Selection of Renewable Energy Projects from the Investor’s Point of View Based on the Fuzzy–Rough Approach and the Bonferroni Mean Operator

Abstract

More and more investments are being made in energy conversion projects from renewable energy sources (RESs), and a large number of investors are entering this sector. The focus of this study is the decision-making by the investor BD Green Energy in the Brčko District of Bosnia and Herzegovina. In order to choose the RES system that would realize this investment in the most efficient way, expert decision-making based on the fuzzy–rough approach and the Bonferroni mean operator was used. Determining the importance of the criteria was conducted using the fuzzy–rough SiWeC (simple weight calculation) method. The results of this method showed that all used criteria have similar importance for the investor. RES system selection was conducted using the fuzzy–rough CoCoSo (combined compromise solution) method. The results of this method showed that investing in photovoltaic (PV) energy is the best for the investor. This research provided guidance on how investors should make investment decisions in RES systems with incomplete information and uncertainty in the decision-making process.

1. Introduction

Increasing concern for the environment in the world has conditioned the development of environmentally friendly projects [1]. More and more attention is being paid to renewable energy sources (RESs). RESs are becoming an essential segment of the global strategy for sustainable development and reduction in greenhouse gas emissions. The use of these energy sources reduces the emission of greenhouse gases that are emitted by fossil fuels. An increasing share of the world is energy produced from RES systems [2], and the demand for electricity is also increasing. Consumption has increased by 4.5 times in the last 60 years [3] and is increasing. That is why many investors consider this branch of energy.

Technology is changing and is aimed at making better use of RESs in order to produce as much energy as possible that has the green energy prefix [4]. In addition, the tendency is to reduce the impact on the environment, especially in the electricity production sector [5]. With new strategic orientations, many countries strive to improve the production of green energy in order to solve the problem of dependence on fossil energy sources [6]. This trend includes more and more industries that must undergo transformation in order for this industry to be sustainable [7].

The demand for electricity is increasing, and more attention is being paid to the production of electricity. A constant increase in electricity prices can be expected in the future. The reason for this should be found in the fact that the increased demand for electricity affects the increase in prices as well. This price will greatly influence the introduction of more RES systems in order to produce a greater amount of electricity, especially from renewable energy sources. That is why it is necessary to increasingly involve both public institutions and private investors in the production of electricity from the RES system.

Investing in these capital projects has an impact on economic and environmental prosperity, where this transition to green energy is often conditioned by the limited resources that countries have at their disposal. In developing countries, which include Bosnia and Herzegovina (BiH), more attention has been paid to RES projects in the last few years. In order to become competitive in the market, Bosnia and Herzegovina must increase energy conversion from RESs. In addition, investors are increasingly investing in these projects in order to achieve certain benefits. The specificity of BiH is its constitutional arrangement, which consists of two entities and the Brčko District of BiH. The entities were legally regulated and provided with guidelines for the development of the RES system. The Brčko District of BiH has yet to pass legal regulations and start investing in the RES system.

The Brčko District of BiH, as a specific administrative unit that has the status of a district, tends to modernize the energy infrastructure. In this way, global trends are followed and long-term stability is ensured. For this reason, efforts are being carried out on the adoption of special laws and by-laws that will provide legal regulation and the possibility of expansion of investment in RES system projects. In this context, the identification and prioritization of these projects becomes crucial for the success of the project. When prioritizing projects, various criteria are considered in order to see as many aspects of those projects as possible. This is why a multi-criteria decision-making process was developed, which is successfully solved using multi-criteria decision-making methods (MCDMs).

By applying MCDMs, the importance of the criteria is first determined, and then the observed capital projects are prioritized. However, investing in capital projects brings with it problems of uncertainty and insecurity, and there are no complete data with which to make a reliable and safe decision. That is why more advanced decision-making systems that include fuzzy and rough approaches are included in the decision-making process. The fuzzy approach enables the use of imprecise information in decision-making [8], while the rough approach includes uncertainty in decision-making. In addition, the rough approach reduces the subjective influence of the experts used in the research. Therefore, in this research, the fuzzy–rough approach is used, which integrates the fuzzy and rough approaches into one whole, using the advantages of both approaches.

In this research, an evaluation of possible capital investment in RES systems projects by the investor BD Green Energy is carried out. This is a newly formed company representing a consortium of foreign and domestic investors who plan to invest in RES systems. Every capital investment entails an initial investment that needs to be recouped over the duration of the project. The longer the payback time, the riskier the investment in a capital project, so it is necessary to determine priorities when investing in RES projects in the Brčko District of BiH. The motivation of this research is reflected in the consideration of all the essential characteristics of the RES system and the inclusion of uncertainty in the decision-making process in order to make a decision that will have the best effects for the investor, BD Green Energy.

Based on all that has been said, the goal of this research is to determine the prioritization of capital investments in RES system projects using the fuzzy–rough approach in order to make a decision that will include uncertainty and thus reduce the risk of this investment. Additionally, the focus of this research is on identifying the importance of criteria for the evaluation of these projects. In addition to this main goal, this research aims to achieve the following objectives:

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Identify the key criteria for the assessment of RES system capital projects on the territory of the Brčko District of BiH.

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Perform an analysis of the possibility of using individual RES system projects on the territory of the Brčko District of BiH.

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Apply a research methodology based on the use of the fuzzy–rough approach that includes uncertainty in decision-making and the application of the Bonferroni mean operator.

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Produce proposals for the prioritization of investment projects in RES systems in order to use the potential available to the Brčko District of BiH.

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Carry out an evaluation of the sustainability of the RES system project on the territory of the Brčko District of Bosnia and Herzegovina.

By achieving these research objectives, the theoretical and practical contributions of both the BD Green Energy company and the Government of the Brčko District of BiH are realized. These contributions are as follows:

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Help the sustainable development of the Brčko District of BiH, where investments in RES systems aimed at reducing CO₂ and increasing energy independence in this area will increase.

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Establish guidelines for the development of the RES system in the Brčko District for both investors and the local government.

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Contribute to the development of the methodology based on the fuzzy–rough approach to energy projects in the future.

