Solving a Multiple User Energy Source Selection Problem Using a Fuzzy Multi-Criteria Group Decision-Making Approach

: In recent years, the evaluation of several energy sources is an extremely signiﬁcant issue that affects socio-environmental development and techno-economic growth in different sectors. To tackle this concern, many researchers have concentrated on preferring desirable energy sources and adopting multi-criteria group decision-making (MCGDM) approaches for only a single type of user (e.g., agricultural, industrial, tourism, or domestic users). However, every energy user plays an important role in shaping energy policy. In fact, for sustainable energy, it is important to include all main energy users at the same time in energy decision-making. The main objective of this work was to propose a fuzzy MCGDM approach to evaluate and prioritize energy sources in Tunisia from various sectors’ point of views. Many criteria are combined, including the following: technical, economic, social, political and environmental. After applying the fuzzy Delphi method, the proposed approach consists of applying a fuzzy TOPSIS method as a multi-criteria approach. Finally, a sensitivity analysis is performed to evaluate the results of the proposed approach and to study how the optimal solution is affected by the objective function coefﬁcients.


Background and Research Motivation
Energy is an important resource for all user sectors in the world. The energy extraction process is characterized by several different practices, techniques, and impacts. However, despite the economic importance of these resources in several countries, and their social and political benefits, these resources cause various economic, environmental, and social impacts in terms of pollution, human health, etc. [1]. These criteria impacts vary mainly due to the practices and techniques used in energy extraction. From this perspective, sustainability studies on energy are vital. Indeed, the aim of sustainable development is to meet industrial, agricultural, domestic, and tourism energy needs, and therefore prosperity for this and future generations, according to various criteria. Generally, the inefficient use of resources and the unbalanced income reparation seem to be problematic for the relative size of sectoral energy source selection. Fulfilling energy requirements is a critical issue for the development of different sectors. Meeting the multiple demands of the industrial, agricultural, domestic, and tourism sectors has the potential to lead to intense energy conflicts. In fact, this has provided a new dimension to existing energy conflicts proposed natural gas for the industrial sector in Greece, based on the PROMETHEE methods. Barragán et al. [18] showed that the solar photovoltaic is the best energy source for the domestic sector in Cuenca using the PROMETHEE method.
According to the VIKOR method, we can establish a compromise ranking list and a compromise solution obtained on the criteria priorities. Some authors have applied the VIKOR method to solve the energy source selection problems, such as in [19]. With the DEA method, we can compare the different energy sources to determine their efficiencies based on various criteria. In the stochastic or fuzzy MCGDM method literature, there is a long history of methodologies that allow decision aiding under uncertain and/or imprecise information. The SMAA is an MCGDM method to assess energy sources while taking into account inaccurate, uncertain, or missing information [20]. On the other hand, fuzzy MCGDM methods enable to us model uncertainties in human judgments while analyzing energy source selection problems [21][22][23]. This study presents MCGDM methods that can be used to optimize the selection of energy by various users with different priorities of criteria levels in a given system. The MCGDM methods were widely utilized to evaluate various energy sources in several countries. However, the utilization of MCGDM methods is almost at a domestic, industrial, agricultural, or tourism scale. Table 1 presents an important list of studies that were used for the energy source selections. In 1995, Ramanathan and Ganesh [4] applied the AHP and goal programming methods to select an energy source for the domestic sector in India. In 2003, Beccali et al. applied the ELECTRE-III method to evaluate a set of renewable energy sources for the agricultural sector in Italy. Haralambopoulos and Polatidis [16] evaluated a set of energy sources using the PROMETHEE method in Greece for the tourism sector. In 2004, Kablan [5] used the AHP method to rank energy sources for the domestic sector in Jordan. In 2007, Diakoulaki and Karangelis used the PROMETHEE method to select