The Planning of Best Site Selection for Wind Energy in Indonesia: A Synergistic Approach Using Data Envelopment Analysis and Fuzzy Multi-Criteria Decision-Making

Abstract

The objective of this study is to create an integrated and sustainability-centered framework to identify optimal locations for wind energy projects in Indonesia. This research employs a novel two-phase multi-criteria decision-making (MCDM) framework that combines the strengths of Data Envelopment Analysis (DEA), Fuzzy Analytic Hierarchy Process (FAHP), and Fuzzy Combined Compromise Solution (F-CoCoSo). Initially, DEA is utilized to pinpoint the most promising sites based on a variety of quantitative factors. Subsequently, these sites are evaluated against qualitative criteria such as technical, economic, environmental, and socio-political considerations using FAHP for criteria weighting and F-CoCoSo for ranking the sites. Comprehensive sensitivity analysis of the criteria weights and a comparative assessment of methodologies substantiate the robustness of the proposed framework. The results converge on consistent rankings across methods, highlighting the effectiveness of the integrated approach. Notably, the results consistently identify Lampung, Aceh, and Riau as the top-ranked provinces, showcasing their strategic suitability for wind plant development. This framework provides a systematic approach for enhancing resource efficiency and strategic planning in Indonesia’s renewable energy sector.

1. Introduction

Renewable energy has become a crucial aspect of sustainable development in many countries, including Indonesia. Indonesia has been actively developing various forms of renewable energy sources, such as hydroelectric power plants, geothermal energy, micro-hydro, solar energy, and wind power. Renewable energy in Indonesia is a topic of growing importance due to the country’s vast potential for various renewable energy sources. Indonesia is rich in renewable energy resources both on land and at sea [1]. The development of wind power plants in Indonesia is crucial due to the country’s abundant wind resources and the need to meet increasing energy demands while reducing reliance on fossil fuels [2]. Indonesia’s vast archipelago and its geographical location near the equator make it an ideal region for the harnessing of wind energy. The country’s diverse topography, including coastlines, plains, and mountainous regions, offers a wide range of potential sites for wind power generation. Additionally, the growing energy demands in urban and rural areas necessitate the exploration of renewable energy sources like wind power to reduce the carbon footprint and ensure energy security. To effectively harness wind energy, it is crucial to identify optimal site locations that offer consistent and strong wind patterns. This involves comprehensive data analysis, including wind speed and direction, topographical features, and environmental considerations, to determine the most favorable sites for wind power installation. Moreover, understanding the socioeconomic and regulatory landscape is essential for the successful implementation of wind energy projects in Indonesia.

Indonesia’s commitment to transitioning toward sustainable and environmentally friendly energy sources aligns with global initiatives such as the Paris Agreement and the United Nations’ Sustainable Development Goals [3,4]. The Indonesian government has set ambitious targets to diversify its energy mix, aiming to have renewables constitute at least 23% by 2025 and 31% by 2050 [5]. Reducing carbon emissions and addressing global environmental concerns are evident in its efforts to harness renewable energy sources like wind energy [6]. The geographical location of Indonesia in the equatorial area influences wind patterns and speeds, making it a suitable region for wind energy utilization [7].

Indonesia, as an archipelagic country with a vast coastline and abundant wind potential, has the opportunity to develop wind energy as an alternative source of electrical power [8,9]. With a population of 270 million, it is experiencing the most rapid growth in energy demand in the Asia–Pacific region. This emphasizes the critical requirement for a secure, cost-effective, and sustainable shift toward energy sources with long-term viability in Southeast Asia [5]. The potential for wind energy in Indonesia is significant due to its extensive coastline, which is the world’s fourth longest at 99,093 km [10].

By tapping into its abundant wind resources, Indonesia can significantly contribute to the global transition toward a more sustainable and low-carbon energy system. The environmental aspects and public acceptance of renewable energy technologies, including wind energy, require significant attention to meet targets for reducing the impact of global warming [11]. The transition to a cleaner energy mix in Indonesia involves overcoming various barriers, including technological, economic, social, and environmental challenges [12]. Additionally, the development of wind energy in Indonesia necessitates not only infrastructure improvements but also the enhancement of human resource capacity in the renewable energy sector [13]. However, there are still areas in Indonesia that have suitable conditions for wind power plant development. Renewable energy wind power plants in Indonesia have significant potential despite facing challenges.

To address the growing need for sustainable energy planning in Indonesia, this study aims to identify optimal locations for wind energy development using a hybrid decision-making framework that integrates Data Envelopment Analysis (DEA), Fuzzy Analytic Hierarchy Process (FAHP), and Fuzzy Combined Compromise Solution (F-CoCoSo). The central research question guiding this work is as follows: “Which locations in Indonesia are most suitable for wind energy development based on a comprehensive, multi-criteria decision-making approach that accounts for both quantitative and qualitative factors?” This study makes two key contributions. Scientifically, it offers a novel, synergistic application of DEA and fuzzy MCDM methods for renewable energy planning, enhancing methodological rigor in complex site-selection problems. Practically, the findings serve as a decision-support tool for Indonesian policymakers, energy planners, and investors by providing transparent, data-driven insights into regional suitability for wind energy projects. In doing so, this research supports national targets for renewable energy integration and sustainable development under the Paris Agreement and SDG commitments.

2. Literature Review

Several studies summarized in

Table 1. Previous relevant studies.

