Balanced scorecard-based analysis of investment decisions for the renewable energy alternatives: A comparative analysis based on the hybrid fuzzy decision-making approach

Energy 175 (2019) 1259e1270

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Balanced scorecard-based analysis of investment decisions for the renewable energy alternatives: A comparative analysis based on the hybrid fuzzy decision-making approach Hasan Dincer*, Serhat Yuksel School of Business, Istanbul Medipol University, Kavacık South Campus, Beykoz, Istanbul, 34810, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 October 2018 Received in revised form 29 December 2018 Accepted 25 March 2019 Available online 29 March 2019

The aim of this study is to evaluate investment decisions for the renewable energy (RE) alternatives. For this purpose, balanced scorecard (BSC)-based 4 dimensions and 8 criteria are identified. Additionally, 5 different RE investment alternatives (biomass, hydropower, geothermal, wind and solar) are examined. DEMATEL method is used to weight these dimensions and criteria whereas RE investment alternatives are weighted by TOPSIS approach. The novelty of this study is that comparative analysis is applied by considering standard fuzzy, interval type-2 (IT2) fuzzy and IT2 hesitant fuzzy (HF) sets. The findings show that competition is the most significant dimension and persistence of research and development is the most important criterion. Furthermore, it is also determined that solar and wind energies have the best performance, but geothermal energy is on the last rank. Therefore, it is recommended that level of the competition in the RE markets should be mainly taken into the consideration by the investors. In other words, investors may have loss in this RE market when there is high competition. Another important point is that investors should also give importance to the development capacity of the RE market. The main reason is that in case of the possibility to improve the products in RE markets by making research and development, investment can lower their cost. Hence, the profitability of the RE investment can increase by examining the market in detail for this purpose. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Renewable energy Fuzzy logic Interval Type-2 fuzzy logic Interval Type-2 hesitant fuzzy logic DEMATEL TOPSIS

1. Introduction Energy resources are very important for countries to reach high welfare levels. Hence, it has many advantages for both developed and developing economies [1]. Firstly, there is a positive relationship between energy usage and economic improvement [2]. In addition, the energy usage makes a contribution to the industrialization and technological development [3]. On the other side, the usage of the non-RE can have some negative impacts, such as damage to human health and environment [4]. Additionally, it can also increase import dependence and volatility in the prices. These issues show that there is a strong need for RE usage [5]. RE is defined as the type of energy from sources in nature. This energy type provides many different benefits in comparison with non-RE. As it can be understood from this definition, it minimizes

* Corresponding author. E-mail addresses: [email protected] (H. Dincer), serhatyuksel@medipol. edu.tr (S. Yuksel). https://doi.org/10.1016/j.energy.2019.03.143 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

negative effects on the environment and human health. For instance, water and air pollution can be decreased with the help of RE usage. Additionally, RE has also significant influence to decrease the cost amount because in comparison with other types due to the never-ending sources [6]. There are mainly five different RE sources. First of all, regarding solar energy, electricity can be produced by using solar panels [3]. Furthermore, wind energy also contributes to this purpose with the help of wind turbines [4]. In addition to them, while burning biomass wastes, biomass energy can be generated [7]. Similarly, by using the power of the water, it is possible to produce hydropower energy [8]. The last type of RE is the geothermal energy which can be provided from geothermal resources [9]. The RE sources attract the attention of the investors because of many different reasons. Firstly, these investments have cost advantage mainly due to the usage of natural resources. Hence, it has a positive influence on the profitability [10]. Secondly, governments can give incentives to the RE investment which encourages the investors for this sector. The main reason of these investments is that RE leads to lower energy dependence [11]. In

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other words, if a country can generate RE, it does not have to import energy from other countries. This situation has a positive effect on the current account balance of this country. In this study, it is aimed to evaluate RE alternatives. For this purpose, 4 dimensions and 8 criteria are determined based on balanced scorecard approach. Additionally, a comparative analysis is performed by considering the hybrid fuzzy decision-making approach. Within this framework, standard fuzzy, IT2 fuzzy and IT2 HF logics are used to make a comparative evaluation. Moreover, DEMATEL model is considered to weight the dimensions and criteria whereas RE investment alternatives are ranked with TOPSIS methodology. This study has many different novelties. First of all, this is the first study in which a comparative analysis is applied by considering standard fuzzy, IT2 fuzzy and IT2 HF sets together. Owing to the using these three approaches, it is believed that the consistency of the analysis results increases. Another important issue is that this study underlines the significant points for the investors to make decisions for RE investment alternatives. Thus, it is thought that is makes a contribution to the literature. There are five different sections in this study. In this introduction section, general information about the importance of the RE is shared. After that, a literature review is applied in the second section. In addition to them, different methodologies used in the analysis process are explained in the third section. On the other hand, the fourth section includes the application related to the RE investment alternatives. In the final section, analysis results and recommendations are given. 2. Literature review Some of the recent studies related to the energy in the literature focused on the economic effect of the renewable energies. Ke
cek et al. [12] aimed to analyse the economic influence of RE sources in Croatia. In this context, input-output model is considered. It is concluded that RE sources have intensive effects on the national economy. Bayulgen and Benegal [13] focused on US energy market and reached the conclusion that RE leads to higher job creation and economic development. Liang et al. [14] evaluated RE developments in China and determined that renewable electricity generation provides higher economic and environmental benefits. Zafar et al. [15]; Kahia et al. [16]; Rafindadi and Ozturk [10] and Koçak and S¸arkgünes¸i [17] also tried to analyse this subject and identified that RE usage has a direct effect on the economic development. In some studies, future of the RE was taken into the consideration. For instance, Hansen et al. [18] aimed to evaluate the RE performance of Germany in 2050. In this circumstance, both technical and economic perspectives of energy sector in this country were analyzed. It is identified that the importance of the RE in the energy sector of Germany will increase in the future. Al Irsyad et al. [19] made RE projection for US and EU countries and identified that there is low uncertainty in solar energy to achieve production target. Chuang et al. [20] assessed wind and solar power in Taiwan by 2030 and defined that nuclear power plants extended their service to 2030. Sweerts et al. [11] investigated the RE potential of Africa. With the help of scenario analysis, it is determined that there will be 15% increase in electricity generation by 2050. Some other researchers also made prediction regarding RE usage in the future [9,21,22]. The technology of the RE was analyzed by some researchers. Lin and Chen [23] focused on the innovation in RE technologies in China. In the analysis process, regression methodology is used in this study by examining the data between 2006 and 2016. They defined that research and development expenditure and economic