the best renewable energy source for the industrial sector in Greece. In 2008, Chatzimouratidis et al. [6] applied the AHP approach to rank several energy sources for the domestic sector in Greece. In the same context, Jaber et al. [24] evaluated various energy sources using the AHP method for the domestic sector in Jordan. Önüt et al. [10] applied the ANP method to rank energy sources for the manufacturing industry in Turkey. In 2009, Ren el al. [25] used the AHP-PROMETHEE methods to determine the best energy source selection for the domestic sector in Japan. In the study of Daim et al. [26], various energy sources were compared using the AHP method for the industrial sector in the USA. Furthermore, Theodorou et al. [27] applied the AHP approach to rank the energy sources for the industrial sector in Cyprus. Kaya et al. [14] used a combinatorial approach based on the VIKOR and AHP methods to find the best renewable energy sources for the industrial sector in Turkey. In 2011, the AHP method was used by Chinese et al. [7] for the industrial sector in Italy. Kaya and Kahraman [23] applied the TOPSIS method to rank a set of energy sources for the domestic sector in Turkey. Catalina et al. [13] applied the ELECTRE III method for the selection of the best combination of energy sources for the domestic sector in France. In 2014, Ahmed and Tahar [8] used the AHP method for the selection of energy sources for the industrial sector in Malaysia. In 2015, Rojas-Zerpa, and Yusta [28] applied the AHP-VIKOR methods to determine the best energy source for the agricultural sector in the Venezuelan Andes. Kontu et al. [20] applied the SMAA method to select the best energy systems for a new sustainable residential area in Finland. Streimikienė et al. [29] used the AHP-ARAS methods for the selection of electricity generation technologies in Lithuania. Garni el al. [9] applied the AHP method to rank the energy sources for the domestic sector in Saudi Arabia.
Çelikbilek et al. [30] applied the ANP-VIKOR methods to rank the different renewable energy sources for the industrial sector in Turkey. Jung et al. [31] used the SMAA method to identify the best renewable energy sources for the tourism sector in Helsinki, Finland. Barragán et al. [18] used the PROMETHEE method to determine the best energy sources for the domestic sector in the city of Cuenca. Talukdar et al. [15] used the TOPSIS method to identify the best renewable energy source for the domestic sector in Dhaka, Bangladesh. Strantzali et al. [32] applied the PROMETHEE method to find the best renewable energy sources for the tourism sector in Greece. Kausika et al. [33] applied the GIS-AHP methods to rank energy sources for the domestic sector of the city of Apeldoorn in the Netherlands. Haddad et al. [34] applied the AHP method to evaluate energy sources for the domestic sector in Algeria. Wu et al. [35] used the PROMETHEE-ANP methods to determine the best energy sources for remote areas. Kumar and Samuel [19] utilized the VIKOR method to rank renewable energy sources for the industrial sector in India. Aboushal [36] used the GIS method to rank a set of renewable energy sources for the domestic sector in Egypt. Rathore and Singh [37] used the ARAS method to select an optimal renewable energy source for the agricultural sector in India. In addition, Taskin Gumus et al. [21], Colak et al. [22], and Kaya et al. [14] applied a combined fuzzy MCDM for energy source selection in Turkey. Pratibha et al. [38] applied the TOPSIS method to evaluate the energy source in India for a domestic sector. Liu et al. [39] applied a hybrid approach based on the ANP and VIKOR methods to select the best renewable energy sources for the domestic sector in China.

Objective of the Study
The recent literature on the subject includes a number of studies that implement the MCGDM method to select a sustainable energy source for a given user (industrial, domestic, agricultural, or tourism). However, the objectives of this paper are to apply a fuzzy MCGDM approach to determine the criteria and energy source selection for multiple users. The contributions of this paper are to determine the priorities of users according to various criteria in the energetic field and to prepare the energy users list for each energy source. Therefore, the fuzzy MCGDM approach is applied to energy field. The procedure consists of evaluating criteria based on energy experts' opinions (fuzzy Delphi method) and the sectoral rankings of energy sources (fuzzy TOPSIS method).
In the next section we present the sectoral energy source selection problems. After that, we give a description of the proposed approach. The results of the proposed approach are presented at the end of this study.