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Develop a research model that includes key criteria for decision-making when prioritizing RES system projects in practice.

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Improve the decision-making process in the complex conditions prevailing in practice, which are characterized by uncertainty and risk in capital projects.

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Upgrade the existing methods and use of the Bonferroni mean operator.

2. Literature Review

In many studies, MCDMs have been used to select which project in the form of an RES system is best suited for a certain area or for an investor. Therefore, in the rest of the text, only some research on this topic will be cited in order to show that MCDMs can be used in the selection of RES systems.

Deveci et al. [9] used the interval-valued intuitionistic fuzzy CODAS (COmbinative Distance-based ASsessment) method to select an RES system in the example of Turkey. Using this methodology, it was determined that it is best to use wind power to generate electricity. Bilgili et al. [10] also used the intuitionistic fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method to examine the possibility of investing in RES systems using the example of Turkey. Unlike the research of Deveci et al. [9], they obtained the results that the best RES system is the energy conversion from saline sources. Using the example of India, Saraswat and Digalwar [11] determined using Shannon’s entropy and fuzzy AHP (analytical hierarchy process) methods that the best RES system is photovoltaic energy, followed by wind and water energy.

Büyüközkan and Güleryüz [12] evaluated the RES system using the linguistic interval fuzzy preference and the DEMATEL (decision-making trial and evaluation laboratory), ANP (analytic network process), and TOPSIS methods. Their results showed that the most suitable RES system for Turkey would be the use of geothermal sources. Lee and Chang [13] evaluated the RES system for the area of Taiwan using the following methods: WSM (weighted sum method), VIKOR (ser. VIseCriteria Optimization and Compromise Solution), TOPSIS, and ELECTRE (elimination and choice translating reality). The results of this approach showed that the best results are shown by the use of hydro sources as an RES system.

Çolak and Kaya [14] used Interval type-2 fuzzy AHP and TOPSIS methods to evaluate RES systems in Turkey. The results of these methods showed that the best-evaluated RES alternative is energy conversion from the wind. These results were confirmed for Turkey by Solangi et al. [15] who used the fuzzy AHP and WASPAS (weighted aggregated sum product assessment) methods. Rani et al. [16] investigated the implementation of RES systems in India using the fuzzy TOPSIS method. The results of this approach showed that wind energy conversion is the best-rated RES system.

When looking at the research carried out in the area of Bosnia and Herzegovina (BiH) with regard to the RES system, it is possible to single out several such studies. Jeločnik et al. [17] studied the implementation of the RES system in the rural areas of the Western Balkans, including BiH, using the fuzzy–rough approach with the LMAWs (Logarithm Methodology of Additive Weights) and CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) methods. The results of this research showed that the use of photovoltaic energy showed the best results of RES alternatives. Puška et al. [18] used the fuzzy DiWeC (direct weight calculation) and RAWEC (ranking of alternatives with weights of criteria) methods to ensure sustainable agriculture in BiH. The results of this approach showed that photovoltaic energy is the best RES alternative.

Based on these studies and many others that are not included in the literature review, it can be concluded that the choice of projects in the form of RES systems depends on the criteria used and on the area under observation. In addition, RES system research in the area of BIH has not been represented on a larger scale so far, but rather in individual papers. Most consider the use of RES systems in general and not from the position of investors, and uncertainty is not included in the decision-making process. All these gaps are considered in this research and results are provided for a specific microlocation from the perspective of investors including uncertainty using the fuzzy–rough approach.

3. Materials and Methods

When conducting research for the needs of BD Green Energy, experts who evaluated projects in RES systems were first identified. In this way, five experts who have many years of experience in implementing the same and similar projects were appointed. All experts are from the field of electrical engineering and mechanical engineering because they are the best acquainted with RES systems and have enough knowledge to be able to determine which RES system to invest in for the Brčko District of BiH. Their task is to provide their opinion on which RES system should be used for electricity production, that is, which system has the best indicators. Establishing the expert’s opinion is only the initial stage in making the final decision. Therefore, this study is defined as preliminary research that will identify which RES systems can be used to produce electricity from sustainable sources. However, the final decision must be made considering, firstly, the situation of the Brčko District of BiH in terms of the number of inhabitants and the current consumption of electricity, and secondly, how to make this region more independent in energy production. This investment would be implemented in those same locations. After the experts were selected, the research steps presented in Figure 1 were implemented.

The first step in the preparatory actions for conducting this research was the determination of research criteria and alternatives. In this research, a total of ten criteria were determined according to which the alternatives are evaluated (

Table 1. Research criteria.

Id	Criterion	Description	References
C1	Implementation costs	Estimate of the total costs required for the implementation of the RES system	[9,10,11,12,13,15,16]
C2	Energy efficiency	The amount of energy generated in relation to the energy invested in the RES system	[10,13,14,15,16]
C3	Impact on ecology	The impact of the RES system on the ecology, which includes the emission of CO2 and water and air pollution	[9,10,11,12,14,16]
C4	Social acceptability	Assessment of how acceptable the RES system is for the social community where it is implemented	[10,12,13,14,15,16]
C5	Technological maturity	The degree of development and reliability of the RES system	[11,12,13,14,15]
C6	System flexibility	The possibility of increasing the RES system depending on the needs of the market	[9,10,11,14]
C7	Long-term sustainability of the project	The possibility of long-term use of RES systems without depleting resources	[12,14,15]
C8	Legal and regulatory requirements	Alignment of the RES system with legal and regulatory standards	[10,11,12]
C9	Implementation timeline	The time required to implement the RES system until it is fully operational	[10,11,12,14]
C10	Financial viability	The possibility of generating long-term income that justifies the RES system	[11,12]

), and then six RES systems were determined in the form of projects that BD Green Energy could invest in within the Brčko District of Bosnia and Herzegovina as follows:

• Photovoltaic (A1): Use of photovoltaic panels to produce electricity.
• Wind power plants (A2): Energy conversion using wind turbines.
• Hydropower (A3): Generation of electricity using hydro potential.
• Biomass (A4): Use of organic material for energy conversion.
• Geothermal energy (A5): Use of heat from the interior of the Earth to produce electricity.
• Energy from waste (A6): Generation of electricity by burning waste.

