices of the alternatives with respect to the sub-criteria. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 424 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Table 8 Linguistic pairwise comparison matrices of the alternatives wrt C11 A1 A2 A3 weights A1 E AB, AR CB, AR 0.820 A2 E 0.080 A3 SLB, SR E 0.101 CR=0.08 wrt C12 A1 A2 A3 weights A1 E E, SR 0.087 A2 E 0.083 A3 AB, AR AB, VHR E 0.829 CR=0.00 wrt C13 A1 A2 A3 weights A1 E AB, VHR AB, HR 0.828 A2 E E, VHR 0.087 A3 E 0.085 CR=0.00 wrt C21 A1 A2 A3 weights A1 E CB, SR CB, HR 0.807 A2 E E, AR 0.099 A3 E 0.094 CR=0.01 wrt C22 A1 A2 A3 weights A1 E AB, HR VSTB, VHR 0.788 A2 E 0.088 A3 SLB, AR E 0.125 CR=0.08 wrt C31 A1 A2 A3 weights A1 E SLB, FR 0.096 A2 E 0.077 A3 CB, HR AB, VHR E 0.827 CR=0.08 wrt C32 A1 A2 A3 weights A1 E SLB. AR 0.104 A2 E 0.082 A3 CB. VHR AB. SR E 0.814 CR=0.08 wrt C41 A1 A2 A3 weights A1 E SLB. AR 0.099 A2 AB. SR E AB. VHR 0.822 A3 E 0.080 CR=0.08 wrt C42 A1 A2 A3 weights A1 E E. HR 0.085 A2 AB. FR E AB. HR 0.828 A3 E 0.088 CR=0.00 wrt C43 A1 A2 A3 weights A1 E SLB. SR 0.123 A2 VSTB. VHR E CB. VHR 0.784 A3 E 0.093 CR=0.09 wrt C51 A1 A2 A3 weights A1 E AB. AR SLB. SR 0.531 A2 E 0.050 A3 CB. SR E 0.418 CR=0.08 wrt C52 A1 A2 A3 weights A1 E VSTB. HR VSTB. AR 0.788 A2 E 0.103 A3 E. FR E 0.110 CR=0.03 wrt C53 A1 A2 A3 weights A1 E 0.097 A2 CB. HR E CB. HR 0.806 A3 E. SR E 0.097 CR=0.01 wrt C61 A1 A2 A3 weights A1 E AB. SR AB. AR 0.838 A2 E 0.080 A3 E. HR E 0.082 CR=0.00 wrt C62 A1 A2 A3 weights A1 E CB. VHR VSTB. HR 0.796 A2 E 0.089 A3 SLB. FR E 0.115 CR=0.00 wrt C63 A1 A2 A3 weights A1 E 0.094 A2 CB. HR E CB. SR 0.807 A3 E. AR E 0.099 CR=0.01 wrt C71 A1 A2 A3 W A1 E E. SR E. AR 0.331 A2 E 0.331 A3 E. AR E 0.338 CR=0.00 wrt C72 A1 A2 A3 W A1 E AB. HR CB. AR 0.821 A2 E 0.076 A3 SLB. HR E 0.103 CR=0.08 When we combine these weights in Table 9, we obtain the alternative locations rank as follows: İçel > Mugla > Antalya. The best location is İçel with a weight of 0.359. It is followed by Mugla (0.324) and Antalya (0.307), respectively. IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 425 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 Table 9 Combination of the weights Alternatives 𝑤𝐶11=0.145 𝑤𝐶12=0.142 𝑤𝐶13=0.713 Local Weights A1 0.820 0.087 0.828 0.722 A2 0.080 0.083 0.087 0.085 A3 0.101 0.829 0.085 0.193 Alternatives 𝑤𝐶21=0.453 𝑤𝐶22=0.547 Local Weights A1 0.807 0.788 0.797 A2 0.099 0.088 0.093 A3 0.094 0.125 0.111 Alternatives 𝑤𝐶31=0.50 𝑤𝐶32=0.50 Local Weights A1 0.096 0.104 0.100 A2 0.077 0.082 0.080 A3 0.827 0.814 0.821 Alternatives 𝑤𝐶41=0.321 𝑤𝐶42=0.312 𝑤𝐶43=0.367 Local Weights A1 0.099 0.085 0.123 0.103 A2 0.822 0.828 0.784 0.810 A3 0.080 0.088 0.093 0.087 Alternatives 𝑤𝐶51=0.713 𝑤𝐶52=0.145 𝑤𝐶53=0.142 Local Weights A1 0.531 0.788 0.097 0.507 A2 0.050 0.103 0.806 0.165 A3 0.418 0.110 0.097 0.328 Alternatives 𝑤𝐶61=0.458 𝑤𝐶62=0.448 𝑤𝐶63==0.094 Local Weights A1 0.838 0.796 0.094 0.749 A2 0.080 0.089 0.807 0.152 A3 0.082 0.115 0.099 0.098 Alternatives 