improvement contribute to the innovation in RE technologies. In addition to them, Matos et al. [24] identified different criteria for RE technologies. Mendoza-Vizcaino et al. [25]; Haas et al. [26]; Foley and Olabi [27] and Benighaus and Bleicher [28] are other studies that underlined the importance of the technology in RE. The effects of the RE on foreign trade were also considered in the literature. Chen et al. [6] tried to explain the relationship between RE and international trade of China. In this framework, Granger causality analysis is taken into the consideration. Additionally, annual data for the years between 1980 and 2014 is evaluated. They determined that there is a bidirectional relationship between foreign trade and RE. Moreover, Ralph and Hancock [29] identified key potential risks of renewable electricity exports in Australia and Southeast Asia. Hassine and Harrathi [30]; Wang et al. [31] and Amri [32] concluded that there is a causality relationship between RE usage and foreign trade. Performance analysis of the RE was also an important subject in the literature. Narayanan et al. [33] evaluated the cost effectiveness of the RE resources. In this study, Belgium is evaluated by using linear programming. It is identified that integration between electricity, heat and transport should be provided in order to minimize the cost of RE. Similarly, Eriksson and Gray [34] focused on the optimization of the RE systems. They reached a conclusion that RE system should be designed by considering technical, economic and environmental factors to increase effectiveness. Zhang et al. [35]; Verma et al. [36]; Lin and Ankrah [37] and Jahangiri et al. [38] also evaluated the performance of RE projects by considering different approaches, such as multi criteria decision making and regression model. Some researchers evaluated the environmental impact on the RE. For example, He et al. [39] aimed to identify the relationship between RE usage and environmental factors. For this purpose, 150 different Chinese companies working on RE are considered. In the analysis process of this study, a threshold effect model is used, and it is concluded that RE usage has a positive influence on the environmental factors. Parallel to this study, Jenniches and Worrell [40] also studied the environmental impacts of RE developments in Germany and reached the similar results. Furthermore, Adefarati and Bansal [41]; Zhao and Luo [42] and Bekun et al. [5] focused on the positive effects of RE on the environment as well. Also, it is thought that electricity can be generated with the help of RE according to many different researchers. For instance, Ahmad and Tahar [43]; Paska and Surma [44] and Park et al. [45] also emphasized this conclusion in their studies for different countries, such as Malaysia, Poland and South Korea. Moreover, Meade and Islam [46]; Rodríguez-Monroy et al. [7]; Moutinho and Robaina rez-Denicia et al. [48] and Zou et al. [49] also defined that [47]; Pe effective usage of RE has an important influence on the electricity generation. There are also some other studies which underlined the different aspects of RE. As an example, Liu [50] and Matschoss et al. [51] examined China’s and Germany’s RE law and policy so as to promote this system. Furthermore, Ali et al. [52] focused on optimal location and sizing of RE resources. Moreover, Hamed and Bressler [53] evaluated the effects of RE sources in Israel and Jordan with respect to the energy security. Also, Kuik et al. [54] studied the competitive advantage of the RE sector with the help of gravity model. It is concluded that wind industry has a competitive advantage. Inhoffen et al. [55] stated the relationship between RE and social interaction and identified that social effect is positive. Ding et al. [56] defined that women play a very significant role in regional RE development. Alves et al. [4] evaluated the RE incentive policies of 194 different countries. As a result of literature review, it is understood that there is a need for new study which focuses on investment decisions for the RE alternatives.

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3. Methodology

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binary relation : ∶ ¼ between;

In this section, different methodologies used in the analysis process are explained. Within this framework, firstly, linguistic term sets under the HF approach are identified. After that, IT2 fuzzy sets (FS) are given. Finally, necessary information is shared regarding DEMATEL and TOPSIS approaches.

In addition to them, the HF linguistic term set is indicated as hS ¼ fSi ; Siþ1 ; …; Sj g.

3.1. Linguistic term sets under the HF approach

3.2. IT2 FS

HF linguistic term set is mainly used with the aim of having flexibility for linguistic expressions. In this circumstance, decision makers consider linguistic values. The main purpose of this process is to identify a membership function. Moreover, the selection of these experts is made under hesitant environment. Within this framework, the symbolic linguistic model is named as S ¼ fS0 ;S1 ;:::; St g. On the other side, context-free grammar can be determined as GH ¼ ðVN ; VT ; I; PÞ which is based on this symbolic linguistic model. During this process, following equations are taken into the consideration [57].

Interval type-1 fuzzy logic (FL) was considered by many different researchers in the literature. However, some of them think that there is uncertainty in this logic. Therefore, IT2 FL was gener~ repreated mainly with the aim of minimizing this uncertainty. A sents a type-2 fuzzy set. In addition to this issue, type-2 membership function is demonstrated by mAðx;uÞ . Moreover, this ~ function can take values within the range of 0 and 1 [58]. This process are defined on equations (1) and (2).

VN ¼ fprimary term; composite term; unary term; binary term; conjunctiong; VT ¼ flower than; greater than; at least; at most; between; and; S0 ; S1 ; :::; St g;

conjunction : ∶ ¼ andg:

 n o ~ jcx 2X; cu 2Jx 4½0; 1 ; or A ðx; uÞ; mAðx;uÞ ~ ð ð mA~ ðx; uÞ=ðx; uÞJx 4½0; 1 ¼

~¼ A

(1)

x2X u2Jx

~¼ A

ð

ð 1=ðx; uÞJx 4½0; 1

(2)

x2X u2Jx

I2VN ; P ¼ fI : ∶ ¼ primary termjcomposite term; composite term : ∶ ¼ composite termprimary term binary relationprimary termconjunctionprimary term; primary term : ∶ ¼ S0 jS1 j…jSt ; unary relation : ∶ ¼ lower thanjgreater thanjat leastjat most;

~ U and A ~ L explain the upper and lower In addition to them, A i i trapezoidal membership function which is described in equation (3).

 U  U   U L   U U U ~ ~ ~ ;A ~ ¼ ~ ¼ A aU ; A i i i i1 ; ai2 ; ai3 ; ai4 ; H1 Ai ; H2 Ai   L  L  ~ ;H A ~ aLi1 ; aLi2 ; aLi3 ; aLi4 ; H1 A 2 i i

(3)

~ U and A ~ L whereas In this context, type-1 FS are represented by A i i others give information about the IT2 fuzzy set. Moreover, equations (4)e(8) indicate the calculation process.

 U L  U L ~ ;A ~ ¼ A ~ ;A ~ 4 A ~ ¼ ~ 4A A 1 2 1 1 2 2  U    U  U     U U U U U U U U ~ ~ ~ ;H A ~ ; min H2 A ; a11 þ a21 ; a12 þ a22 ; a13 þ aU 2 1 2 23 ; a14 þ a24 ; min H1 A1 ; H1 A2  L    L  L     L L L L L L L L L ~ ~ ~ ~ a11 þ a21 ; a12 þ a22 ; a13 þ a23 ; a14 þ a24 ; min H1 A1 ; H1 A2 ; min H2 A1 ; H2 A2

(4)

 U L  U L ~ ;A ~ ¼ A ~ ;A ~ . A ~ ¼ ~ .A A 1 2 1 1 2 2  U    U  U     U U U U U U U U ~ ~ ~ ;H A ~ ; min H2 A ; a11  a24 ; a12  a23 ; a13  aU 2 1 2 22 ; a14  a21 ; min H1 A1 ; H1 A2  L    L  L     L L L L L L L L L ~ ;H A ~ ~ ;H A ~ ; min H2 A a11  a24 ; a12  a23 ; a13  a22 ; a14  a21 ; min H1 A 1 2 1 2 1 2

(5)

 U L  U L ~ ;A ~ ¼ A ~ ;A ~ 5 A ~ ¼ ~ 5A A 1 2 1 1 2 2  U    U  U     U U U U U U U U ~ ~ ~ ;H A ~ ; min H2 A ; a11  a21 ; a12  a22 ; a13  aU 2 1 2 23 ; a14  a24 ; min H1 A1 ; H1 A2   L    L  L    L L L L L L L L L ~ ;H A ~ ~ ;H A ~ a11  a21 ; a12  a22 ; a13  a23 ; a14  a24 ; min H1 A ; min H2 A 1 2 1 2 1 2

(6)

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"