No	Study	Case Study	Year	Weighted Method
1	Rose & Apt [24]	US	2015
2	Sánchez-Lozano et al. [26]	Spain	2016	Fuzzy-AHP
3	Değirmenci et al. [27]	Turkey	2018	AHP
4	Mohammadzadeh Bina et al. [28]	Iran	2018	Equal weight
5	Ayodele et al. [29]	Nigeria	2018	Interval type-2 fuzzy AHP
6	Güler et al. [30]	Turkey	2018
7	Wang et al. [14]	Vietnam	2018	FAHP and FTOPSIS
8	Solangi et al. [25]	Pakistan	2018	AHP and FUZZY
9	Y. Wu et al. [31]	China	2019	Entropy-based fuzzy
10	Liu et al. [22]	Saskatchewan	2019
11	Pambudi & Nananukul [32]	Indonesia	2019
12	Deveci et al. [33]	Turkey	2020	Fuzzy method
13	Xu et al. [19]	China	2020	IAHP
14	Ari & Gencer [18]	Turkey	2020	AHP-SMAA
15	Mostafaeipour et al. [34]	Iran	2020
16	Elhonsy et al. [35]	Egypt	2021	Shannon’s Entropy
17	Azzioui et al. [36]	Morocco	2021	Dynamic AHP
18	Saraswat et al. [37]	India	2021	Fuzzy-AHP
19	Feloni & Karandinaki [38]	Chania	2021	WLC
20	Asadi & Pourhossein [39]	Iran	2021	AHP
21	Sotiropoulou & Vavatsikos [40]	Greece	2021	IDW
22	Zahid et al. [41]	Pakistan	2021	AHP
23	Wang et al. [42]	Vietnam	2021	FAHP, FWASPAS
24	Xu et al. [43]	China	2021	AHP
25	Nagababu et al. [44]	India	2022	Fuzzy-AHP
26	Gao et al. [45]	Mongolia	2022	DEMATEL
27	Shorabeh et al. [46]	Iran	2022	OWA
28	Y. Wu et al. [47]	China	2022	DEMATEL, ANP
29	Ajanaku et al. [48]	Virginia	2022	FAHP
30	Kumar et al. [49]	India	2022
31	Ioannou et al. [50]	Greece	2019	AHP, TOPIS
32	Li et al. [51]	China	2025	AHP, TOPSIS
33	Bychkov et al. [52]		2023	GIS
34	Xenitidis et al. [53]		2023	GIS
35	Lu et al. [54]	Greece	2023	NN
36	Xenitidis et al. [55]	China	2023	NN
37	Josimović et al. [56]	Serbia	2023	GIS, PROMETHE
38	Laska et al. [57]	Poland	2017	PROMETHE

and

Table 2. The literature review on MCDM techniques.

No	Authors [Reference]	Wind Power	Geology Condition	Electricity Demand	Distance to Residential Areas	Distance from Roads	Distance to Transmission Line	Costs	Land Use	Land Price	Support Mechanisms	Policies and Laws	Social Impact	Natural Disaster	Wildlife and Habitat	Visual Impact	Ecological Damage
1	Villacreses et al. [58]	x			x	x	x		x					x
2	Mostafaeipour et al. [34]	x			x					x				x
3	Jun et al. [59]	x	x	x		x		x					x		x	x	x
4	Wang et al. [14]	x			x	x		x	x		x	x	x
5	Ari & Gencer [18]					x	x					x
6	Guo et al. [60]	x							x							x
7	A.U. Rehman et al. [61]	x	x	x		x	x		x		x
8	Ali et al. [62]	x		x		x
9	X. Wu et al. [63]	x	x			x				x
10	Pambudi & Nananukul [32]	x			x	x		x
11	Kokologos et al. [64]				x	x										x
12	Sánchez-Lozano et al. [26]	x	x		x	x	x								x
13	Ayodele et al. [29]		x		x	x	x								x
14	Y. Wu et al. [31]	x						x					x				x
	This research	x	x	x	x	x	x	x	x	x	x	x	x	x	x	x	x

have employed multi-criteria decision-making (MCDM) approaches to address the location selection problem for renewable energy plants, including wind power plants. In a similar vein, another study by Wang et al. [14] proposes a two-stage MCDM-based spherical fuzzy set approach for offshore wind power plant site selection, addressing the complex nature of optimal location selection amidst conflicting decision-making factors. Nguyễn et al. [15] focus on a Spherical Fuzzy Multi-Criteria Decision-Making model tailored for selecting wind turbine suppliers, which aligns with the complexity of wind power plant site selection, and emphasize a systematic decision-making approach in complex projects. One study tackles the challenge of choosing the best wind turbine for a farm, a critical aspect for maximizing wind energy utilization, by employing a two-level decision-making strategy that integrates fuzzy logic and MCDM, demonstrating the methodology’s effectiveness with data from Qassim, Saudi Arabia [16]. Rouyendegh et al. [17] discuss using the Intuitionistic Fuzzy TOPSIS method for wind power plant site selection in Turkey, aiming to harness wind energy efficiently while reducing costs and considering factors like wind potential and social benefits. Arı and Gencer [18] delve into comparing deterministic and stochastic approaches for wind power plant site selection in Turkey, highlighting a hybrid method that combines simulation-based analysis with deterministic variables, with findings favoring Burhaniye-Pelitköy as the optimal location. Xu et al. [19] explore the complexities of policymaking and technology management in China’s offshore wind power industry, analyzing hierarchical relationships among various factors to offer a comprehensive perspective on development. Sadeghi and Karimi [20] utilize GIS and AHP in Tehran, Iran, to select suitable sites for solar farms and wind turbines, enhancing power network stability through multi-criteria evaluation methods. Qawaqzeh et al. [21] examine emergency modes of wind power plants using computer simulation, focusing on the impact of sudden voltage drops and short circuits, which is crucial for designing wind farms. Liu et al. [22] present a GIS-based Decision-Making Support System for site selection in Saskatchewan, highlighting the role of GIS in optimizing the selection process. Camargo et al. [23] present a model for optimal portfolio selection, considering wind complementarity among sites under a budget constraint, offering a stochastic risk-averse optimization approach. Rose and Apt [24] discuss the use of reanalysis data sets for wind power analyses, developing a model to estimate variability and the smoothing effect of aggregating wind plants in the U.S. Great Plains. Finally, Solangi et al. [25] provide insights into site selection for wind power projects in Pakistan, employing Factor Analysis, AHP, and Fuzzy TOPSIS methodologies for a structured approach to identifying suitable locations for development.

While there have been several studies on the site selection of wind power plants using DEA and fuzzy MCDM techniques, there is a research gap in the specific context of Indonesia. Mostafaeipour et al. [34] introduce DEA for prioritizing wind turbine installation locations in Iran, specifically in the East Azerbaijan region, comparing different cities for optimal development. Wang et al. [42] present a novel approach that combines Data Envelopment Analysis and fuzzy MCDM to select wind plant sites in Vietnam. They emphasize the importance of both quantitative and qualitative criteria, showcasing the methodology’s effectiveness in identifying optimal locations for wind plants, with Binh Thuan province ranking highly for its robustness and practical applicability, providing valuable insights for decision-makers in renewable energy projects. Kumar et al. [49] assess the operational performance of wind power plants in India using a two-stage DEA Tobit model, focusing on factors like turbine age and site elevation on efficiency. Sameie and Arvan [65] showcase a simulation-based DEA model for evaluating wind plant locations, applying mathematical optimization to select the best sites based on efficiency and performance. Therefore, there is a need for research that specifically addresses the site selection of wind power plants in Indonesia using DEA and fuzzy MCDM approaches.