Using the mentioned criteria and alternatives, the decision-making model and a survey questionnaire were formed. In the first part of the questionnaire, the experts should determine the importance of the criteria for the selection of RES systems, and in the second part of the questionnaire, the experts should determine how the RES systems meet these criteria. In order for the experts to evaluate the criteria and alternatives, they had at their disposal linguistic values with a value scale of seven levels ranging from very bad to very good. A unique scale value was used for the evaluation of criteria and alternatives, thus facilitating evaluation by experts (

Table 2. Linguistic values and membership functions.

Linguistic Values	Membership Functions
Very bad (VB)	(1, 1, 2)
Bad (B)	(1, 2, 3)
Medium bad (MB)	(2, 3, 4)
Medium (M)	(4, 5, 6)
Medium good (MB)	(6, 7, 8)
Good (G)	(7, 8, 9)
Very good (VG)	(8, 9, 9)

).

In order to use these values in this research, they were transformed into fuzzy colors by applying the defined membership function (Table 2). This function determines which fuzzy value belongs to a particular linguistic value. Triangular fuzzy numbers were used in this research, and they are determined by the membership function into which certain linguistic values are transformed into fuzzy numbers. So, the linguistic value very bad is transformed into a fuzzy number (1, 1, 2) (Table 2). Based on this membership function, the transformation of linguistic values into fuzzy numbers is determined.

Since it is necessary to evaluate the criteria and alternatives in this research, in order to facilitate the evaluation process, the same linguistic values were used. The next step was the harmonization of experts’ ratings, which was conducted using the Bonferroni mean operator. The reconciliation is the score I to determine the importance of criterion I to evaluate the alternative. By applying this operator, the steps of the fuzzy–rough SiWeC (simple weight calculation) and CoCoSo (combined compromise solution) methods are corrected, with the fact that the SiWeC method is corrected more than the CoCoSo method. These methods are explained below.

The SiWeC method belongs to the methods that determine the weight based on the evaluations of decision makers or experts. This method belongs to the methods for subjective determination of criteria weights. The SiWeC method is designed to make it easier for experts to determine the importance of weights in such a way that experts evaluate how important a certain criterion is to them, without taking into account other criteria [19]. By applying this approach, experts do not have to rank criteria, compare each other, or determine the importance of one criterion in relation to another. In order to use this method, special steps are developed to adapt it to the fuzzy–rough approach. Those steps are as follows:

Step 1. Determination of the importance of criteria by expert evaluation. In this step, experts evaluate individual criteria according to their importance and assign them appropriate linguistic values.

Step 2. Transformation of linguistic values into fuzzy numbers. In this step, defined membership functions are used to transform the linguistic value into a fuzzy number:

$${\tilde{x}}_{ij}=\left(x_{ij}^l,x_{ij}^m,x_{ij}^u\right)$$

(1)

where $x_{ij}^l$ is the first fuzzy number, $x_{ij}^m$ is the second fuzzy number, and $x_{ij}^u$ is the fuzzy number.

Step 3. Transformation of fuzzy numbers into fuzzy–rough numbers. In this step, the lower and upper limits of the rough number are determined for each individual fuzzy number.

$$\underset{\_}{Lim}\left(c_i^e\right)={\displaystyle \frac{1}{{\underset{\_}{N}}^e}}{\sum }_{i=1}^{{\underset{\_}{N}}^e}\phi ϵ\underset{\_}{Apr}\left(c_i^e\right),$$

(2)

$$\overline{Lim}\left(c_i^e\right)={\displaystyle \frac{1}{{\underset{\_}{N}}^e}}{\sum }_{i=1}^{{\overline{N}}^e}\phi ϵ\overline{Apr}\left(c_i^e\right),$$

(3)

When the lower limit is determined, the same and smaller values are taken from the value of each criterion for the expert, and the average of these values is calculated. When determining the upper limit, the same or higher values are taken for each criterion and expert, and the average value of these values is requested. In this way, a fuzzy–rough decision-making matrix is formed as follows:

$$FR\left({\tilde{x}}_{ij}\right)=\left(\left[x_{ij}^{lL},x_{ij}^{lU}\right],\left[x_{ij}^{mL},x_{ij}^{mU}\right],\left[x_{ij}^{uL},x_{ij}^{uU}\right]\right)$$

(4)

Step 4. Normalization of the initial fuzzy–rough decision matrix.

$${\stackrel{=}{n}}_{ij}=\left(\left[{\displaystyle \frac{{\alpha }^{lL}}{{max}_i{\alpha }_i^{uU}}}.{\displaystyle \frac{{\alpha }^{lU}}{{max}_i{\alpha }_i^{uU}}}\right]. \left[{\displaystyle \frac{{\alpha }^{mL}}{{max}_i{\alpha }_i^{uU}}}.{\displaystyle \frac{{\alpha }^{mU}}{{max}_i{\alpha }_i^{uU}}}\right].\left[{\displaystyle \frac{{\alpha }^{uL}}{{max}_i{\alpha }_i^{uU}}}.{\displaystyle \frac{{\alpha }^{uU}}{{max}_i{\alpha }_i^{uU}}}\right]\right)$$

(5)

where ${max}_i{\alpha }_i^{uU}$ is the highest value of the fuzzy–rough number for all values of the fuzzy–rough decision matrix.

Step 5. Calculation of the standard deviation value (${\mathrm{s}\mathrm{t}.\mathrm{d}\mathrm{e}\mathrm{v}}_{\mathrm{j}}$) for individual experts. Here, the value of the standard deviation for all values of fuzzy–rough numbers for individual experts is calculated.

Step 6. Plotting of normalized scores with standard deviation values.

$${\stackrel{=}{v}}_{\mathrm{i}\mathrm{j}}={\stackrel{=}{n}}_{\mathrm{i}\mathrm{j}}\times {\mathrm{s}\mathrm{t}.\mathrm{d}\mathrm{e}\mathrm{v}}_{\mathrm{j}}$$

(6)

In the seventh step, the step from the original SiWeC method where the sum of values is calculated with the Bonferroni mean operator calculation step is changed. With this operator, the average value for all criteria is calculated.