𝑤𝐶71=0.652 𝑤𝐶72=0.348 Local Weights A1 0.331 0.821 0.502 A2 0.331 0.076 0.242 A3 0.338 0.103 0.256 Alternatives 𝑤𝐶1=0.04 𝑤𝐶2=0.03 𝑤𝐶3=0.28 𝑤𝐶4=0.35 𝑤𝐶5=0.09 𝑤𝐶6=0.18 𝑤𝐶7=0.02 Global Weights A1 0.722 0.797 0.100 0.103 0.507 0.749 0.502 0.307 A2 0.085 0.093 0.080 0.810 0.165 0.152 0.242 0.359 A3 0.193 0.111 0.821 0.087 0.328 0.098 0.256 0.324 In Table 10, we present the comparison of the proposed method with classical AHP. Table10 Comparison with classical AHP Alternatives Method Antalya Icel Mugla z-Fuzzy number based AHP 0.307 0.359 0.324 Classical AHP 0.312 0.362 0.326 The rankings in both methods are the same, and the priorities are close as well. However, Z-fuzzy AHP considers a different uncertainty environment. This may well cause a different ranking in another problem. 6. Conclusions and future research directions Solar PV power plant location selection is a typical multi-criteria decision making problem based on many tangible and intangible criteria that are appropriate for assessing linguistically. Z-fuzzy AHP is a relatively new approach to classical AHP with a fuzzy environment. Z-fuzzy numbers are represented by restriction and reliability membership IJAHP Article: Otay, Kahraman/Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy Process 426 Vol. 10 Issue 3 2018 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v10i3.540 functions. The study fills the gap in the literature by proposing a Z-fuzzy number based AHP method to determine the best location for a solar PV power plant. In this study, Z- fuzzy numbers are converted to regular fuzzy numbers and then ordinary fuzzy operations are applied. We applied Buckley’s fuzzy AHP approach after the conversion in our Z-fuzzy AHP approach. The comparative analysis showed that the proposed extension of fuzzy AHP produced the same rank of the PV power plant location alternatives as the classical AHP did. The consistency of each fuzzy pairwise comparison matrix was calculated after they were defuzzified. The proposed method should be used under vagueness and when reliability to this vagueness is not equal to one. It has been observed that reliability levels have a significant effect on the weights that are obtained. As the reliability values are largely different from one another in a pairwise comparison matrix, the weights can be quite different from each other. Hence, reliability levels should be carefully determined when using this method. For further research, there are many possible ways to extend this work. For instance, intuitionistic Z-fuzzy numbers can be replaced with ordinary Z-fuzzy numbers. Another possibility is to replace intuitionistic Z-fuzzy numbers with Pythagorean Z-fuzzy numbers, neutrosophic Z-fuzzy numbers or hesitant Z-fuzzy numbers. The results can then be compared with the ones obtained in this study. Future studies can also perform a sensitivity analysis to see if there is a change when the parameters change. 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