3. Methods

This section outlines the wind power plant site selection methodology, as illustrated in Figure 1. The proposed approach combines Data Envelopment Analysis (DEA), Analytic Hierarchy Process (AHP), and Fuzzy Combined Compromise Solution (F-CoCoSo) to develop a comprehensive decision-making framework for selecting optimal sites for wind power plants in Indonesia.

3.1. Data Envelopment Analysis (DEA)

Data Envelopment Analysis (DEA) is a commonly used mathematical approach to measure the efficiency of decision-making units (DMUs) based on multiple inputs and outputs. In this study, DEA is used to screen and select the most efficient locations to host solar installations. The CCR, BCC, SBM, and EBM models are examples of DEA models that can be used to assess DMU efficiency. These models differ in terms of the assumptions they make about inputs and outputs, as well as the type of efficiency measured [66].

3.1.1. Charnes, Cooper, Rhodes Model (CCR)

The CCR model is a type of DEA model commonly used to evaluate the efficiency of decision-making units (DMUs) based on multiple inputs and outputs. This model measures the technical effectiveness of a DMU, assuming that each DMU can be represented by a set of inputs and outputs specified in Equation (1).

$$\begin{gathered} {\theta }^{*}=\underset{\theta ,\lambda ,s^{-}}{\min }\theta \\ \mathrm{subject\; to\hspace{1em}\hspace{1em} } \\ \theta x_0=X\lambda -s^{-} \\ {y}_0\le Y\lambda , \\ \lambda \ge 0, s^{-}\ge 0 \end{gathered}$$

(1)

3.1.2. Banker, Charnes, and Cooper Model (BCC)

Banker et al. [67] extended the applicability of the BCC model to variable return to scale (VRS) when it is a non-Archimedean element, and $s_i^{-}$ and $s_r^{+}$ represent the input and output slack variables, respectively.

$$\begin{gathered} min \varnothing -\epsilon ({{\displaystyle \sum }}_{i=1}^m{s}_i^{-}+{{\displaystyle \sum }}_{r=1}^s{s}_r^{+}) \\ \mathrm{subject\; to\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}} \\ {{\displaystyle \sum }}_{j=1}^n{\lambda }_j x_{ij}+s_i^{-}=\varnothing x_{i0} \left(i=1,\mathrm{\dots },\mathrm{p}\right) \\ {{\displaystyle \sum }}_{j=1}^n{\lambda }_j y_{rj}-s_r^{+}=y_{ro} \left(r=1,\mathrm{\dots },\mathrm{q}\right) \\ {{\displaystyle \sum }}_{k=1}^n{\lambda }_k=1 \\ {\lambda }_k\ge 0, k=1, 2,\dots ,n \\ {s}_i^{-}\ge 0,i=1,2,\dots ,\mathrm{p} \\ {s}_j^{+}\ge 0,j=1,2,\dots ,\mathrm{q} \end{gathered}$$

(2)

To distinguish between technical inefficiency and scale, the BCC model was evaluated based on technical efficiency at possible operational sizes. In addition to growth, decline, and constant return scales, several other scales are also recognized. Sometimes, “pure technical efficiency” is used to describe the efficiency metric of BCC models.

3.1.3. Slack-Based Measure Model (SBM)

The effectiveness of a DMU is determined by a ratio which is known as the “slack-based measure” (SBM) score. This value is determined by dividing the DMU’s actual output by the minimal number of inputs required to achieve that output, depending on the inputs and outputs of the other DMUs included in the analysis. A DMU with an SBM score of 1 is technically efficient, while a DMU with an SBM score of less than 1 is inefficient.

$$\begin{gathered} {\tau }^{*}=\min 1-{\displaystyle \frac{1}{m}}{\displaystyle \sum }_{i=1}^m{\displaystyle \frac{s_i^{-}}{x_{i0}}} \\ \mathrm{subject\; to} \\ {x}_{i0}={\sum }_{j=1}^n{x}_{ij}{\lambda }_j+s_i^{-} \left(i=1,\dots , m\right) \\ {y}_{i0}\le {\displaystyle \sum }_{j=1}^n{y}_{ij}{\lambda }_j \left(i=1,\dots , s\right) \\ {\lambda }_j\ge 0 \left(\forall j\right), s_i^{-}\ge 0 \left(\forall i\right) \end{gathered}$$

(3)

3.1.4. Epsilon-Based Measure Model (EBM)

Various input and output variables are used by DEA to measure efficiency. The CCR model is a simple model, similar to the radial approach, which emphasizes proportional changes in inputs and outputs while considering slack. Similar to the non-radial method, the SBM model shows slack but does not account for changes in input/output proportionality. EBM models calculate epsilon as a scalar, which represents the diversity or dispersion of the observed data set. This library of symbols and notations was used during the development of the EBM model. Input and output matrices $j=1, 2, \mathrm{\dots } , n$ as well as $m$ inputs $i=1, 2, \mathrm{\dots } , m$ and $s$ outputs $r=1, 2, \mathrm{\dots } , s$ are used to support the model containing n DMUs. $X=\left\{x_{ij}\right\}\in R^{m\times n}$ and $Y=\left\{y_{rj}\right\}\in R^{s\times n}$. Both $X$ and $Y$ are nonnegative matrices. The input-oriented EBM model with a constant return to scale is depicted in [68] Equation (4).

$$\begin{gathered} {\delta }^{*}=\underset{\theta ,\lambda ,s^{-}}{\mathit{Min}}\theta -{\epsilon }_x{{\displaystyle \sum }}_{i=1}^m{\displaystyle \frac{w_i^{-}{s}_i^{-}}{x_{io}}} \\ \mathrm{subject\; to\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} } \\ {\displaystyle \sum }_{j=1}^n{x}_{ij}{\lambda }_j=\theta x_{io}-s_i^{-} \left(i=1,\dots ,\mathrm{m}\right) \\ {\displaystyle \sum }_{j=1}^n{y}_{rj}{\lambda }_j\ge y_{ro} \left(r=1,\dots ,\mathrm{s}\right) \\ {\lambda }_j\ge 0, j=1, 2,\dots ,n \\ {s}_i^{-}\ge 0,i=1,2,\dots ,\mathrm{m} \end{gathered}$$

(4)

It implies that ${\lambda }_j$ is the DMU’s intense vector, the DMU under evaluation is represented by the subscript “$o$”, and the amount of slack and weight are represented by the $s_i^{-}$ and $w_i^{-}$ in the $i$th input, respectively. Finally, a parameter ${\epsilon }_x$ specifies the radial qualities and is dependent on the degree of input dispersion.