Step 7. Calculation of average values for individual criteria using the Bonferroni mean operator.

$${\stackrel{=}{s}}_j={\left({\displaystyle \frac{1}{k(k-1)}}{\sum }_{\begin{array}{c}i.j=1\\ i\ne j\end{array}}^k{\stackrel{=}{n}}_i^{\left(UL\right)p}{\stackrel{=}{n}}_i^{\left(UL\right)q}\right)}^{{\displaystyle \frac{1}{p+q}}}$$

(7)

Step 8. Calculation of fuzzy–rough criteria weight criteria weight values.

$${\stackrel{=}{w}}_{ij}=\left(\left[{\displaystyle \frac{s_j^{lL}}{\sum _{j=1}^n{s}_j^{uU}}}.{\displaystyle \frac{s_j^{lU}}{\sum _{j=1}^n{s}_j^{uL}}}\right]. \left[{\displaystyle \frac{s_j^{mL}}{\sum _{j=1}^n{s}_j^{mU}}}.{\displaystyle \frac{s_j^{mU}}{\sum _{j=1}^n{s}_j^{mL}}}\right].\left[{\displaystyle \frac{s_j^{uL}}{\sum _{j=1}^n{s}_j^{lU}}}.{\displaystyle \frac{s_j^{uU}}{\sum _{j=1}^n{s}_j^{lL}}}\right]\right)$$

(8)

After the steps of the fuzzy–rough SiWeC method are presented, the fuzzy–rough CoCoSo method is presented. The CoCoSo method was first used in their research by Yazdani et al. [20]. This method is a combination of two methods: simple additive weighting (SAW) and exponentially weighted product model (WPM) [21]. The steps of the fuzzy–rough CoCoSo method are as follows:

Step 1. Formation of the initial decision matrix. In this step, experts evaluate alternatives with selected criteria using linguistic values.

The second and third steps are the same as the fuzzy–rough SiWeC method, as follows:

Step 2. Transformation of linguistic values into fuzzy numbers.

Step 3. Transformation of fuzzy numbers into fuzzy–rough numbers.

After this step, the Bonferroni mean operator is used to align the experts’ ratings and form a common initial fuzzy–rough decision matrix.

Step 4. Formation of the joint fuzzy–rough decision matrix. In this step, the average value for each criterion and alternative and for all experts is calculated using the Bonferroni mean operator as follows:

$$FR\left({\tilde{x}}_{ij}\right)={\left({\displaystyle \frac{1}{k(k-1)}}{\sum }_{\begin{array}{c}i.j=1\\ i\ne j\end{array}}^k{\stackrel{=}{x}}_i^{\left(UL\right)p}{\stackrel{=}{x}}_i^{\left(UL\right)q}\right)}^{{\displaystyle \frac{1}{p+q}}}$$

(9)

Step 4. Normalization of the fuzzy–rough decision matrix.

$${\stackrel{=}{n}}_{ij}=\left(\left[{\displaystyle \frac{x_{ij}^{lL}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}};{\displaystyle \frac{x_{ij}^{lU}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}}\right]\left[{\displaystyle \frac{x_{ij}^{mL}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}};{\displaystyle \frac{x_{ij}^{mU}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}}\right]\left[{\displaystyle \frac{x_{ij}^{uL}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}};{\displaystyle \frac{x_{ij}^{uU}-x_{i min}^{lL}}{x_{i max}^{uU}-x_{i min}^{lL}}}\right]\right)$$

(10)

where ${\alpha }_{i max}^{uU}$ is the maximum value of the fuzzy rough number for a certain criterion; ${\alpha }_{i min}^{lL}$ is the minimum value of the fuzzy rough number for a certain criterion.

Step 5. Determining the v $S_i$ and $P_i$ values.

$${\stackrel{=}{S}}_i=\sum _{j=1}^n\left({\stackrel{=}{n}}_{ij}·{\stackrel{=}{\omega }}_j\right)$$

(11)

$${\stackrel{=}{P}}_i=\sum _{j=1}^n{\left({\stackrel{=}{n}}_{ij}\right)}^{{\stackrel{=}{\omega }}_j}$$

(12)

Step 6. Transformation of fuzzy–rough numbers into crips numbers.

$$S_i=\left({\displaystyle \frac{S_i^{lL}+S_i^{lU}+S_i^{mL}+S_i^{mU}+S_i^{uL}+S_i^{uU}}{6}}\right)$$

(13)

$$P_i=\left({\displaystyle \frac{P_i^{lL}+P_i^{lU}+P_i^{mL}+P_i^{mU}+P_i^{uL}+P_i^{uU}}{6}}\right)$$

(14)

Step 7. Calculations of relative weights of alternatives for three strategies.

$${\xi }_{ia}={\displaystyle \frac{P_i+S_i}{\sum _{i=1}^m\left(P_i+S_i\right)}}$$

(15)

$${\xi }_{ib}={\displaystyle \frac{S_i}{\underset{i}{\min }{S}_i}}+{\displaystyle \frac{P_i}{\underset{i}{\min }{P}_i}}$$

(16)

$${\xi }_{ic}={\displaystyle \frac{\lambda \left(S_i\right)+(1-\lambda )\left(P_i\right)}{\left(\lambda \underset{i}{\max }{S}_i+(1-\lambda )\underset{i}{\max }{P}_i\right)}};0\le \lambda \le 1$$

(17)

Value $\lambda$ is usually 0.5 although this value can be from zero (0) to one (1).

Step 8. Determination of the final ranking.

$${\xi }_i={\left({\xi }_{ia}·{\xi }_{ib}·{\xi }_{ic}\right)}^{1/3}+{\displaystyle \frac{1}{3}}({\xi }_{ia}+{\xi }_{ib}+{\xi }_{ic})$$

(18)

The best alternative has the highest value of the CoCoSo method and vice versa.