Study Area
Each country should study their sectoral energy source selection as a specific case study. Although Tunisia is a fossil fuel producing country and its climate is conducive to the production of renewable energies, in Tunisia, energy studies are very limited. Energy transitions bring about fundamental changes at various levels in Tunisia, thus it needs broad, all-sector support. To design an accepted energy transition that is sustainable and socially compatible, it must aim at compromises in balancing differing sectoral interests through inclusive processes and fairly distributed outcomes. Tunisia suffers from an energy shortage due to the increased demand for energy that has exceeded the demand for national production. According to the Tunisian Ministry of Energy, over the past few years, primary energy resources have been declining by about 6% per year. This loss is mostly due to the natural degradation of fossil fuels. Moreover, Tunisia's primary energy needs have increased by more than 2% per year [40]. On the other hand, policy makers are well advised to consult energy specialists from all levels and sectors of society to manage the complexity and contingency of energy transitions. In this paper, the prioritization of each criterium is estimated in each sector using experts' opinions through the fuzzy Delphi method. The industrial, agricultural, domestic, and tourism sectors are defined, and comparisons from one to another are regarded as a sectoral energy transaction. This approach is adopted as a convenient way to gauge sectoral energy source selection.

The Proposed Approach
Energy source selection usually involves economic and political influences as well as social and environmental analyses. These interdependent impacts among competing sectors, especially the uncertainty related to energy availability, make the problem rather complex and uncertain. However, a new integrated methodological framework with a fuzzy MCGDM approach is proposed as a decision-making model to solve the multiple users and energy source selection problems. The proposed approach is shown in Figure 1.

Fuzzy Delphi Method
The Delphi method was proposed by Norman and Olaf [41] to collect datasets with a group of decision makers. The main steps of the fuzzy Delphi method are illustrated as follows:

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Step 1. Assume that K energy experts , = 1, … , , are invited to propose the lists of evaluation criteria, energy sources, and the main energy consumable sectors.

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Step 2. The experts are invited to get the importance of the evaluation sources , = 1, … , , with respect to different criteria , = 1, … , , using linguistic variables.
For each criterion of energy source , an expert is consulted to assign a score.
This score can be seen as the expression of his opinion with respect to the preference of criterion by energy sources. This paper used a new approach to evaluate the different energy sources for various sectors. Firstly, the fuzzy Delphi method is used to consult the experts and to prepare the necessary datasets. Next, the best non-fuzzy performance technique is used to prepare the priorities of different sectors based on the fuzzy Delphi datasets. After that, the fuzzy TOPSIS method is applied for the sectoral rankings of energy sources according to the final results of the fuzzy AHP and Delphi methods. Finally, the fuzzy MCGDM approach is validated with uncertain parameter values by a sensitivity analysis.

Fuzzy Delphi Method
The Delphi method was proposed by Norman and Olaf [41] to collect datasets with a group of decision makers. The main steps of the fuzzy Delphi method are illustrated as follows: - Step 1. Assume that K energy experts EX k , k = 1, . . . , K, are invited to propose the lists of evaluation criteria, energy sources, and the main energy consumable sectors. - Step 2. The experts are invited to get the importance of the evaluation sources A i , i = 1, . . . , n, with respect to different criteria C j , i = 1, . . . , m, using linguistic variables. For each criterion C j of energy source A i , an expert is consulted to assign a score. This score can be seen as the expression of his opinion with respect to the preference of criterion by energy sources. - Step 3. The same experts are invited to get the importance of the evaluation main energy consumable sectors S e , e = 1, . . . , E, with respect to various criteria C i , i = 1, . . . , m, using linguistic variables. - Step 4. Convert the linguistic variables into triangular fuzzy numbers (i.g. R ijk = l ijk , m ijk , u ijk for criterion j and energy source i by expert k or R ejk = a ejk , b ejk , c ejk for criterion j and sector e).