 U  U   ~ ;H A ~ ~ ¼ k  aU ; k  aU ; k  aU ; k  aU ; H A ; kA 1 1 2 1 1 11 12 13 14   L  L  L L L L ~ ~ k  a11 ; k  a12 ; k  a13 ; k  a14 ; H1 A1 ; H2 A1

y¼

  U  U  ~ 1 1 A 1 U 1 U 1 U ~ ~  aU ¼ ; 11 ;  a12 ;  a13 ;  a14 ; H1 A1 ; H2 A1 k k k k k    L  L 1 1 1 1 ~ ;H A ~  aL11 ;  aL12 ;  aL13 ;  aL14 ; H1 A 2 1 1 k k k k

3.3. DEMATEL The expression of “Decision Making Trial and Evaluation Laboratory” is represented by the word of DEMATEL. The main purpose of this methodology is to weight different criteria by considering their significance. In addition to this condition, DEMATEL model can also be used to measure the impact and dependence among these criteria [59]. The direction matrix is generated in the first step. In this context, the defined scales are considered. In the second step, the initial influence matrix is computed which can be seen on equation (9).

a21 a22 a32 « an2

a13 a23 a33 « an3

1

/ / / /

3 a1n a2n 7 7 a3n 7 7 « 5 ann

(9)

Furthermore, the step three includes the normalization of the direct effect matrix. This process is demonstrated on equations (10) and (11).

N ¼ A=s

(10)

3 n n X X max max aij ; aij 5 s ¼ max4 1in 1jn

(11)

i¼1

Also, the total influence matrix is created in the fourth step that is shown in equations (12) and (13).

T ¼ N þ N2 þ N2 þ … þ Nh   ¼ N I þ N þ N 2 þ … þ N h1 ðI  NÞðI  NÞ1

(12)

  T ¼ N I  Nh ðI  NÞ1 ¼ NðI  NÞ1 ; when lim Nh ¼ ½0nn h/∞

(13) On the other side, the influential network relation map is developed in the fifth step. Equations (14)e(16) give information about the calculation process.

  T ¼ tij nn ; i; j ¼ 1; 2; …; n 2 r¼4

n X j¼1

n1

¼ ðri Þn1 ¼ ðr1 ; …; ri ; …; rn Þ

1n

1n

¼ ðy1 ; …; yi ; …; yn Þ

(16)

In these equations, r identifies the sum of all vector rows and y expresses the sum of all vector columns. Moreover, a threshold value which shows that a criterion influences the other factor is defined in the final step.

The word TOPSIS is generated from the expression of “Technique for Order Preference by Similarity to Ideal Solution”. This approach mainly aims to rank different alternatives. In this process, positive and negative solutions are defined to reach this objective [60]. Firstly, values are normalized as demonstrated in equation (17).

Xij rij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm 2 i ¼ 1; 2; 3; ::::m and j ¼ 1; 2; 3; :::n i¼1 X ij

(17)

On the other side, these values are weighted in the second step. Furthermore, the positive (Aþ ) and negative (A ) ideal solutions are identified in the third step. These solutions are explained in equations (18) and (19).



Aþ ¼ v1j ; v2j ; …; vmj ¼ maxv1j for c j2n

(18)



A ¼ v1j ; v2j ; …; vmj ¼ minv1j for c j2n

(19) (Dþ ) i

In the fourth step, the distances to the best and the worst alternative (D i ) are determined as in equations (20) and (21).

Dþ i

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u n  vij  Aþ ¼t j

(20)

j¼1

D i

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u n  vij  A ¼t j

(21)

Also, the relative closeness to the ideal solution is calculated in the final step with the help of equation (22).

RCi ¼

D i for i ¼ 1; 2; :::; m and 0  RCi  1 Dþ þ D i i

(22)

4. Comparative analysis of extended method In this study, a hybrid decision making method is proposed by using the extended methods that are IT2 HF DEMATEL and IT2 HF TOPSIS. A comparative analysis is applied by including the triangular and trapezoidal fuzzy numbers to provide the robustness of the extended method. The details of the hybrid method are summarized below. 4.1. Proposed hybrid decision making approach

(14)

3 tij 5

 0 ¼ yj

j¼1

2

J¼1

tij

3.4. TOPSIS

(8)

a11 6 a21 6 A¼6 6 a31 4 « an1

#0

i¼1

(7)

2

n X

(15)

The hybrid decision making model under the hesitancy has twostage including the DEMATEL and TOPSIS method based on IT2 FS. The flowchart of the proposed model is illustrated in Fig. 1. The flowchart of proposed hybrid method is detailed as below. Phase 1: Determine the problem of investment decision on the RE industry. There are several aspects of RE topic as seen in the

H. Dincer, S. Yuksel / Energy 175 (2019) 1259e1270

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considered by using the triangular and trapezoidal fuzzy numbers. IT2 HF DEMATEL approach is used in this step accordingly. Converting fuzzy data into crisp scores defuzzification method is applied to convert the triangular fuzzy numbers [62]. The method of Kahraman et al. [63] is considered for the defuzzification regarding the trapezoidal membership function of the IT2 fuzzy set. Phase 6: TOPSIS is used for ranking alternatives. Ranking alternatives with IT2 FS is one of the best techniques of multicriteria decision making problem under the uncertainty. Accordingly, the hesitant evaluations of expert opinions are measured by IT2 HF TOPSIS and similarly, the defuzzification process is applied by the ranking method for IT2 FS [61] and the evaluations are compared with the results of triangular and trapezoidal functions for the coherence of the extended method. Analysis results are detailed in the following section.

4.2. Analysis results

Fig. 1. The flowchart of the hybrid method.

literature. It is aimed to provide the multidimensional perspectives of investment decision such as financial and non-financial criteria. For this purpose, the key terms of balanced scorecard approach are adapted to the investment decision for the RE alternatives. Phase 2: Based on the literature review, eight criteria based on the balanced scorecard perspectives are defined for ranking the RE alternatives. Table 1 represents the selected dimensions and criteria. Phase 3: Three decision makers are appointed to have a consensus on the criterion and alternative together with their linguistic evaluations for the criteria and alternatives. Selected experts have at least ten-year experience in the energy industry. Phase 4: Linguistic evaluations are provided from the decision makers for the criteria and alternatives. Thus, it is possible to convert to the evaluations into the fuzzy numbers with Tables 3 and 6. Phase 5: DEMATEL method is applied for weighting factors. The method is combined with IT2 FS to measure the effect of the linguistic evaluations under the hesitancy more accurately. However, to provide the robustness of the analysis, a comparative approach is

The first stage of the proposed hybrid model is interval type 2 HF DEMATEL for weighting the criteria. For this purpose, initially, the provided evaluations from the decision makers have been illustrated in the direct-relation matrix and three decision makers have been appointed to select the priorities among the criteria. Table 2 shows the linguistic scales and fuzzy evaluations for the criteria. Linguistic priorities of decision makers for the direct-relation of criteria are presented in Table 3. Linguistic evaluations of decision makers have been converted into the FS and the averaged values are considered to construct the direct-relation matrix for the criteria. Appendix A represents the direct-relation matrix for the triangular FS. Similar procedure has been applied for the direct relation matrix based on IT2 FS by using the trapezoidal membership function. In the following process, the normalized values have been computed and the results of fuzzy DEMATEL are seen in appendix B. Final step before the defuzzification process is to calculate the total relation matrix. The results of the triangular and trapezoidal fuzzy numbers have been examined in appendix C and D respectively. The final step of the first stage is the defuzzification of matrix. The matrix is defuzzified by the ranking method for the trapezoidal IT2 FS and by the converting fuzzy data into crisp scores for the triangular fuzzy numbers. Appendix E and F show the defuzzified values and the impact-relation degrees based on triangular and trapezoidal fuzzy numbers for the criteria respectively. To construct the impact and relationship map and degrees of each criterion, the averaged value of the defuzzified matrix has been defined as a threshold value and thus, it is understood that the criterion with higher value than threshold has the possible impact on the other criterion in the matrix. Accordingly, the values highlighted in bold are illustrated in appendix F and G. The tables illustrate that all the criteria have an impact on C8 while the weakest impact on C5. However, C3 has the impact on all the