3.2. FAHP

In

Table 3. Explanation of the FAHP scale.

Fuzzy Set	Definition	Fuzzy Scale
$\tilde{1}$	Equal importance	(1, 1, 1)
$\tilde{2}$	Weak importance	(1, 2, 3)
$\tilde{3}$	Not bad	(2, 3, 4)
$\tilde{4}$	Preferable	(3, 4, 5)
$\tilde{5}$	Importance	(4, 5, 6)
$\tilde{6}$	Fairly important	(5, 6, 7)
$\tilde{7}$	Very important	(6, 7, 8)
$\tilde{8}$	Absolute	(7, 8, 9)
$\tilde{9}$	Perfect	(8, 9, 10)

, we see that the triangular fuzzy numbers are the linguistic terms for the pairwise comparison scale and the fuzzy scale assigned. The relative importance of the two criteria is ranked on a scale from 1 to 9 based on the linguistic variables provided. A tilde sign (~) is placed above the parameter symbol to indicate uncertainty. Thus, the following are the details of the FAHP process [69].

Stage 1: To produce the integrated fuzzy pairwise comparison matrix used in the FAHP calculation, we apply geometrical integration as seen in Equation (5). $\widetilde{l_{ij}}$ denotes the importance of the $i$th criterion over the $j$th criterion.

$$\tilde{M}=\left(\begin{array}{cccc}1& \widetilde{l_{12}}& \cdots & \widetilde{l_{1n}}\\ \widetilde{l_{21}}& 1& \cdots & \widetilde{l_{2n}}\\ \cdots & \cdots & \cdots & \cdots \\ \widetilde{l_{n1}}& \widetilde{l_{n2}}& \cdots & 1\end{array}\right)=\left(\begin{array}{cccc}1& \widetilde{l_{12}}& \cdots & \widetilde{l_{1n}}\\ 1/\widetilde{l_{12}}& 1& \cdots & \widetilde{l_{2n}}\\ \cdots & \cdots & \cdots & \cdots \\ 1/\widetilde{l_{1n}}& 1/\widetilde{l_{2n}}& \cdots & 1\end{array}\right)$$

(5)

$$\widetilde{l_{ij}}=\left\{\begin{array}{c}{\tilde{9}}^{-1},{\tilde{8}}^{-1},{\tilde{7}}^{-1},{\tilde{6}}^{-1},{\tilde{5}}^{-1},{\tilde{4}}^{-1},{\tilde{3}}^{-1},{\tilde{2}}^{-1},{\tilde{1}}^{-1},\tilde{1},\tilde{2},\tilde{3},\tilde{4},\tilde{5},\tilde{6},\tilde{7},\tilde{8},\tilde{9} such that i\ne j\\ 1 such that i=j\end{array}\right.$$

Stage 2: Equation to determine the fuzzy geometric mean of each criterion (6):

$$\widetilde{r_i}={\left({\displaystyle \prod }_{j=1}^n\widetilde{l_{ij}}\right)}^{1/n}such that i=1, 2, \dots ,n$$

(6)

where $\widetilde{r_i}$ is approximated by the fuzzy geometric mean, and $\widetilde{l_{ij}}$ is a fuzzy comparison value generated by a panel of decision-makers based on the $i$th criterion over the $j$th criterion.

Stage 3: The fuzzy preference weight for each criterion is determined using the following Equation (7):

$$\widetilde{w_i}=\widetilde{r_i}\otimes {\left(\widetilde{r_1}\oplus \widetilde{r_2}\oplus \dots \oplus \widetilde{r_n}\right)}^{-1}$$

(7)

where $\widetilde{w_i}$ is the fuzzy weights of the $i\mathrm{th}$ criterion.

Stage 4: To obtain a clear result, we need to defuzzify the preference weights using the average weight criterion $G_i$, as shown in Equation (8):

$$G_i={\displaystyle \frac{l{w}_i+m{w}_i+u{w}_i}{3}}$$

(8)

where $\widetilde{w_i}$ is the fuzzy weight of the $i$th criterion, which can be presented as $\widetilde{w_i}=\left(l{w}_i,m{w}_i,u{w}_i\right)$, such that $l{w}_i,m{w}_i,u{w}_i$ are the lower bound, middle bound, and upper bound of $\widetilde{w_i}$, respectively.

Stage 5: The relative importance of each criterion, as determined by the normalized preference weight $H_i$, is obtained by Equation (9).

$$H_i={\displaystyle \frac{G_i}{{\sum }_{i=1}^n{G}_i}}$$

(9)

3.3. Fuzzy Combined Compromise Solution Method (F-CoCoSo)

Fuzzy Combined Compromise Solution (Fuzzy CoCoSo) utilizes a combination of an exponentially weighted outcome and a simple additive weighting framework to provide a solution for MCDM problems. Once the criteria and alternatives have been identified, the Fuzzy CoCoSo model can be implemented to rank the options based on their performance.

Step 1: A decision matrix is indicated as in the equation below. Stage 1: Defining an initial fuzzy decision-making matrix including a set of n criteria (i.e., criteria) and m alternatives.

Stage 2: Defining an extended initial fuzzy decision-making matrix by introducing the fuzzy ideal $\tilde{\mathit{A}}\left(\mathit{I}\mathit{D}\right)$ and anti-ideal $\tilde{\mathit{A}}\left(\mathit{A}\mathit{I}\right)$ solutions

$$\begin{gathered} \tilde{Z}={\left[\widetilde{z_{ij}}\right]}_{k\times n}=\left[\begin{array}{ccc}\widetilde{z_{11}}& \dots & \widetilde{z_{1n}}\\ ⋮& \ddots & ⋮\\ \widetilde{z_{k1}}& \dots & \widetilde{z_{kn}}\end{array}\right]. \\ \mathrm{with} i=1,2,\dots ,\mathrm{k}; j=1,2\dots n \end{gathered}$$

(10)

where $\widetilde{z_{ij}}$ is the fuzzy value of the $i$th alternative of the $j$th criterion, $k$ is the number of alternatives and $n$ is the number of attributes.