After determining the importance of the criteria using the fuzzy–rough SiWeC method and ranking the alternatives using the fuzzy–rough CoCoSo method, two more analyses were performed, namely comparative analysis and sensitivity analysis. A comparative analysis was conducted to confirm the results obtained in this case with the fuzzy–rough CoCoSo method. This was carried out by using a summary decision matrix and the same weight, but the ranking of alternatives was conducted using other fuzzy–rough methods. In this way, we examined whether different steps of those methods provide the same or different results. If the results are similar or the same, then the original results are confirmed. Sensitivity analysis was used to examine how individual criteria weights affect the final ranking. In this way, we examined how certain criteria affect the ranking of alternatives. By means of this analysis, the pros and cons of certain alternatives can be determined to identify which criteria should be improved in order to make an alternative better.

4. Results

When filling out the questionnaire, the experts first determined the importance of the criteria and then evaluated the alternatives based on these criteria. For this reason, the weights of the criteria were calculated first and then the alternatives were ranked. In addition, it was necessary to have criteria weights in order to rank the alternatives. The task of the experts in evaluating the criteria was to determine the importance of individual criteria by applying a defined scale of values (

Table 3. Evaluation of criteria by experts.

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
Expert 1 (E1)	G	VG	VG	MG	G	MG	VG	M	M	G
Expert 2 (E2)	VG	VG	VG	MG	G	G	VG	MG	MG	G
Expert 3 (E3)	MG	VG	G	G	MG	MG	VG	M	MB	G
Expert 4 (E4)	G	VG	G	MG	MG	M	G	M	M	G
Expert 5 (E5)	VG	VG	G	MG	G	M	G	M	M	G

). Once the ratings were collected, the process of transforming these linguistic values into fuzzy–rough numbers began.

First, the linguistic value was transformed into a fuzzy number using the membership function (Table 2). In the example of the value of expert E1 for criterion C1, the linguistic value good (G) was transformed into a fuzzy number (7, 8, 9). The transformation was carried out in the same way for other values. Then, the lower and upper bounds of the rough number were found for each individual fuzzy number. The calculation of this example was as follows:

$$C_{11}^{lL}={\displaystyle \frac{7+6+7}{3}}=6.67;C_1^{lU}={\displaystyle \frac{7+8+7+8}{4}}=7.50;$$

$$C_{11}^{mL}={\displaystyle \frac{8+7+8}{3}}=7.67; C_{11}^{mU}={\displaystyle \frac{8+9+8+9}{4}}=8.50;$$

$$C_{11}^{uL}={\displaystyle \frac{9+9+8+9+9}{5}}=8.80;C_{11}^{uU}={\displaystyle \frac{9+9+9+9}{4}}=9.00.$$

The values of fuzzy–rough numbers for all other values were calculated in the same way (

Table 4. Calculation of the fuzzy–rough SiWeC method.

	C1						C2							C10
	l	u	l	u	l	u	l	u	l	u	l	u	…	l	u	l	u	l	u
E1	6.67	7.50	7.67	8.50	8.80	9.00	8.00	8.00	9.00	9.00	9.00	9.00	…	7.00	7.00	8.00	8.00	9.00	9.00
E2	7.20	8.00	8.20	9.00	8.80	9.00	8.00	8.00	9.00	9.00	9.00	9.00	…	7.00	7.00	8.00	8.00	9.00	9.00
E3	6.00	7.20	7.00	8.20	8.00	8.80	8.00	8.00	9.00	9.00	9.00	9.00	…	7.00	7.00	8.00	8.00	9.00	9.00
E4	6.67	7.50	7.67	8.50	8.80	9.00	8.00	8.00	9.00	9.00	9.00	9.00	…	7.00	7.00	8.00	8.00	9.00	9.00
E5	7.20	8.00	8.20	9.00	8.80	9.00	8.00	8.00	9.00	9.00	9.00	9.00	…	7.00	7.00	8.00	8.00	9.00	9.00
Normalized decision matrix
	C1						C2							C10
E1	0.74	0.83	0.85	0.94	0.98	1.00	0.89	0.89	1.00	1.00	1.00	1.00	…	0.72	0.78	0.78	0.89	0.89	1.00
E2	0.80	0.89	0.91	1.00	0.98	1.00	0.89	0.89	1.00	1.00	1.00	1.00	…	0.89	0.78	0.78	0.89	0.89	1.00
E3	0.67	0.80	0.78	0.91	0.89	0.98	0.89	0.89	1.00	1.00	1.00	1.00	…	0.67	0.78	0.78	0.89	0.89	1.00
E4	0.74	0.83	0.85	0.94	0.98	1.00	0.89	0.89	1.00	1.00	1.00	1.00	…	0.72	0.78	0.78	0.89	0.89	1.00
E5	0.80	0.89	0.91	1.00	0.98	1.00	0.89	0.89	1.00	1.00	1.00	1.00	…	0.72	0.78	0.78	0.89	0.89	1.00
Multiplied by the standard deviation value
	C1						C2							C10
E1	0.12	0.14	0.14	0.16	0.16	0.17	0.15	0.15	0.17	0.17	0.17	0.17	…	0.12	0.13	0.13	0.15	0.15	0.17
E2	0.11	0.12	0.13	0.14	0.14	0.14	0.12	0.12	0.14	0.14	0.14	0.14	…	0.12	0.11	0.11	0.12	0.12	0.14
E3	0.12	0.14	0.14	0.16	0.16	0.17	0.16	0.16	0.18	0.18	0.18	0.18	…	0.12	0.14	0.14	0.16	0.16	0.18
E4	0.13	0.14	0.14	0.16	0.17	0.17	0.15	0.15	0.17	0.17	0.17	0.17	…	0.12	0.13	0.13	0.15	0.15	0.17
E5	0.14	0.15	0.16	0.17	0.17	0.17	0.15	0.15	0.17	0.17	0.17	0.17	…	0.12	0.13	0.13	0.15	0.15	0.17
Average values were calculated using the Bonferroni mean operator
	C1						C2							C10
E1	0.12	0.14	0.14	0.16	0.16	0.16	0.15	0.15	0.16	0.16	0.16	0.16	…	0.13	0.13	0.15	0.15	0.16	0.16
Criteria weights
	C1						C2							C10
E1	0.08	0.10	0.10	0.12	0.13	0.15	0.10	0.10	0.12	0.13	0.13	0.15	…	0.08	0.09	0.10	0.11	0.13	0.15

). After the fuzzy–rough decision matrix was formed, the next step was the normalization of this decision matrix (Expression 5). This was conducted by dividing all values by nine (9) because this is the largest value for all fuzzy–rough values. Then, the standard deviation was calculated for each expert and the values of their ratings were multiplied by this value (Expression 6). The Bonferroni mean operator was then used to obtain the average values for the individual values of the fuzzy–rough numbers for each criterion (Expression 7). The last step was to calculate the final values by dividing the individual values of fuzzy–rough numbers by the sum of values (Expression 8).