Table 1 Determinants of investment decision for the RE. Dimensions

Criteria

References

Profit-based (Dimension 1)

Growth in commercialization (Criterion 1) Effective cost management (Criterion 2) Increase in the customer expectations (Criterion 3) Access to the potential consumers (Criterion 4) Active involvement of personnel for innovation (Criterion 5) Enhancing internal capacity with training (Criterion 6) Benchmarking the market services (Criterion 7) Persistence of research and development (Criterion 8)

Zafar et al. [15]; Amri [32]; Chen et al. [6] Hassine and Harrathi [30]; Kahia et al. [16] He et al. [39]; Mollahosseini et al. [21] Zou et al. [49]; Adefarati and Bansal [41] Buonomano et al. [2]; Ding et al. [56] Meade and Islam [46]; Moutinho and Robaina [47] Kuik et al. [54]; Ali et al. [52] Ahmad and Tahar [43]; Benighaus and Bleicher [28]

Consumer-based (Dimension 2) Organizational (Dimension 3) Competition (Dimension 4)

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H. Dincer, S. Yuksel / Energy 175 (2019) 1259e1270 Table 2 Linguistic and fuzzy scales for the criteria. Linguistic Scales

Triangular Fuzzy Numbers

Interval Type 2 Fuzzy Numbers

Very very low (VVL) Very low (VL) Low (L) Medium (M) High (H) Very high (VH) Very very high (VVH)

(0,0.1,0.2) (0.1,0.2,0.35) (0.2,0.35,0.5) (0.35,0.5,0.65) (0.5,0.65,0.8) (0.65,0.8,0.9) (0.8,0.9,1)

((0,0.1,0.1,0.2; 1,1), (0.05,0.1,0.1,0.15; 0.9,0.9)) ((0.1,0.2,0.2,0.35; 1,1), (0.15,0.2,0.2,0.3; 0.9,0.9)) ((0.2,0.35,0.35,0.5; 1,1), (0.25,0.35,0.35,0.45; 0.9,0.9)) ((0.35,0.5,0.5,0.65; 1,1), (0.4,0.5,0.5,0.6; 0.9,0.9)) ((0.5,0.65,0.65,0.8; 1,1), (0.55,0.65,0.65,0.75; 0.9,0.9)) ((0.65,0.8,0.8,0.9; 1,1), (0.7,0.8,0.8,0.85; 0.9,0.9)) ((0.8,0.9,0.9,1; 1,1), (0.85,0.9,0.9,0.95; 0.9,0.9))

Adapted from Baykasoglu and Golcuk [59].

Table 3 Direct-relation matrix by the linguistic evaluations. C1

C1 C2 C3 C4 C5 C6 C7 C8

C1 C2 C3 C4 C5 C6 C7 C8

C2

C3

C4

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

e VH M L M M H VH C5 DM1

e H H H H L H H

e VH H M L L H M

M e H VH M M H H

M e VH H M M H H

M M e M L M M M

M M H e M L H H

DM2

DM3

DM2

DM3

M H VH e L M M H C8 DM1

L L VH e L L H H

DM3

M M e H M L H VH C7 DM1

L M e H L M VH H

DM2

H e VH H M M H VH C6 DM1

DM2

DM3

L L H M e H H M

M L H L e VH L L

L M M M e H M L

M M H L VH e H VH

M L VH M VH e H H

L L H M H e M M

VH VH H L VH H e VH

M VH M M H L e H

H M M L H M e H

VVH VH H VH M M M e

VH VH VH H M H VH e

H H H H L M H e

Table 4 Comparative results of dimensions and criteria. Factors

Triangular Fuzzy

Trapezoidal Fuzzy

Hesitant IT2 Fuzzy

Dimensions

Criteria

Dimensions

Criteria

Dimensions

Criteria

Dimensions

Criteria

D1

C1 C2 C3 C4 C5 C6 C7 C8

0.251

0.122 0.129 0.129 0.120 0.114 0.119 0.132 0.136

0.252

0.123 0.129 0.129 0.119 0.113 0.118 0.131 0.137

0.251

0.122 0.129 0.128 0.119 0.114 0.118 0.131 0.138

D2 D3 D4

0.248 0.233 0.268

0.249 0.231 0.269

0.247 0.232 0.270

Table 5 Linguistic and fuzzy scales for the alternatives. Linguistic Scales

Triangular Fuzzy Numbers

Interval Type 2 Fuzzy Numbers

Very Poor (VP) Poor (P) Medium Poor (MP) Fair (F) Good (G) Very Good (VG) Best (B)

(0,0,0.1) (0,0.1,0.3) (0.1,0.3,0.5) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.7,0.9,1) (0.9,1,1)

((0,0,0,0.1; 1,1), (0,0,0,0.05; 0.9,0.9)) ((0,0.1,0.1,0.3; 1,1), (0.05,0.1,0.1,0.2; 0.9,0.9)) ((0.1,0.3,0.3,0.5; 1,1), (0.2,0.3,0.3,0.4; 0.9,0.9)) ((0.3,0.5,0.5,0.7; 1,1), (0.4,0.5,0.5,0.6; 0.9,0.9)) ((0.5,0.7,0.7,0.9; 1,1), (0.6,0.7,0.7,0.8; 0.9,0.9)) ((0.7,0.9,0.9,1; 1,1), (0.8,0.9,0.9,0.95; 0.9,0.9)) ((0.9,1,1,1; 1,1), (0.95,1,1,1; 0.9,0.9))

Source: Adapted from Chen and Lee, [61]; Baykasoglu and Golcuk, [59].

criteria whereas C6 has just an impact on C8. And also, the values of (r-y) define that C3 is the most influencing factor among the criteria as C6 is the most influenced for both methods. The overall results demonstrate that the impact and relation map and degrees for the

criteria is completely same for both fuzzy numbers. Additionally, interval type 2 HF DEMATEL method is applied to understand the effect of decision makers’ opinion under the hesitancy. The defuzzified matrix with the hesitant approach has been

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Table 6 Decision matrix by the linguistic evaluations. A1

C1 C2 C3 C4 C5 C6 C7 C8

A2

A3

A4

A5

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

F F F F MP F F F

G G G G F G G G

VG G VG F F F VG VG

F F F F F F F F

G G G G G G G G

VG F VG VG VG G VG MP

MP MP MP F F MP MP MP

F F F G G F F F

G F MP VG F G G G

F F G G F F G G

G G VG VG G G VG G

VG VG VG G F VG F G

F G G G G G G G

G VG VG VG B VG VG VG

G F F VG G G VG B

Increase in the customer

management (C2)

Growth in consumers (C4)

Persistence of research and development (C8) (C5)

Benchmarking the market services (C7)

Enhancing internal capacity with training (C6)