Step 3: The fuzzy value is normalized by applying Equations (11) (for the cost criteria) and (12) (for the beneficial criteria) as described below:

$$\begin{array}{r}\widetilde{r_{ij}}=\left(r_{ij}^l,r_{ij}^m,r_{ij}^u\right)={\displaystyle \frac{\max \left(\widetilde{z_{ij}}\right)-\widetilde{z_{ij}}}{\max \left(\widetilde{z_{ij}}\right)-\min \left(\widetilde{z_{ij}}\right)}}=\hfill \\ \left({\displaystyle \frac{\max \left(z_{ij}^u\right)-z_{ij}^u}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}},{\displaystyle \frac{\max \left(z_{ij}^u\right)-z_{ij}^m}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}},{\displaystyle \frac{\max \left(z_{ij}^u\right)-z_{ij}^l}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}}\right)\hfill \end{array}$$

(11)

$$\begin{array}{r}\widetilde{r_{ij}}=\left(r_{ij}^l,r_{ij}^m,r_{ij}^u\right)={\displaystyle \frac{\widetilde{z_{ij}}-\min \left(\widetilde{z_{ij}}\right)}{\max \left(\widetilde{z_{ij}}\right)-\min \left(\widetilde{z_{ij}}\right)}}=\hfill \\ \left({\displaystyle \frac{z_{ij}^l-\min \left(z_{ij}^l\right)}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}},{\displaystyle \frac{z_{ij}^m-\min \left(z_{ij}^l\right)}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}},{\displaystyle \frac{z_{ij}^u-\min \left(z_{ij}^l\right)}{\max \left(z_{ij}^u\right)-\min \left(z_{ij}^l\right)}}\right).\hfill \end{array}$$

(12)

where $\widetilde{r_{ij}}$ is the normalized value of $\widetilde{z_{ij}}$.

Step 4: The sum of the weighted comparability sequence $\widetilde{S_i}$ and the power-weighted comparability sequence $\widetilde{P_i}$ for each alternative is estimated by Equations (13) and (14):

$${\tilde{S}}_i=\left(S_i^l,S_i^m,S_i^u\right)=\sum _{j=1}^n\widetilde{w_{jc}}\widetilde{r_{ij}}=\left(\sum _{j=1}^n w_{jc}^l{r}_{ij}^l,\sum _{j=1}^n w_{jc}^m{r}_{ij}^m,\sum _{j=1}^n w_{jc}^u{r}_{ij}^u\right);$$

(13)

$${\tilde{P}}_i=\left(P_i^l,P_i^m,P_i^u\right)=\sum _{j=1}^n{\left(\widetilde{r_{ij}}\right)}^{\widetilde{w_{jc}}}=\left(\sum _{j=1}^n{\left(r_{ij}^l\right)}^{w_{jc}^u},\sum _{j=1}^n{\left(r_{ij}^m\right)}^{w_{jc}^m},\sum _{j=1}^n{\left(r_{ij}^u\right)}^{w_{jc}^l}\right)$$

(14)

Step 5: Three fuzzy appraisal scores $\left(\widetilde{f_{ia}},\widetilde{f_{ib}},\widetilde{f_{ic}}\right)$ are calculated based on the aggregation strategies:

$$\widetilde{f_{ia}}=\left(f_{ia}^l,f_{ia}^m,f_{ia}^u\right)=\frac{{\tilde{P}}_l+{\tilde{S}}_i}{\sum _{i=1}^k\left({\tilde{P}}_i+{\tilde{S}}_i\right)}=\left(\frac{P_i^l+S_i^l}{\sum _{i=1}^k\left(P_i^u+S_i^u\right)},\frac{P_i^m+S_i^m}{\sum _{i=1}^k\left(P_i^m+S_i^m\right)},\frac{P_i^u+S_i^u}{\sum _{i=1}^k\left(P_i^l+S_i^l\right)}\right)$$

(15)

$$\begin{gathered} \widetilde{f_{ib}}=\left(f_{ib}^l,f_{ib}^m,f_{ib}^u\right)={\displaystyle \frac{\widetilde{S_i}}{\min \left(\widetilde{S_i}\right)}}+{\displaystyle \frac{\widetilde{P_i}}{\min \left(\widetilde{P_i}\right)}}= \\ \left(\frac{S_i^l}{\min \left(S_i^l\right)}+\frac{P_i^l}{\min \left(P_i^l\right)},\frac{S_i^m}{\min \left(S_i^l\right)}+\frac{P_i^m}{\min \left(P_i^l\right)},\frac{S_i^u}{\min \left(S_i^l\right)}+\frac{P_i^u}{\min \left(P_i^l\right)}\right); \end{gathered}$$

(16)

$$\begin{gathered} \widetilde{f_{ic}}=\left(f_{ic}^l,f_{ic}^m,f_{ic}^u\right)={\displaystyle \frac{\lambda \left(\widetilde{S_i}\right)+\left(1-\lambda \right)\left(\widetilde{P_i}\right)}{\lambda \max \left(\widetilde{S_i}\right)+\left(1-\lambda \right)\max \left(\widetilde{P_i}\right)}}= \\ \left({\displaystyle \frac{\lambda \left(S_i^l\right)+\left(1-\lambda \right)\left(P_i^l\right)}{\lambda \max \left(S_i^u\right)+\left(1-\lambda \right)\max \left(P_i^u\right)}},{\displaystyle \frac{\lambda \left(S_i^m\right)+\left(1-\lambda \right)\left(P_i^m\right)}{\lambda \max \left(S_i^u\right)+\left(1-\lambda \right)\max \left(P_i^u\right)}},{\displaystyle \frac{\lambda \left(S_i^u\right)+\left(1-\lambda \right)\left(P_i^u\right)}{\lambda \max \left(S_i^u\right)+\left(1-\lambda \right)\max \left(P_i^u\right)}}\right) \end{gathered}$$

(17)

Initially, the efficient value $\lambda$ is set as 0.5 ($\lambda =0.5$).

Step 6: The fuzzy appraisal scores $\left(\widetilde{f_{ia}},\widetilde{f_{ib}},\widetilde{f_{ic}}\right)$ are transformed into crisp appraisal scores $\left(f_{ia},f_{ib},f_{ic}\right)$ by applying these below formulas:

$$f_{ia}={\displaystyle \frac{f_{ia}^l+f_{ia}^m+f_{ia}^u}{3}}$$

(18)

$$f_{ib}={\displaystyle \frac{f_{ib}^l+f_{ib}^m+f_{ib}^u}{3}}$$

(19)

$$f_{ic}={\displaystyle \frac{f_{ic}^l+f_{ic}^m+f_{ic}^u}{3}}$$

(20)

Step 7: The final score $\left(f_i\right)$ and its ranking for each alternative are computed based on crisp appraisal scores:

$$f_i={\left(f_{ia}{f}_{ib}{f}_{ic}\right)}^{1/3}+\left({\displaystyle \frac{1}{3}}\right)\left(f_{ia}+f_{ib}+f_{ic}\right).$$

(21)

The alternative with the highest score in the Fuzzy CoCoSo model results is considered the best option.