The results of this approach show that only with criteria C8 legal and regulatory requirements and C9 time frame of implementation is there a minor difference in weights, and these criteria are the worst rated, while with other criteria the difference is quite small.

After the weights of the criteria were calculated, the alternatives were ranked based on the experts’ ratings for certain criteria (

Table 5. Evaluations of alternatives by experts.

E1	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
A1	M	MG	VG	G	VG	G	VG	MG	MG	G
A2	M	G	G	MG	G	G	VG	MG	M	MG
A3	MG	VG	M	M	VG	MG	G	G	MB	G
A4	M	MG	MG	MG	G	MG	MG	M	M	MG
A5	MG	G	VG	MG	MG	M	VG	MG	MB	G
A6	M	MG	G	MG	MG	MG	MG	M	M	MG
E2	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
A1	M	G	VG	G	VG	VG	VG	MG	G	G
A2	M	G	G	M	G	G	G	MG	MB	MG
A3	M	VG	MB	M	VG	M	MG	G	MB	G
A4	M	MG	M	MG	G	MG	M	M	M	MG
A5	MG	G	VG	MG	G	M	VG	MG	M	G
A6	MP	MG	MG	M	MG	MG	MG	M	M	M
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
E5	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
A1	M	G	VG	G	VG	G	VG	MG	G	G
A2	M	MG	MG	MB	G	MG	MG	M	MB	M
A3	M	G	MB	M	VG	MB	M	MG	MB	MG
A4	M	MG	MG	MG	MG	MG	MG	M	M	MG
A5	M	MG	VG	MG	MG	MB	G	M	MB	MG
A6	M	MG	MG	M	MG	MG	MG	M	M	MG

). After the experts evaluated the alternatives, the ranking was calculated using the fuzzy–rough CoCoSo method.

The first two steps were carried out in the same way as in the case of the fuzzy–rough SiWeC method, and after that, the experts’ ratings were reconciled using the Bonferroni mean operator (Expression 9). Using this operator, a collective fuzzy–rough decision matrix was formed. The next step was to normalize this decision matrix. With this normalization, the lowest and highest values of the alternatives for individual criteria were found, and the normalization formula (Expression 10) was applied. For the first criterion and alternative A1, normalization was carried out as follows:

$$n_{11}=\left[{\displaystyle \frac{4.0-3.4}{7.3-3.4}}=0.16;{\displaystyle \frac{4.0-3.4}{7.3-3.4}}=0.16\right]\left[{\displaystyle \frac{5.0-3.4}{7.3-3.4}}=0.42;{\displaystyle \frac{5.0-3.4}{7.3-3.4}}=0.42\right]\left[{\displaystyle \frac{6.0-3.4}{7.3-3.4}}=0.67 ;{\displaystyle \frac{6.0-3.4}{7.3-3.4}}=0.67\right]$$

Applying the same method, normalization was calculated for all values of the collective fuzzy–rough decision matrix. This was followed by the determination of the $S_i$ and $P_i$ values. The procedure was as follows:

$$S_{11}=\left[0.16·0.08=0.01;0.16·0.10=0.02\right]\left[0.42·0.10=0.04;0.42·0.12=0.05\right]\left[0.67·0.13=0.07 ;0.67·0.15=0.10\right]$$

$$P_{11}=\left[{0.16}^{0.15}=0.77;{0.16}^{0.13}=0.79\right]\left[{0.42}^{0.12}=0.90;{0.42}^{0.10}=0.92\right]\left[{0.67}^{0.10}=0.96 ;{0.67}^{0.08}=0.97\right]$$

After all of the $S_i$ and $P_i$ values were calculated, the aggregate values of these values were determined for each alternative (

Table 6. Calculation of the fuzzy–rough CoCoSo method.

Id	${\stackrel{\mathbf{=}}{\mathit{S}}}_{\mathit{i}}$	${\stackrel{\mathbf{=}}{\mathit{P}}}_{\mathit{i}}$	${\mathit{S}}_{\mathit{i}}$	${\mathit{P}}_{\mathit{i}}$	${\mathit{\xi }}_{\mathit{i}\mathit{a}}$	${\mathit{\xi }}_{\mathit{i}\mathit{b}}$	${\mathit{\xi }}_{\mathit{i}\mathit{c}}$	${\mathit{\xi }}_{\mathit{i}}$	Rank
A1	[0.44, 0.53] [0.75, 0.89] [1.11, 1.31]	[9.24, 9.37] [9.74, 9.80] [9.94, 9.96]	0.84	9.68	0.18	3.25	1.00	2.32	1
A2	[0.20, 0.34] [0.44, 0.64] [0.80, 1.08]	[6.59, 8.82] [9.09, 9.48] [9.62, 9.81]	0.58	8.90	0.17	2.53	0.90	1.93	4
A3	[0.20, 0.32] [0.44, 0.62] [0.76, 1.01]	[5.72, 7.94] [9.00, 9.41] [9.54, 9.75]	0.56	8.56	0.16	2.43	0.87	1.85	5
A4	[0.23, 0.30] [0.48, 0.60] [0.85, 1.04]	[7.70, 7.97] [9.28, 9.44] [9.72, 9.80]	0.59	8.98	0.17	2.55	0.91	1.94	3
A5	[0.28, 0.40] [0.53, 0.72] [0.88, 1.14]	[7.54, 9.01] [9.26, 9.58] [9.70, 9.86]	0.66	9.16	0.17	2.75	0.93	2.05	2
A6	[0.10, 0.16] [0.31, 0.42] [0.64, 0.82]	[4.64, 6.60] [8.85, 9.13] [9.48, 9.62]	0.41	8.05	0.15	2.00	0.80	1.61	6

). After that, the fuzzy–rough value was transformed into the crips value (Expressions (13) and (14)). Then, the values for the strategies (Expressions 15–17) were calculated, and finally, the value for the fuzzy–rough CoCoSo method (Expression 18) was calculated. The results of this method, based on the evaluation of experts, showed that the best RES system is photovoltaic (A1), followed by thermal energy (A5). The RES system energy from waste (A6) received the worst results. Based on these results, it is recommended that BD Green Energy invest in the construction of photovoltaic plants because they have shown the best investment results in the territory of the Brčko District of BiH.