Fig. 2. Impact and relation map of the investment decision criteria for the RE.

constructed and the impact and relation map is illustrated in appendix G. The impact and relation degrees of HF approach are almost same with other the proposed fuzzy methods. Exceptionally, C5 has also an impact on C2. Fig. 2 represents the impact and relation map among the criteria under the hesitancy. However, the global and local weights of the criteria have been computed comparatively in Table 4. Analysis with the triangular, trapezoidal and Hesitant IT2 fuzzy numbers has the coherent results for weighting the criteria and dimensions. Accordingly, the comparative results also demonstrate that D4 is the most important factor among the dimension set while D3 has the weakest importance. And also, C8 is the most important criteria for all the methods while C5 has the weakest importance in the investment decision of RE. The second stage of the hybrid model continues with interval type 2 HF TOPSIS for ranking alternatives. In the first step of this stage, the linguistic decision matrix has been constructed by using the choices of decision makers for each alternative on the criteria. Table 5 defines the linguistic and fuzzy scales for alternative evaluation. Linguistic evaluations of the decision makers are presented in Table 6. Following step is to provide the fuzzy decision matrix based on triangular and trapezoidal fuzzy numbers. The matrices with the averaged values of the decision makers are illustrated in appendix H and I respectively. And then, the defuzzified values have been computed to obtain the weighted decision matrix. Table 7 defines the defuzzification results of the decision matrix for the IT2 FS.

Weighting results by using IT2 fuzzy DEMATEL have been multiplied by the defuzzified values and the weighted decision matrix have been provided for computing the ideal solution. The results are seen in Table 8.

Table 7 Defuzzified decision matrix.

C1 C2 C3 C4 C5 C6 C7 C8

A1

A2

A3

A4

A5

7.86 7.47 7.86 7.07 6.27 7.07 7.86 7.86

8.01 7.24 8.01 8.01 7.97 7.64 8.01 6.84

6.67 6.27 5.87 7.86 7.07 6.67 6.67 6.67

7.86 7.86 8.64 8.26 7.07 7.86 7.86 7.87

7.47 7.86 7.86 8.64 8.48 8.26 8.64 8.86

Table 8 Weighted decision matrix.

C1 C2 C3 C4 C5 C6 C7 C8

A1

A2

A3

A4

A5

0.96 0.97 1.01 0.84 0.72 0.83 1.03 1.09

0.98 0.94 1.03 0.95 0.91 0.90 1.05 0.95

0.81 0.81 0.75 0.93 0.81 0.79 0.88 0.92

0.96 1.02 1.11 0.98 0.81 0.93 1.03 1.09

0.91 1.02 1.01 1.03 0.97 0.97 1.13 1.23

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Table 9 Comparative performance results of RE alternatives. Alternatives

Alternative Alternative Alternative Alternative Alternative

Triangular Fuzzy

1 2 3 4 5

(Biomass) (Hydropower) (Geothermal) (Wind) (Solar)

Trapezoidal Fuzzy

Hesitant IT2 Fuzzy

Relative Closeness

Ranking performance

Relative Closeness

Ranking performance

Relative Closeness

Ranking performance

0.043 0.044 0.036 0.048 0.052

4 3 5 2 1

0.502 0.578 0.167 0.687 0.842

4 3 5 2 1

0.452 0.654 0.190 0.727 0.907

4 3 5 2 1

The results of positive and negative ideal solution for triangular, trapezoidal, and IT2 HF numbers are presented comparatively in appendix J. The comparative values of relative closeness and final ranking results are computed in Table 9. Performance results of RE alternatives demonstrate that Solar (A5) has the best performance in the balanced scorecard-based analysis of investment decisions while Geothermal (A3) is the worst alternative in the multidimensional evaluation of RE investments. It is concluded that the ranking results of each method are compatible, and the extended hybrid approach based on IT2 HF method is also coherent with the essential methods such as the triangular FS.

5. Conclusions In this study, it is aimed to make analysis regarding investment decisions for the RE alternatives. In this context, 4 dimensions and 8 criteria based on balanced scorecard approach are identified. On the other side, 5 different RE investment alternatives (biomass, hydropower, geothermal, wind and solar) are evaluated. The dimensions and criteria are weighted by DEMATEL and the alternatives are ranked with TOPSIS approach. Moreover, a comparative analysis is applied by considering standard fuzzy, IT2 fuzzy and IT2 HF sets. According to the results of the DEMATEL approach, it is defined that the triangular, trapezoidal and hesitant IT2 fuzzy numbers has the coherent results for weighting the criteria and dimensions. Competition is the most important dimension and persistence of research and development is the most significant criterion. These issues show that investors should consider the level of the competition in the RE markets to make decisions for investment. It means that in case of high competition, it is not so appropriate to invest in these RE alternatives. This condition was also emphasized by Ahmad and Tahar [43] and Benighaus and Bleicher [28]. Another important point is that investors should give importance to the development capacity of the market. It indicates that

when there is a possibility to improve the products by making research and development, it can give an opportunity to minimize the costs. Because this situation has a positive effects on the profitability, investors can make investment these renewable investment alternatives. Therefore, the development capacity of these different RE markets should be examined in a detailed manner by the investors before making this investment decision. In addition to them, the analysis results of TOPSIS method demonstrate that solar has the best performance while geothermal is the worst alternative of RE investments. Furthermore, wind is the second best RE investment alternative. Buonomano et al. [2]; Jenniches and Worrell [40] and Yun et al. [3] also underlined the importance of this situation in their studies. It is also identified that in this process, the results of three different analyses are coherent with each other. These results provide a view for the investors to make investment decisions for RE alternatives. In this study, standard fuzzy, IT2 fuzzy and IT2 HF approaches are used to make comparative analysis. However, in the future studies, there may be comparison between IT2 HF TOPSIS with IT2 HF VIKOR and MOORA. Similarly, it is also believed that a comparison between IT2 HF DEMATEL with IT2 HF AHP and ANP will also contribute to the literature. Nomenclature BSC Balanced Scorecard DEMATEL: Decision Making Trial and Evaluation Laboratory FL: Fuzzy Logic FS Fuzzy Sets HF Hesitant Fuzzy IT2 Interval type-2 RE Renewable Energy TOPSIS Technique for Order Preference by Similarity to Ideal Solution Appendix

Appendix A Direct-relation matrix. C1

C2

C3

C4

C1 C2 C3 C4 C5 C6 C7 C8

0.00 0.60 0.45 0.35 0.35 0.25 0.50 0.50 C5

0.00 0.75 0.60 0.50 0.50 0.40 0.65 0.65

0.00 0.87 0.75 0.65 0.65 0.55 0.80 0.78

0.40 0.00 0.60 0.55 0.35 0.35 0.50 0.55 C6

0.55 0.00 0.75 0.70 0.50 0.50 0.65 0.70

0.70 0.00 0.87 0.83 0.65 0.65 0.80 0.83

0.30 0.35 0.00 0.45 0.25 0.30 0.50 0.50 C7

0.45 0.50 0.00 0.60 0.40 0.45 0.65 0.65

0.60 0.65 0.00 0.75 0.55 0.60 0.78 0.78

0.30 0.35 0.60 0.00 0.25 0.25 0.45 0.50 C8

0.45 0.50 0.75 0.00 0.40 0.40 0.60 0.65

0.60 0.65 0.87 0.00 0.55 0.55 0.75 0.80

C1 C2 C3 C4

0.25 0.25 0.45 0.30

0.40 0.40 0.60 0.45

0.55 0.55 0.75 0.60

0.30 0.25 0.55 0.30

0.45 0.40 0.70 0.45

0.60 0.55 0.83 0.60

0.50 0.55 0.40 0.25

0.65 0.70 0.55 0.40

0.78 0.82 0.70 0.55

0.65 0.60 0.55 0.55

0.78 0.75 0.70 0.70

0.90 0.87 0.83 0.83

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Appendix A (continued ) C1 C5 C6 C7 C8