4. A Case Study in Indonesia

In this section, the proposed integrated framework is implemented to determine the optimal locations for wind power plants among 33 nominated provinces in Indonesia. Figure 2 displays the wind resource distribution across Indonesia.

4.1. Using DEA Models to Screen Prospective Locations

During the initial phase of the research process using DEA, a comprehensive analysis is conducted on 33 provinces, which are regarded as decision-making units (DMUs), as indicated in

Table 4. Average wind speed in Indonesia.

No	Location	DMU	Wind Speed (m/s)
1	Aceh	LOC-01	4.39
2	Bali	LOC-02	4.76
3	Banten	LOC-03	5.77
4	Bengkulu	LOC-04	4.45
5	DI Yogyakarta	LOC-05	5.72
6	DKI Jakarta	LOC-06	3.9
7	Gorontalo	LOC-07	4.86
8	Jambi	LOC-08	3.97
9	West Java	LOC-09	5.34
10	Central Java	LOC-10	5.23
11	East Java	LOC-11	5.6
12	West Kalimantan	LOC-12	4.04
13	South Kalimantan	LOC-13	4.7
14	Central Kalimantan	LOC-14	4.12
15	East Kalimantan	LOC-15	3.67
16	Bangka Belitung	LOC-16	4.55
17	Riau Islands	LOC-17	4.55
18	Lampung	LOC-18	4.48
19	Maluku	LOC-19	5.92
20	North Maluku	LOC-20	3.82
21	West Nusa Tenggara	LOC-21	5.16
22	East Nusa Tenggara	LOC-22	6.34
23	Papua	LOC-23	5.22
24	West Papua	LOC-24	4.07
25	Riau	LOC-25	3.85
26	West Sulawesi	LOC-26	3.88
27	South Sulawesi	LOC-27	5.98
28	Central Sulawesi	LOC-28	4.23
29	East Sulawesi	LOC-29	4.04
30	North Sulawesi	LOC-30	4.82
31	West Sumatra	LOC-31	4.11
32	South Sumatra	LOC-32	4.3
33	North Sumatra	LOC-33	4.33

. During this phase, our objective is to evaluate the list of locations by selecting DMUs (decision-making units) with a perfect efficiency score of 1. This evaluation is based on two inputs, namely, land cost and intensity of natural disaster occurrence, as well as three outputs, which are wind power density, quantity of proper geological areas, and population. The evaluation process is illustrated in Figure 3.

Input factors:

(I1) Land cost: The cost of acquiring the land is a significant factor that will impact the decision to host wind parks. It is an input variable, as a lower cost is preferred.

(I2) Intensity of natural disaster occurrence: Wind turbines are subject to significant damage or complete destruction as a result of natural disaster events such as storms and floods. Therefore, the frequency of natural disasters in a particular area is an important factor that is taken into account as an input variable in the DEA model. Wind turbines should be built in regions with a reduced likelihood of catastrophic events.

Output factors:

(O1) Wind power density: This refers to wind energy potential at a specific location, measured in numerical terms. The power density, which represents the average annual power per square meter of the turbine’s swept area, is determined at various heights above the ground. The determination of wind power density takes into account the influence of wind velocity and air density. The study area’s significant wind power potential renders it appealing to investors in renewable energy. Therefore, it serves as a reliable measure of performance.

(O2) Quantity of proper geological areas: It is necessary to conduct an investigation of the geological conditions, including the composition and quality of the soil, as well as other substructure conditions in order to determine if they are suitable for the construction of a power plant. Placing plants in unstable and pliable soil leads to subsidence and complete destruction of their overall framework. The indicator collects and utilizes the available area of suitable grounds near each province as an output variable, taking into account its increasing trend.

(O3) Population: A higher population in a region indicates that it is more suitable for the installation of wind turbines. Therefore, this criterion should be regarded as a result of the DEA model.

The data regarding the input and output factors of 33 locations has been gathered, as presented in

Table A1. Data collection of inputs and outputs.

Location	DMU	(I1)	(I2)	(O1)	(O2)	(O3)
Aceh	LOC-01	4000	0.037	161	540.79	5.41
Bali	LOC-02	17,000	0.015	145	441.51	4.42
Banten	LOC-03	16,000	0.017	209	1225.2	12.25
Bengkulu	LOC-04	6000	0.007	130	206.01	2.06
DI Yogyakarta	LOC-05	7000	0.012	196	376.19	3.76
DKI Jakarta	LOC-06	24,000	0.009	90	1068	10.68
Gorontalo	LOC-07	4000	0.005	158	119.27	1.19
Jambi	LOC-08	2500	0.008	76	363.11	3.63
West Java	LOC-09	10,000	0.176	189	4940.5	49.41
Central Java	LOC-10	7500	0.293	185	3703.2	37.03
East Java	LOC-11	13,000	0.119	229	4115	41.15
West Kalimantan	LOC-12	6000	0.015	70	554.14	5.54
South Kalimantan	LOC-13	8000	0.017	119	418.21	4.18
Central Kalimantan	LOC-14	6000	0.010	65	274.11	2.74
East Kalimantan	LOC-15	8000	0.013	58	385.98	3.86
Bangka Belitung Islands	LOC-16	4000	0.013	94	149.46	1.49
Riau Islands	LOC-17	8000	0.003	114	217.98	2.18
Lampung	LOC-18	4000	0.014	122	917.66	9.18
Maluku	LOC-19	8000	0.006	225	188.17	1.88
North Maluku	LOC-20	8000	0.005	78	131.93	1.32
West Nusa Tenggara	LOC-21	8000	0.016	170	547.37	5.47
East Nusa Tenggara	LOC-22	8000	0.014	288	546.63	5.47
Papua	LOC-23	10,000	0.004	131	441.86	4.42
West Papua	LOC-24	12,000	0.001	100	118.33	1.18
Riau	LOC-25	4000	0.008	56	661.44	6.61
West Sulawesi	LOC-26	6000	0.003	99	145.86	1.46
South Sulawesi	LOC-27	8000	0.032	277	922.58	9.23
Central Sulawesi	LOC-28	6000	0.014	115	306.61	3.07
East Sulawesi	LOC-29	7000	0.006	81	270.17	2.70
North Sulawesi	LOC-30	5000	0.010	158	265.95	2.66
West Sumatra	LOC-31	5000	0.032	128	564.06	5.64
South Sumatera	LOC-32	6000	0.031	89	865.7	8.66
North Sumatera	LOC-33	5000	0.035	143	1511.52	15.12

(Appendix A). The statistical analysis of these factors, including maximum, minimum, average, and standard deviation, is presented in

Table 5. Statistical analysis of factors in DEA model.