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Step 5. Determine of the consensus index of each expert relative to other experts using the similarity measure function. The energy experts consulted were asked to give their opinion on the evaluation matrices. This process was repeated several times until a consensus emerged. In this step, a new consensus index algorithm is proposed as mentioned in Figure 2.  Each expert prepares two matrices (energy source evaluation matrix and sector evaluation matrix). The consensus algorithm performs the two activities "determining their energy consensus index" and "determining their sector consensus index" in parallel to check the degree of consensus of each matrix. Using the proposed consensus algorithm, the energy consensus index or the sector consensus index can be calculated for each tour ( ) and for each energy expert . Rules have been introduced into the proposed algorithm. First, a rule has been proposed to calculate the sum of the rank of expert k and its relative compatibility with other experts. If the value of this rule is 0, the consensus index is 100%. Subsequently, an average degree of agreement or , was introduced; when or ≥ 0, the degree of expert consensus is accepted, otherwise, the algorithm forces another round of Each expert prepares two matrices (energy source evaluation matrix and sector evaluation matrix). The consensus algorithm performs the two activities "determining their energy consensus index" and "determining their sector consensus index" in parallel to check the degree of consensus of each matrix. Using the proposed consensus algorithm, the energy consensus index sc ijkp or the sector consensus index sc ejkp can be calculated for each tour (p or q) and for each energy expert k.
Rules have been introduced into the proposed algorithm. First, a rule has been proposed to calculate the sum of the rank of expert k and its relative compatibility with other experts. If the value of this rule is 0, the consensus index is 100%. Subsequently, an average degree of agreement sc ijkp or sc ejkq , was introduced; when sc ijkp or sc ejkq ≥ 0, the degree of expert consensus is accepted, otherwise, the algorithm forces another round of consultation. - Step 6. Aggregate the fuzzy evaluations by R ij = l ij , m ij , u ij or R ej = a ej , b ej , c ej , whose main target is to aggregate the evaluation matrices experts to a single matrix, where Step 7. Defuzzification of the fuzzy sector decision matrix ( R ejk ) based on best nonfuzzy performance (BNP) which is expressed in Equation (3).
Therefore, the final results of the fuzzy Delphi method are the fuzzy energy sources evaluation R ij and the priorities of different sectors BNP ej , which will be the main inputs of the fuzzy TOPSIS method.

Fuzzy TOPSIS Method
The TOPSIS approach was developed by Hwang and Yoon [42] for ranking the alternatives according to various criteria in several fields. In this paper, the fuzzy TOPSIS approach is applied in the energy field to rank the best sectoral energy sources. The process of the fuzzy TOPSIS approach is illustrated as follows: Equation (4) normalizes the benefit criteria decision matrices. Equation (5) normalizes the cost criteria decision matrices. Equation (6) determines the weighted normalized fuzzy decision matrices v ije . Equation (7) specifies the positive ideal solutions (A + e ) for each sector e. Equation (8) specifies the negative ideal solutions (A − e ) for each sector e. Equation (9) determines the distances from the positive ideal solutions (d + ie ) for each sector e. Equation (10) determines the distances from the negative ideal solutions (d − ie ) for each sector e. Equation (11) computes the closeness coefficient (CC ie ) for each energy source i and for each sector e. The water resource with the highest CC ie value represents the best energy sources for sector e. According to the fuzzy MCGDM approach, the sectoral rankings of energy sources are shown.

Sensitivity Analysis of FMCGDM Approach
A sensitivity analysis of FMCGDM results is applied to assess how the optimal solution is affected by the coefficients of the objective function. For sensitivity analysis of the fuzzy MCGDM approach, we propose a new linear model. This model is based on the assumption that the objective function seeks to maximize the closeness coefficient (CC ie ) for each energy source i and for each sector e.
Max Z(x) = CC ei × y ei (12) Subject to: Equation (13) ensures that the three best energy sources are selected for each sector. Equation (14) introduces binary variables to the problem.

Results
The proposed approach is based on three input types, including the following: (1) four energy experts; (2) the different criteria observed in Tunisian energy; (3) the evaluations of the different user energy sectors according to the different criteria using the results of energy expert consultations.

Consulting the Experts and Preparing the Datasets
In this study, we consulted four energy experts EX k , k = 1, . . . , 4, to propose the lists of evaluation criteria, energy sources, and the main energy consumable sectors. Table 2 presents the list of evaluation criteria, Table 3 presents the list of energy sources, and Table 4 presents the list of energy consumable sectors.   Table 3. List of energy sources.

Aspect Symbols Energy Sources Description
Renewable source A1 Geothermal Stored and created inside the earth in the form of thermal energy.