0.00 0.55 0.35 0.25

C2 0.00 0.70 0.50 0.40

0.00 0.83 0.65 0.55

0.60 0.00 0.45 0.50

C3 0.75 0.00 0.60 0.65

0.87 0.00 0.75 0.78

0.55 0.35 0.00 0.55

C4 0.70 0.50 0.00 0.70

0.83 0.65 0.00 0.83

0.30 0.40 0.50 0.00

0.45 0.55 0.65 0.00

0.60 0.70 0.78 0.00

Appendix B Normalized direct relation matrix. C1

C2

C3

C4

C1 C2 C3 C4 C5 C6 C7 C8

0.00 0.11 0.08 0.06 0.06 0.04 0.09 0.09 C5

0.00 0.13 0.11 0.09 0.09 0.07 0.12 0.12

0.00 0.15 0.13 0.12 0.12 0.10 0.14 0.14

0.07 0.00 0.11 0.10 0.06 0.06 0.09 0.10 C6

0.10 0.00 0.13 0.13 0.09 0.09 0.12 0.13

0.13 0.00 0.15 0.15 0.12 0.12 0.14 0.15

0.05 0.06 0.00 0.08 0.04 0.05 0.09 0.09 C7

0.08 0.09 0.00 0.11 0.07 0.08 0.12 0.12

0.11 0.12 0.00 0.13 0.10 0.11 0.14 0.14

0.05 0.06 0.11 0.00 0.04 0.04 0.08 0.09 C8

0.08 0.09 0.13 0.00 0.07 0.07 0.11 0.12

0.11 0.12 0.15 0.00 0.10 0.10 0.13 0.14

C1 C2 C3 C4 C5 C6 C7 C8

0.04 0.04 0.08 0.05 0.00 0.10 0.06 0.04

0.07 0.07 0.11 0.08 0.00 0.13 0.09 0.07

0.10 0.10 0.13 0.11 0.00 0.15 0.12 0.10

0.05 0.04 0.10 0.05 0.11 0.00 0.08 0.09

0.08 0.07 0.13 0.08 0.13 0.00 0.11 0.12

0.11 0.10 0.15 0.11 0.15 0.00 0.13 0.14

0.09 0.10 0.07 0.04 0.10 0.06 0.00 0.10

0.12 0.13 0.10 0.07 0.13 0.09 0.00 0.13

0.14 0.15 0.13 0.10 0.15 0.12 0.00 0.15

0.12 0.11 0.10 0.10 0.05 0.07 0.09 0.00

0.14 0.13 0.13 0.13 0.08 0.10 0.12 0.00

0.16 0.15 0.15 0.15 0.11 0.13 0.14 0.00

Appendix C Total relation matrix based on triangular fuzzy numbers. C1

C2

C3

C4

C1 C2 C3 C4 C5 C6 C7 C8

0.07 0.17 0.17 0.13 0.12 0.12 0.17 0.19 C5

0.23 0.36 0.37 0.31 0.30 0.28 0.36 0.37

0.93 1.10 1.19 1.04 1.02 0.98 1.15 1.16

0.14 0.08 0.20 0.17 0.13 0.14 0.18 0.20 C6

0.33 0.26 0.41 0.36 0.32 0.30 0.38 0.39

1.08 1.01 1.25 1.11 1.06 1.03 1.20 1.21

0.11 0.13 0.09 0.14 0.10 0.12 0.16 0.18 C7

0.28 0.30 0.25 0.31 0.27 0.27 0.34 0.34

0.97 1.01 1.00 1.00 0.95 0.93 1.08 1.09

0.11 0.13 0.19 0.07 0.10 0.11 0.15 0.18 C8

0.29 0.31 0.37 0.21 0.27 0.26 0.33 0.35

0.98 1.02 1.15 0.89 0.95 0.93 1.09 1.10

C1 C2 C3 C4 C5 C6 C7 C8

0.10 0.10 0.15 0.11 0.05 0.15 0.13 0.12

0.26 0.27 0.33 0.27 0.19 0.29 0.30 0.29

0.91 0.95 1.07 0.93 0.82 0.92 1.02 1.01

0.12 0.12 0.18 0.12 0.16 0.08 0.16 0.18

0.29 0.30 0.38 0.30 0.34 0.21 0.35 0.36

1.00 1.03 1.18 1.02 1.03 0.87 1.12 1.13

0.15 0.17 0.17 0.12 0.16 0.14 0.09 0.20

0.34 0.36 0.37 0.30 0.34 0.30 0.26 0.38

1.07 1.11 1.20 1.05 1.06 1.01 1.04 1.18

0.19 0.19 0.20 0.18 0.13 0.15 0.19 0.11

0.38 0.39 0.42 0.37 0.32 0.32 0.39 0.29

1.14 1.18 1.28 1.14 1.08 1.07 1.23 1.12

Appendix D Total relation matrix based on trapezoidal fuzzy numbers. C1 C1 ((0.08,0.23,0.23,0.93; 1,1), (0.11,0.23,0.23,0.51; 0.90,0.90)) C2 ((0.18,0.36,0.36,1.10; 1,1), (0.22,0.36,0.36,0.66; 0.90,0.90)) C3 ((0.17,0.37,0.37,1.04; 1,1), (0.22,0.37,0.37,0.70; 0.90,0.90)) C4 ((0.14,0.31,0.31,1.04; 1,1), (0.18,0.31,0.31,0.61; 0.90,0.90)) C5 ((0.13,0.30,0.30,1.02; 1,1), (0.17,0.30,0.30,0.59; 0.90,0.90)) C6 ((0.11,0.28,0.28,0.98; 1,1), (0.15,0.28,0.28,0.56; 0.90,0.90)) C7 ((0.17,0.36,0.36,1.15; 1,1), (0.21,0.36,0.36,0.68; 0.90,0.90))

C2

C3

C4

((0.15,0.33,0.33,1.08; 1,1), (0.19,0.33,0.33,0.64; 0.90,0.90)) ((0.09,0.26,0.26,1.01; 1,1), (0.13,0.26,0.26,0.56; 0.90,0.90)) ((0.20,0.41,0.41,1.25; 1,1), (0.25,0.41,0.41,0.75; 0.90,0.90)) ((0.17,0.36,0.36,1.11; 1,1), (0.22,0.36,0.36,0.66; 0.90,0.90)) ((0.14,0.32,0.32,1.06; 1,1), (0.18,0.32,0.32,0.62; 0.90,0.90)) ((0.13,0.30,0.30,1.03; 1,1), (0.17,0.30,0.30,0.60; 0.90,0.90)) ((0.18,0.38,0.38,1.20; 1,1), (0.22,0.38,0.38,0.71; 0.90,0.90))