Factors	Unit	Max	Min	Avg	SD	Factors
(I1)	1000 IDR/M2	24,000	2500	7909.1	5452.30	(I1)
(I2)	Probability score	0.293	0.001	0.030	0.0818	(I2)
(O1)	W/m2	288	56	137.8	65.83	(O1)
(O2)	1000 Ha	4941	118	833.5	1441.31	(O2)
(O3)	Million	49	1	8.3	14.4	(O3)
Factors	Unit	Max	Min	Avg	SD	Factors
(I1)	1000 IDR/M2	24,000	2500	7909.1	5452.30	(I1)
(I2)	Probability score	0.293	0.001	0.030	0.0818	(I2)

. This step is executed to ascertain the prospective locations (DMUs) that possess an efficiency score of 1.

An efficiency score of 1 was achieved by 11 decision-making units (DMUs) in the DEA analysis, indicating optimal performance. These DMUs are Aceh (LOC-01), DKI Jakarta (LOC-06), Gorontalo (LOC-07), West Java (LOC-09), Central Java (LOC-10), Lampung (LOC-18), Maluku (LOC-19), Papua (LOC-23), West Papua (LOC-24), Riau (LOC-25), and North Sumatra (LOC-33). As shown in

Table 6. Efficiency scores of 33 locations.

No	Location	DMU	CCR-I	BCC-I	SBM-I-C	EBM-I-C
1	Aceh	LOC-01	1.0000	1.0000	1.0000	1.0000
2	Bali	LOC-02	0.4262	0.4266	0.4001	0.4261
3	Banten	LOC-03	0.8715	1.0000	0.8171	0.8715
4	Bengkulu	LOC-04	0.6829	0.7214	0.6623	0.6829
5	DI Yogyakarta	LOC-05	0.7440	0.7601	0.7331	0.7412
6	DKI Jakarta	LOC-06	1.0000	1.0000	1.0000	1.0000
7	Gorontalo	LOC-07	1.0000	1.0000	1.0000	1.0000
8	Jambi	LOC-08	0.8953	1.0000	0.8289	0.8810
9	West Java	LOC-09	1.0000	1.0000	1.0000	1.0000
10	Central Java	LOC-10	1.0000	1.0000	1.0000	1.0000
11	East Java	LOC-11	0.9249	1.0000	0.9215	0.9249
12	West Kalimantan	LOC-12	0.5338	0.5770	0.4896	0.5338
13	South Kalimantan	LOC-13	0.4570	0.4734	0.4459	0.4570
14	Central Kalimantan	LOC-14	0.4395	0.6283	0.4037	0.4395
15	East Kalimantan	LOC-15	0.3956	0.4997	0.3452	0.3956
16	Bangka Belitung Islands	LOC-16	0.5982	0.7067	0.4627	0.5685
17	Riau Islands	LOC-17	0.9258	1.0000	0.8682	0.9258
18	Lampung	LOC-18	1.0000	1.0000	1.0000	1.0000
19	Maluku	LOC-19	1.0000	1.0000	1.0000	1.0000
20	North Maluku	LOC-20	0.4652	0.7118	0.4633	0.4652
21	West Nusa Tenggara	LOC-21	0.6549	0.6585	0.6370	0.6549
22	East Nusa Tenggara	LOC-22	0.9655	1.0000	0.9631	0.9655
23	Papua	LOC-23	1.0000	1.0000	1.0000	1.0000
24	West Papua	LOC-24	1.0000	1.0000	1.0000	1.0000
25	Riau	LOC-25	1.0000	1.0000	1.0000	1.0000
26	West Sulawesi	LOC-26	0.8274	1.0000	0.8010	0.8274
27	South Sulawesi	LOC-27	0.9434	1.0000	0.7618	0.9084
28	Central Sulawesi	LOC-28	0.5229	0.5446	0.4941	0.5158
29	East Sulawesi	LOC-29	0.6187	0.7530	0.5796	0.6186
30	North Sulawesi	LOC-30	0.8276	0.8301	0.7684	0.8124
31	West Sumatra	LOC-31	0.7009	0.7149	0.5293	0.6819
32	South Sumatra	LOC-32	0.5423	0.6046	0.5262	0.5422
33	North Sumatra	LOC-33	1.0000	1.0000	1.0000	1.0000

, these locations are considered the most promising sites for wind power plant development. In the second phase of analysis, these selected DMUs are further evaluated using the Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy Combined Compromise Solution (F-CoCoSo) models.

While the DEA methodology is explained in more technical detail due to the mathematical differences among its variants (e.g., CCR, BCC, SBM, EBM), the Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy Combined Compromise Solution (F-CoCoSo) follow standardized procedures that are widely applied in MCDM studies. Therefore, their methodological descriptions are presented more concisely, focusing on the core steps and equations relevant to this study. Nonetheless, all critical phases from constructing the fuzzy pairwise comparison matrix to defuzzification and final ranking are described in Section 3.2 and illustrated in Table 3,

Table 7. The list of criteria and their description.