A2 Solar
Obtained energy from the sun by radiation.

A3
Wind Obtained using special blades to catch the wind and convert it into electrical energy.

A4 Hydraulic
Obtained energy from flowing water.

A5 Biomass
Composed of organic matter like industrial waste, agricultural waste, wood, and bark.
Nonrenewable source A6 Natural Gas Formed deep beneath the earth's surface.

A7 Oil
Formed when heat and pressure compress the remains of prehistoric plants, animals, and aquatic life under the bed of the sea or lakes for millions of years, thus becoming a fossil fuel.

A8
Coal Extracted from the earth through underground mining or surface mining. In this study, in order to be able to obtain the triangular fuzzy matrices, we utilized the fuzzy linguistic variables presented in Table 5. Medium Strong MS (4.00, 5.00, 5.00) 7 Strong S (4.00, 5.00, 6.00) 8 Very Strong VS (6.00, 7.00, 7.00) 9 Absolutely Strong AS (7.00, 7.00, 7.00) The calculus detail is given in the Supplementary Materials. For each criterion C j of energy source A i , an expert is consulted to assign a score. This score can be seen as the expression of his opinion with respect to the preference of criterion by energy sources. All scores are presented in Table S1. After that, the experts consulted prepared an evaluation of the main energy consuming sectors S e , i = 1, . . . , 5, with respect to various criteria C i , i = 1, . . . , 11, using linguistic variables. Table S2 presents all theses decision opinions on sectors. Next, the consensus index is calculated based on the proposed consensus algorithm. The algorithm has ensured that the degrees of consensus are greater than 75% based on the different scores (sc ijkp or sc ejkq ) presented in Table S1. Then, the aggregation of energy source decision matrices is determined according to Equation (1) in Table S3. The aggregation of sector decision matrices is determined according to Equation (2) in Table S4.
In this study, the defuzzification of the fuzzy sector decision matrix ( R ejk ) is obtained with the BNP technique according to Equation (3). The results obtained are normalized (w ej ) and they are presented in Table 6. Next, the final results of the fuzzy Delphi method are the fuzzy energy sources evaluation R ij and the priorities of different sectors BNP ej , which will be the main inputs of the fuzzy TOPSIS method.

Preparing the Sectoral Rankings of Energy Sources
According the fuzzy TOPSIS method, the sectoral rankings of energy sources are shown in Table 7. The calculation of the closeness coefficient sectoral rankings of energy sources is done according to Equations (4)- (11), and the results of this step are given in Table 7. Finally, the rankings of the energy sources of each user sector are determined.

Sensitivity Analysis of FMCGDM Approach
Sensitivity Analysis of FMCGDM results is applied to assess how the optimal solution is affected by the coefficients of the objective function. For sensitivity analysis of the fuzzy MCGDM approach, we applied the linear proposed model according to Equations (12)- (14). Using LINDO software, the sensitivity report for this problem appears in Figure 3.

Discussion
The discussion section follows a comparison of the results obtained with the results of previous research in the field. From several previous studies, a gap was found in the research because researchers rank the energy sources for a single energy user sector. In addition, a sensitivity analysis is the study of how the uncertainty in the output of a mathematical model can be divided between various uncertainties in its inputs.