((0.12,0.28,0.28,0.97; 1,1), (0.16,0.28,0.28,0.56; 0.90,0.90)) ((0.13,0.30,0.30,1.01; 1,1), (0.17,0.30,0.30,0.59; 0.90,0.90)) ((0.14,0.31,0.31,1.00; 1,1), (0.12,0.25,0.25,0.55; 0.90,0.90)) ((0.14,0.31,0.31,1.00; 1,1), (0.12,0.25,0.25,0.55; 0.90,0.90)) ((0.14,0.31,0.31,1.00; 1,1), (0.15,0.27,0.27,0.55; 0.90,0.90)) ((0.11,0.27,0.27,0.93; 1,1), (0.15,0.27,0.27,0.54; 0.90,0.90)) ((0.16,0.34,0.34,1.08; 1,1), (0.20,0.34,0.34,0.64; 0.90,0.90))

((0.12,0.29,0.29,0.98; 1,1), (0.16,0.29,0.29,0.57; 0.90,0.90)) ((0.13,0.31,0.31,1.02; 1,1), (0.17,0.31,0.31,0.60; 0.90,0.90)) ((0.18,0.37,0.37,1.15; 1,1), (0.23,0.37,0.37,0.69; 0.90,0.90)) ((0.07,0.21,0.21,0.89; 1,1), (0.10,0.21,0.21,0.49; 0.90,0.90)) ((0.11,0.27,0.27,0.95; 1,1), (0.15,0.27,0.27,0.55; 0.90,0.90)) ((0.10,0.26,0.26,0.93; 1,1), (0.14,0.26,0.26,0.54; 0.90,0.90)) ((0.15,0.33,0.33,1.09; 1,1), (0.20,0.33,0.33,0.64; 0.90,0.90)) (continued on next page)

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Appendix D (continued ) C2

C3

C4

C8 ((0.17,0.37,0.37,1.16; 1,1), (0.22,0.37,0.37,0.69; 0.90,0.90)) C5

C1

((0.19,0.39,0.39,1.21; 1,1), (0.24,0.39,0.39,0.72; 0.90,0.90)) C6

((0.16,0.34,0.34,1.09; 1,1), (0.21,0.34,0.34,0.65; 0.90,0.90)) C7

((0.17,0.35,0.35,1.10; 1,1), (0.21,0.35,0.35,0.66; 0.90,0.90)) C8

C1 ((0.10,0.26,0.26,0.91; 1,1), (0.14,0.26,0.26,0.53; 0.90,0.90)) C2 ((0.11,0.27,0.27,0.95; 1,1), (0.14,0.27,0.27,0.55; 0.90,0.90)) C3 ((0.15,0.33,0.33,1.07; 1,1), (0.19,0.33,0.33,0.63; 0.90,0.90)) C4 ((0.11,0.27,0.27,0.93; 1,1), (0.15,0.27,0.27,0.54; 0.90,0.90)) C5 ((0.06,0.19,0.19,0.82; 1,1), (0.09,0.19,0.19,0.44; 0.90,0.90)) C6 ((0.14,0.29,0.29,0.92; 1,1), (0.18,0.29,0.29,0.55; 0.90,0.90)) C7 ((0.13,0.30,0.30,1.02; 1,1), (0.17,0.30,0.30,0.59; 0.90,0.90)) C8 ((0.12,0.29,0.29,1.01; 1,1), (0.16,0.29,0.29,0.59; 0.90,0.90))

((0.12,0.29,0.29,1.00; 1,1), (0.16,0.29,0.29,0.59; 0.90,0.90)) ((0.12,0.30,0.30,1.03; 1,1), (0.16,0.30,0.30,0.60; 0.90,0.90)) ((0.18,0.38,0.38,1.18; 1,1), (0.23,0.38,0.38,0.70; 0.90,0.90)) ((0.12,0.30,0.30,1.02; 1,1), (0.16,0.30,0.30,0.59; 0.90,0.90)) ((0.17,0.34,0.34,1.03; 1,1), (0.21,0.34,0.34,0.62; 0.90,0.90)) ((0.07,0.21,0.21,0.87; 1,1), (0.10,0.21,0.21,0.47; 0.90,0.90)) ((0.10,0.24,0.24,0.86; 1,1), (0.13,0.24,0.24,0.51; 0.90,0.90)) ((0.13,0.28,0.28,0.92; 1,1), (0.17,0.28,0.28,0.55; 0.90,0.90))

((0.16,0.34,0.34,1.07; 1,1), (0.20,0.34,0.34,0.63; 0.90,0.90)) ((0.18,0.36,0.36,1.11; 1,1), (0.22,0.36,0.36,0.66; 0.90,0.90)) ((0.17,0.37,0.37,1.20; 1,1), (0.21,0.37,0.37,0.71; 0.90,0.90)) ((0.12,0.30,0.30,1.05; 1,1), (0.17,0.30,0.30,0.61; 0.90,0.90)) ((0.17,0.34,0.34,1.06; 1,1), (0.21,0.34,0.34,0.63; 0.90,0.90)) ((0.13,0.30,0.30,1.01; 1,1), (0.17,0.30,0.30,0.59; 0.90,0.90)) ((0.09,0.26,0.26,1.04; 1,1), (0.13,0.26,0.26,0.57; 0.90,0.90)) ((0.18,0.38,0.38,1.18; 1,1), (0.23,0.38,0.38,0.70; 0.90,0.90))

((0.19,0.38,0.38,1.14; 1,1), (0.24,0.38,0.38,0.68; 0.90,0.90)) ((0.19,0.39,0.39,1.18; 1,1), (0.24,0.39,0.39,0.70; 0.90,0.90)) ((0.20,0.42,0.42,1.28; 1,1), (0.25,0.42,0.42,0.76; 0.90,0.90)) ((0.18,0.37,0.37,1.14; 1,1), (0.22,0.37,0.37,0.68; 0.90,0.90)) ((0.13,0.32,0.32,1.08; 1,1), (0.18,0.32,0.32,0.63; 0.90,0.90)) ((0.14,0.32,0.32,1.07; 1,1), (0.19,0.32,0.32,0.63; 0.90,0.90)) ((0.19,0.39,0.39,1.23; 1,1), (0.23,0.39,0.39,0.73; 0.90,0.90)) ((0.11,0.29,0.29,1.12; 1,1), (0.15,0.29,0.29,0.62; 0.90,0.90))

Appendix E Defuzzified matrix and impact-relation degrees based on triangular fuzzy numbers.

C1 C2 C3 C4 C5 C6 C7 C8

C1

C2

C3

C4

C5

C6

C7

C8

r

y

rþy

r-y

0.34 0.47 0.50 0.43 0.41 0.39 0.48 0.49

0.44 0.38 0.54 0.47 0.43 0.42 0.50 0.51

0.39 0.42 0.38 0.42 0.38 0.37 0.46 0.46

0.40 0.43 0.50 0.33 0.38 0.38 0.46 0.47

0.38 0.40 0.46 0.39 0.30 0.40 0.42 0.40

0.42 0.44 0.51 0.42 0.45 0.33 0.48 0.47

0.47 0.50 0.51 0.43 0.45 0.42 0.40 0.50

0.51 0.53 0.55 0.49 0.44 0.45 0.53 0.42

3.37 3.55 3.94 3.37 3.24 3.16 3.72 3.73

3.51 3.69 3.28 3.34 3.15 3.52 3.67 3.91

6.87 7.24 7.22 6.72 6.39 6.67 7.39 7.64

0.14 0.13 0.66 0.03 0.08 0.36 0.05 0.19

Appendix F Defuzzified matrix and impact-relation degrees based on trapezoidal fuzzy numbers.