In order to confirm the results of applying the fuzzy–rough CoCoSo method, a comparative analysis was performed with the results obtained using other methods. Other methods that were applied are fuzzy–rough SAW, fuzzy–rough ARAS (Additive Ratio Assessment), fuzzy–rough CRADIS, fuzzy–rough MABAC (multi-attributive border approximation area comparison), fuzzy–rough WPM, and fuzzy–rough WASPAS. These methods were taken for the following reasons. The steps of the SAW and WPM methods are also used by the CoCoSo method. The ARAS method has a different normalization technique, which was used to examine whether normalization has a role in this example in the ranking of alternatives. The CRADIS method also applies a different normalization technique, and its steps do not include the steps of the SAW and WPM methods. The MABAC method uses the same normalization technique, but the weighting of criteria is carried out in a different way than in other methods. The WASPAS method resembles the steps of the CoCoSo method, but it does not take into account the strategies used by the CoCoSo method and applies a different normalization. The results of all these methods show the same ranking order of alternatives, so the results of the fuzzy–rough CoCoSo method confirm that investing in photovoltaic energy provides the best results in the Brčko District of BiH (Figure 2). This analysis showed that the best-ranked alternative is A1 for the RES system.

At the end of the analysis, a sensitivity analysis was conducted. This analysis can be seen in various ways. However, the goal of the analysis is always the same, to examine how the change in the weights of the criteria affects the final ranking of the alternatives. In this research, the weights obtained by the fuzzy–rough SiWeC method were used, and the weights for individual criteria were changed by 30, 60, and 90%. Since there are 10 criteria and the weights were changed three times, 30 scenarios were formed for the sensitivity analysis. The results of these scenarios show that there are changes in the ranking of the three RES systems (Figure 3). Thus, there was no change in the ranking of the best RES systems. RES systems A4 and A2 saw the most changes. This is because their results were the closest to each other. With the application of the value of one of the criteria, the ranking order of these alternatives also changes. If the ranking of an alternative improves when the weight of the criterion is reduced, it means that the alternative had weaker indicators for that criterion. In order to improve certain RES systems, the indicators of the criteria must be improved to the extent that their weights are reduced and the ranking is changed for the better.

5. Discussion

The tendency in the world is to make more and more efforts to produce as much energy as possible from RES systems [22]. Efforts are made to use the advantages of a certain area and thus choose a certain RES system that is most suitable for that area. This is because not all areas have the same characteristics regarding the application of certain RES systems. This research aimed at examining which RES system is the best for the investor, in this case, the BD Green Energy company, to realize in the form of a project. This company plans to invest in RES systems in the Brčko District of BiH. The specificity of this area is that this municipality in Bosnia and Herzegovina has the status of a district, and it only passes laws that will be applied in that territory. A further specificity of this area is that these laws have not yet been passed and there are no large investments in RES systems in this local community. Most of the investments are made by households and companies that use the produced electricity from the RES system for their personal needs. Therefore, it was important to investigate which RES system is the best investment for BD Green Energy.

Choosing an RES system is very important for investors in order to produce projects that will be used to realize this investment. If the investment is directed to an RES system that will not provide the best results, the payback time of that project will increase or even result in a loss for the investor because it will not be possible to recover the initial investment. The specificity of the RES system is that large initial funds are needed to put a certain RES system into operation [23]. For this reason, this research belongs to the capital investment for which projects are formed. Thus, it is necessary to investigate which of these RES systems will have the shortest return time and satisfy the other criteria that were taken in this research. The criteria are very diverse in this research and include different segments such as economic, ecological, social, and technical factors. The aim of this research is to make a compromise decision that satisfies all criteria in the best way. It would be best if a particular RES system was the best in all segments, but this is often not the case in practice; therefore, MCDMs are used, which present a compromise decision to the investor. It is precisely the task of these methods to help in making decisions [24].

When selecting an RES system, it is necessary to pay attention to the ownership model of these systems. In order to use some RES systems, it is necessary to obtain approval from the competent authorities. Thus, for the use of watercourses or geothermal potential, it is necessary to obtain a concession from state authorities. This further complicates the implementation of some RES systems in practice. That is why it is necessary to take into account the ownership model when choosing an RES system.

The application of certain methods is the specificity of this research. The focus is on decision-making using imprecise information and including uncertainty. The imprecise information is due to the fact that it is not possible to have all of the information about the criteria or alternatives, but partial information is available, which may be imprecise. Thus, this is the reason why the fuzzy approach was used in this research. In order for the decision to be as good as possible, it is necessary to include uncertainty in decision-making, which was achieved in this research by using the rough approach. Applying both of these approaches contributes to decision-making stability, which allows investors to be more confident in their decision-making. This approach was used using fuzzy–rough SiWeC and CoCoSo methods.

The fuzzy–rough SiWeC method was used to determine the importance of the criteria used in this research, based on the evaluation of experts. The advantage of this method is the simplicity of calculating the weight of the criteria [19]. This method uses only individual weight ratings of the criteria, and it is not necessary to apply multiple other analyses that include ranking or comparison. The results of this method showed that all criteria are important for the investor, although two criteria are less important than others, namely C8 legal and regulatory requirements and C9 time frame of implementation. The reason why these criteria are less important is that there are currently no legal and regulatory requirements in the Brčko District of BiH, and all RES alternatives are treated the same, that is, they are not treated at all. Moreover, it is not possible to invest in RES alternatives if there are no regulations, so the implementation time frame is less important because preparatory actions can be carried out and the main work commences only when there are regulations. This increases the implementation time of all RES alternatives.