Discussion
The discussion section follows a comparison of the results obtained with the results of previous research in the field. From several previous studies, a gap was found in the research because researchers rank the energy sources for a single energy user sector.
For example, Garni el al. [9] mentioned that the photovoltaic is the best source of energy for the domestic sector in Saudi Arabia, using the AHP method. In contrast, Chatzimouratidis et al. [6] proposed the geothermal source for the same sector in Greece. In Italy, the study of Chinese et al. [7] showed that natural gas is the best energy source for the industrial sector using the AHP method and Beccali et al. [12] selected the geothermal source for the agricultural sector based on ELECTRE methods. In addition, the study of Kaya and Kahraman [14] ranked wind power as the best source for the domestic sector in Turkey and the study of Talukdar et al. [15] selected the solar photovoltaic source for the domestic sector in Bangladesh, according to the TOPSIS method.
In this paper, multi-sector energy ranking is discussed. Table 7 shows the final sectoral energy sources ranking of the proposed approach. The results show that: -Biomass energy is ranked first, followed by wind energy, and solar energy is ranked third for the agricultural sector. These energy sources are the best solutions to ensure a sustainable energy source selection for the agricultural sector in the long term. According to the consulted experts, biomass energy is very profitable in agricultural areas. -Wind, solar, and biomass energies are successively the best energy sources for the domestic sector. These energy sources are the best solutions to ensure a sustainable energy source selection for the domestic sector in the long term. -For the industrial sector, the first three energy sources are wind, solar, and biomass energies. These energy sources are the best solutions to ensure a sustainable energy source selection for the industrial sector in the long term. -Wind energy is ranked first, followed by solar energy and then hydraulic energy for the tourism sector. These energy sources are the best solutions to ensure sustainable energy source selection for the tourism sector in the long term. According to the consulted experts, hydraulic energy is very profitable for tourism in coastal areas. -For the transport sector, natural gas energy is ranked first, followed by oil energy, and coal energy is ranked third. These energy sources are the best solutions to ensure a sustainable energy source selection for the transport sector in the long term. According to the experts consulted, fossil fuels are the most profitable sources for the transport sector at the present time.
In addition, Figure 3 indicates the amounts by which the objective function coefficients can be changed unilaterally without affecting the character of the optimal solution. The allowable increase/decrease associated with the original coefficient of a decision variable tells us the range within which the coefficient of a given decision variable in the objective function may be increased/decreased without changing the optimal solution, where all other data are fixed.

Conclusions
This paper applies a fuzzy MCGDM approach to evaluate and prioritize energy sources for various sectors based on technical, economic, environmental, social, and political criteria. A sensitivity analysis of the FMCGDM results is used to see how the optimal solution is affected by the objective function coefficients and to see how the optimal value is affected by the right-hand side values.
Sectoral energy sources ranking is obtained using the FMCGDM method. The priorities of criteria are estimated in each sector using experts' opinions through the fuzzy Delphi method. The industrial, agricultural, domestic, and tourism sectors are defined, and comparisons from one to another is regarded as a sectoral energy transaction. This approach is adopted as a convenient way to gauge sectoral energy source selections. The proposed approach is useful to be applied for other problems containing multiple objectives, sources, and users.
Every study has limitations that should be addressed in future research. In this regard, we will consult a large number of national experts as well as international experts. As a future research suggestion, different optimization models can be utilized to solve the sectoral or intersectoral energy source selection problem and the results can be compared with this study. Furthermore, different extensions of MCGDM or MAMCA methods can be applied to these problems. Finally, robustness analyses based on mathematical programs can be realized.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/en14144313/s1, Table S1: Decision matrices of energy sources, Table S2: Decision opinions of sectors, Table S3: Aggregate matrix of decision energy sources, Table S4: Aggregate matrix of decision sectors.  Acknowledgments: This research was supported by Taif University Researchers Supporting Project number (TURSP-2020/229), Taif University, Taif, Saudi Arabia. Firstly, the authors are grateful for this financial support. Secondly, the authors would like to thank the four following experts: Ahmed Kammoun, director of SPECTRA company; Rami Gharsallah, director of Joule Energy Company; Ahmed Naifar, Director of Nour Energy Company; and Ridha Elleuch, Doctor in physics and renewable energy. Finally, the authors thank the editor and the anonymous referees for their valuable comments on an earlier version of this paper.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following acronyms and notations are used in this manuscript: : Triangular fuzzy numbers for criterion j and energy source i by expert k; R ejk : Triangular fuzzy numbers for criterion j and user sector e by expert k; sc ijkp : Energy consensus index; sc ejkp : Sector consensus index; R ij : Aggregated Triangular fuzzy numbers for criterion j and energy source i by expert k; R ej : Aggregated Triangular fuzzy numbers for criterion j and user sector e by expert k; BNP ej : Best Non-fuzzy Performance numbers for criterion j and user sector e; r ij : Normalized the criteria decision matrices; v ije : Weighted normalized fuzzy decision matrices; A +