C1 C2 C3 C4 C5 C6 C7 C8

C1

C2

C3

C4

C5

C6

C7

C8

r

y

rþy

r-y

0.31 0.44 0.46 0.39 0.38 0.36 0.45 0.45

0.41 0.34 0.50 0.44 0.40 0.39 0.47 0.48

0.36 0.38 0.34 0.39 0.35 0.34 0.42 0.43

0.36 0.39 0.46 0.30 0.35 0.34 0.42 0.43

0.33 0.35 0.41 0.34 0.27 0.36 0.38 0.37

0.37 0.38 0.47 0.38 0.41 0.29 0.43 0.44

0.42 0.44 0.46 0.39 0.42 0.38 0.35 0.47

0.46 0.47 0.51 0.45 0.40 0.41 0.48 0.39

3.03 3.20 3.61 3.08 2.98 2.86 3.41 3.46

3.25 3.43 3.01 3.04 2.82 3.18 3.33 3.58

6.28 6.63 6.62 6.12 5.79 6.04 6.73 7.04

0.21 0.23 0.60 0.04 0.16 0.32 0.08 0.12

Appendix G Defuzzified matrix and impact-relation degrees based on hesitant IT2 FS.

C1 C2 C3 C4 C5 C6 C7 C8

C1

C2

C3

C4

C5

C6

C7

C8

r

y

rþy

r-y

0.32 0.44 0.47 0.40 0.39 0.37 0.46 0.47

0.43 0.36 0.51 0.46 0.42 0.41 0.48 0.50

0.36 0.39 0.35 0.39 0.36 0.35 0.43 0.44

0.37 0.39 0.46 0.30 0.36 0.35 0.42 0.45

0.35 0.36 0.42 0.35 0.28 0.38 0.39 0.39

0.38 0.39 0.48 0.38 0.42 0.30 0.43 0.46

0.43 0.45 0.48 0.40 0.44 0.40 0.37 0.49

0.47 0.48 0.53 0.47 0.42 0.43 0.49 0.41

3.10 3.26 3.70 3.16 3.08 2.99 3.47 3.60

3.33 3.56 3.06 3.11 2.93 3.23 3.45 3.69

6.43 6.82 6.76 6.28 6.02 6.23 6.93 7.29

0.22 0.30 0.64 0.05 0.15 0.24 0.02 0.09

H. Dincer, S. Yuksel / Energy 175 (2019) 1259e1270

1269

Appendix H Decision matrix based on triangular fuzzy numbers. A1

C1 C2 C3 C4 C5 C6 C7 C8

A2

A3

A4

A5

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

DM1

DM2

DM3

0.50 0.43 0.50 0.37 0.23 0.37 0.50 0.50

0.70 0.63 0.70 0.57 0.43 0.57 0.70 0.70

0.87 0.83 0.87 0.77 0.63 0.77 0.87 0.87

0.50 0.37 0.50 0.50 0.50 0.43 0.50 0.30

0.70 0.57 0.70 0.70 0.70 0.63 0.70 0.50

0.87 0.77 0.87 0.87 0.87 0.83 0.87 0.70

0.30 0.23 0.17 0.50 0.37 0.30 0.30 0.30

0.50 0.43 0.37 0.70 0.57 0.50 0.50 0.50

0.70 0.63 0.57 0.87 0.77 0.70 0.70 0.70

0.50 0.50 0.63 0.57 0.37 0.50 0.50 0.50

0.70 0.70 0.83 0.77 0.57 0.70 0.70 0.70

0.87 0.87 0.97 0.93 0.77 0.87 0.87 0.90

0.43 0.50 0.50 0.63 0.63 0.57 0.63 0.70

0.63 0.70 0.70 0.83 0.80 0.77 0.83 0.87

0.83 0.87 0.87 0.97 0.93 0.93 0.97 0.97

Appendix I Decision matrix based on trapezoidal fuzzy numbers. A1

A2

A3

A4

C1 ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90))

((0.5,0.8,0.8,0.77; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90))

((0.30,0.50,0.50,0.70; 1,1), ((0.5,0.7,0.7,0.87; 1,1), (0.40,0.50,0.50,0.60; 0.90,0.90)) (0.6,0.7,0.7,0.78; 0.90,0.90))

C2 ((0.43,0.63,0.63,0.83; 1,1), (0.53,0.63,0.63,0.73; 0.90,0.90)) C3 ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) C4 ((0.37,0.57,0.57,0.77; 1.00,1.00), (0.47,0.57,0.57,0.67; 0.90,0.90)) C5 ((0.23,0.43,0.43,0.63; 1.00,1.00), (0.33,0.43,0.43,0.53; 0.90,0.90)) C6 ((0.37,0.57,0.57,0.77; 1.00,1.00), (0.47,0.57,0.57,0.67; 0.90,0.90))

((0.37,0.67,0.67,0.67; 1.00,1.00), (0.47,0.57,0.57,0.67; 0.90,0.90)) ((0.5,0.8,0.8,0.77; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.5,0.8,0.8,0.77; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.5,0.8,0.8,0.70; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.43,0.73,0.73,0.73; 1,1), (0.53,0.63,0.63,0.73; 0.90,0.90))

((0.23,0.43,0.43,0.63; 1.00,1.00), (0.33,0.43,0.43,0.53; 0.90,0.90)) ((0.17,0.37,0.37,0.57; 1.00,1.00), (0.27,0.37,0.37,0.47; 0.90,0.90)) ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.37,0.57,0.57,0.77; 1.00,1.00), (0.47,0.57,0.57,0.67; 0.90,0.90)) ((0.30,0.50,0.50,0.70; 1,1), (0.40,0.50,0.50,0.60; 0.90,0.90))

((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.30,0.50,0.50,0.70; 1.00,1.00), (0.40,0.50,0.50,0.60; 0.90,0.90)) ((0.40,0.60,0.60,0.80; 1,1), (0.50,0.60,0.60,0.70; 0.90,0.90)) ((0.30,0.50,0.50,0.70; 1.00,1.00), (0.40,0.50,0.50,0.60; 0.90,0.90)) ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90))

C7 ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) C8 ((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90))

((0.5,0.8,0.8,0.77; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.30,0.60,0.60,0.60; 1,1), (0.40,0.50,0.50,0.60; 0.90,0.90))

((0.30,0.50,0.50,0.70; 1,1), (0.40,0.50,0.50,0.60; 0.90,0.90)) ((0.30,0.50,0.50,0.70; 1,1), (0.40,0.50,0.50,0.60; 0.90,0.90))

((0.5,0.7,0.7,0.87; 1,1), (0.6,0.7,0.7,0.78; 0.90,0.90)) ((0.5,0.7,0.7,0.90; 1,1), (0.6,0.7,0.7,0.80; 0.90,0.90))

Appendix J The comparative results of positive and negative ideal solution. Alternatives

Alternative Alternative Alternative Alternative Alternative

1 2 3 4 5

Triangular Fuzzy

(Biomass) (Hydropower) (Geothermal) (Wind) (Solar)

Trapezoidal Fuzzy

Hesitant IT2 Fuzzy

Diþ

Di-

Diþ

Di-

Diþ

Di-

7.665 7.655 7.729 7.623 7.594

0.347 0.356 0.286 0.386 0.414

0.401 0.336 0.651 0.245 0.120

0.404 0.461 0.131 0.537 0.639

0.446 0.256 0.655 0.216 0.071

0.369 0.483 0.154 0.578 0.695

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