The fuzzy–rough CoCoSo method was used for ranking, i.e., determining which of the RES alternatives provides the best results. This ranking method itself works on the basis of a compromise of strategies [25]. The results of this method, based on the evaluation of experts, showed that the RES system based on photovoltaic energy provides the best results for the investor. So, this research has shown that the BD Green Energy company should invest in the construction of photovoltaic farms that produce electricity from the energy of the sun. These results are due to the resources available to the Brčko District of BiH. Several rivers flow through the territory of the Brčko District of Bosnia and Herzegovina, but their flows are calm and therefore classic hydropower plants would not provide the best results. Moreover, agricultural production is not at a high level, so there would be a lot of biomass for energy conversion. There is a lot of waste, but during the process of energy conversion, CO₂ is released from the waste. Thermal energy has not been researched in the Brčko District of BiH, and this area does not have constant winds. These results were also confirmed by comparative analysis. The results of the sensitivity analysis showed that by changing the weights of the criteria, the ranking of the three RES systems was changed. This analysis showed what needs to be improved in certain RES systems in order to achieve better results for investors. However, it is difficult to improve some RES systems because it depends on the resources available to a certain area. So, it is necessary to adapt to those resources and try to use them in the best way.

It should be mentioned that RES systems do not have to be exclusively used for the production of electricity, as they can have different applications. There is a great demand for thermal energy, which is used to heat various commercial and residential buildings. The area of the Brčko District does not have a heating plant that would deliver this type of energy to citizens and industry; thus, it is necessary to take into account that RES systems can be used for this purpose as well. Many countries have taken advantage of the opportunity to deliver thermal energy for heating based on biomass, waste incineration, and geothermal energy. For this reason, it is necessary for the BD Green Energy company to consider the possibility of upgrading this project, where the focus will not be exclusively on electricity, but also on the delivery of thermal energy. This can also be realized through a new investment.

5.1. Theoretical and Practical Implications of the Research

The implications offered by this research in terms of theory are first reflected in the research model, which is set from the investor’s point of view. The applied criteria were used in order for the investor to have the best possible information regarding which RES system to invest in. In addition, the theoretical concept of the symbiosis of MCDMs with mean operators was developed. In addition, the theoretical basis for the fuzzy–rough SiWeC method extended with the Bonferroni mean operator was developed.

The practical implications of this research are reflected in the evaluation of both important criteria and the fulfillment of these criteria by the RES system. The application of the model and examples from practice provide guidelines for the further development of RES system implementation by investors. Then, an extended fuzzy–rough Bonferroni approach was developed, which aims to enable decision-making with incomplete information and decision-making under conditions of uncertainty. This approach provides a way to harmonize experts’ ratings based on the Bonferroni mean operator.

The application of this research on the practical example of the territory of the Brčko District of BiH allows us to determine which RES system provides the best results in terms of energy conversion. In addition, a hybrid form of decision-making based on the fuzzy–rough approach and the Bonferroni mean operator was developed.

5.2. Research Limitations and Future Research Directions

This research has certain limitations that should be addressed in future research. First, ten criteria were selected and observed together without taking into account their affiliation. It is necessary to say that these criteria were determined by the experts based on the fulfillment of the set goals of the research in terms of understanding which RES system needs to be applied in the Brčko District of BiH in order to achieve additional profits. In addition, forming criteria in this way makes it possible to allocate the same importance to all criteria. In future research, this approach can be further developed by adding additional criteria and grouping them according to relatedness. In this way, the weight of the main criteria and auxiliary criteria can be determined.

The following limit may apply to rated RES systems, as other RES systems could also be applied. For this reason, it is necessary to include other RES systems in future research in order to establish whether some other RES system provides better results and is better for investors. However, due to the fact that Bosnia and Herzegovina is a developing country, RES system technology has not been developed to the required extent, and these systems are mostly used in practice. With the further development of science and technology, it is possible that new RES systems will appear and they should be included in future research.

The limitation of this research is related to its exclusivity in the production of electrical energy using the RES system. However, the tendency is to produce thermal energy using the RES system, which can be used for heating buildings. Therefore, in future research, it is necessary to consider the possibility of investing in the production of thermal energy using RES alternatives. This is due to the fact that demand for heating can be more significant than demand for electricity.

This study can be a starting point for considering the possibility of using the RES alternative in practice in this region. However, in order to make a final decision, it is necessary to take into account the size of the area and the number of inhabitants located in the territory of the Brčko District of BiH. Moreover, it is necessary to take into account the real possibility of supplying electricity to this area. Therefore, to make a final decision, it is necessary to consider a lot of facts and not rely only on the opinions of experts. Expert opinions can be used in the initial decision-making process, and further, it is necessary to make a decision in accordance with all relevant information. All of these aspects need to be considered in future research. It is recommended that BD Green Energy use other information and not just the opinion of experts when making final decisions.

This research used the Bonferroni mean operator and it was shown that it can be incorporated into the existing methodology of MCDMs. In future research, it is necessary to include other mean operators, and even devote one study to these operators in order to establish which one best harmonizes with the experts’ evaluations. In addition, this approach has shown ease of use and additional flexibility, so it needs to be developed in future research.

6. Conclusions

This research was conducted from an investor’s perspective. Furthermore, the specificity of this research is that it provides the necessary information to the BD Green Energy company regarding which RES system to invest in in the form of projects so that the benefits of that investment will be as good as possible. In order to do this, a decision-making model based on the use of 10 criteria and six RES systems was created. The evaluation of the criteria using the fuzzy–rough approach based on the SiWeC method proved that most criteria are equally important for the investor. The assessment and evaluation of the RES system using the fuzzy–rough CoCoSo method showed that investing in photovoltaic plants is the best approach for the BD Green Energy company. These results were also confirmed by comparative analysis. In order to obtain even better benefits from this investment, the company must examine which location would provide better results and reduce the additional costs of building a photovoltaic plant. However, the implementation of this decision should await the adoption of legal regulations that will regulate the implementation of the RES system in the Brčko District of BiH.