Main Criteria	Criteria	Definition
C1. Technical	C11. Availability of skilled workers	Qualified individuals with extensive training and expertise in the wind turbine industry, such as installers, technicians, and other people.
	C12. Power factor and capacity factor	The capacity factor of a wind turbine is influenced by various factors, such as wind speed, maintenance, downtime, repair downtime, and other related factors.
	C13. Terrain slope	The fluctuation of the topography of the Earth’s surface.
C2. Economic	C21. Costs	Expenses associated with the building, operation, and maintenance of a wind power facility.
	C22. Consumption of electricity	An analysis of the energy use in different regions.
	C23. Proximity to public transportation	Quantifying the distance between a proximate road and other potential sites.
	C24. Proximity to residential areas	The spatial separation between the population centers (cities or towns) and the numerous prospective locations.
	C25. Terms of network accessibility	Proximity to preexisting electrical transmission lines.
C3. Social	C31. Land acquisition	The government has power over the maximum amount of land that can be used for renewable energy projects.
	C32. Support mechanisms	Political or public dedication to endorse wind projects, such as implementing feed-in tariffs, providing preferential financing, reducing taxes, or offering other forms of subsidies.
	C33. Public acceptance	The consensus among social partners, consumer awareness regarding wind power, and its market adoption.
	C34. Rules and regulations of the government	The impact of rules and regulations on the development of wind energy systems.
C4. Environmental	C41. Impact on wildlife and endangered species	The impact of wind power facilities on animal habitats and endangered species.
	C42. Visual impact	The emergence of alterations in the physical environment resulting from the planned construction of a wind farm.
	C43. Ecological damage	The environmental impact caused by the development of wind farms includes the erosion of water and soil, as well as the accumulation of building debris.

and

Table 8. Expertise and Qualification Requirements for Wind Energy.

Expert	Work Experience	Education	Skilled Field
Expert 1	6 years	Master’s	Geographical Analysis
Expert 2	4 years	Doctorate	Wind Resource Assessment
Expert 3	5 years	Doctorate	Environmental Impact
Expert 4	7 years	Bachelor’s	Engineering and Design
Expert 5	4 years	Bachelor’s	Regulatory Compliance
Expert 6	5 years	Master’s	Community Engagement
Expert 7	9 years	Master’s	Economic Analysis
Expert 8	8 years	Bachelor’s	Logistics and Accessibility
Expert 9	4 years	Doctorate	Legal and Land Acquisition
Expert 10	3 years	Master’s	Sustainability Planning

. The criteria applied in the FAHP and F-CoCoSo stages are consistent with those found in prior wind energy site selection research, as summarized in Table 2 and explained in Table 7.

4.2. Phase II: Ordering the Remaining Locations by Rank

During this stage, the remaining locations from the initial phase are evaluated and ranked using the FAHP (Fuzzy Analytic Hierarchy Process) and F-CoCoSo (Fuzzy Cognitive Consensus Solution) models. The Fuzzy Analytic Hierarchy Process (FAHP) is utilized to allocate fuzzy preference weights to criteria by means of pairwise evaluation of expert opinions. The performance evaluation of the criteria and their preference weights are represented by linguistic phrases utilizing triangular fuzzy numbers. Therefore, F-CoCoSo is utilized to assess and prioritize the sites.

4.2.1. Estimating Fuzzy Weights Using the FAHP Model

In the FAHP method, the relative preferred fuzzy weight of each criterion is determined by considering four primary types of factors: technical, economic, social/political, and environmental. These factors are subdivided into 15 specific criteria, as detailed in Table 7.

To validate and refine the evaluation criteria, as well as to obtain consistent fuzzy pairwise comparison judgments, a panel of ten qualified experts was engaged. These experts were selected through purposive sampling to ensure a diverse representation of knowledge and practical experience relevant to wind energy planning. Their expertise spans key areas such as geographical analysis, environmental impact assessment, engineering design, regulatory frameworks, and sustainability. The expert profiles are summarized in Table 8.

The evaluation of each criterion in the Fuzzy Analytic Hierarchy Process (FAHP) is expressed using triangular fuzzy numbers, which represent pessimistic, most likely, and optimistic values.

Table 9. The relative significance of fuzzy weights of FAHP.

Criteria	Attribute	Fuzzy Geometric Mean			Triangular Fuzzy Weights			Significance Level
C11 Availability of skilled workers	max	0.7520	1.0278	1.4077	0.0357	0.0664	0.1250	0.0667
C12 Power factor and capacity factor	max	0.6922	0.9463	1.3078	0.0328	0.0612	0.1161	0.0617
C13 Terrain slope	min	0.8299	1.1543	1.5800	0.0394	0.0746	0.1403	0.0747
C21 Costs	min	0.6875	0.9280	1.2689	0.0326	0.0600	0.1127	0.0603
C22 Consumption of electricity	max	0.7209	0.9746	1.3299	0.0342	0.0630	0.1181	0.0632
C23 Proximity to public transportation	min	0.7766	1.0804	1.4844	0.0369	0.0698	0.1318	0.0700
C24 Proximity to residential areas	min	0.7803	1.0641	1.4314	0.0370	0.0688	0.1271	0.0684
C25 Terms of network accessibility	min	1.0715	1.4941	1.9701	0.0508	0.0966	0.1749	0.0946
C31 Land acquisition	max	0.8661	1.2218	1.6577	0.0411	0.0790	0.1472	0.0785
C32 Support mechanisms	max	0.5772	0.7634	1.0562	0.0274	0.0493	0.0938	0.0501
C33 Public acceptance	max	0.5283	0.6978	0.9741	0.0251	0.0451	0.0865	0.0460
C34 Rules and regulations of the government	max	0.6912	0.9458	1.3106	0.0328	0.0611	0.1164	0.0617
C41 Impact on wildlife and endangered species	min	0.8416	1.1786	1.5886	0.0399	0.0762	0.1410	0.0755
C42 Visual impact	max	1.0299	1.4534	1.9326	0.0489	0.0939	0.1716	0.0923
C43 Ecological damage	min	0.4175	0.5438	0.7725	0.0198	0.0351	0.0686	0.0363

demonstrates the application of the fuzzy geometric mean to determine the relative significance of the preference weights for all criteria. For example, the fuzzy weights for the criterion ‘Availability of skilled workers’ (C11) are as follows: the pessimistic value is 0.0357, the most likely value is 0.0664, and the optimistic value is 0.1250. Similarly, the criterion ‘Power factor and capacity factor’ (C12) has a pessimistic weight of 0.0328, a most likely weight of 0.0612, and an optimistic weight of 0.1161. This method of calculation is applied consistently across all criteria. The fuzzy preference weights are then converted into crisp values by applying the average weight criterion. This conversion process results in relative preference weights, which quantify the significance of each criterion. Figure 4 illustrates this conversion process. The criteria identified as most significant based on their weights are ‘Terms of network accessibility’ at 0.0946, ‘Visual impact’ at 0.0923, and ‘Land acquisition’ at 0.0785.

In addition to the listed environmental and social factors, it is important to recognize the impact of noise dispersion and shadow flicker on public health and perception. These elements are associated with the operation of wind turbines and can influence public acceptance, ecological concerns, and visual impact. Therefore, such effects are implicitly considered under the criteria of ‘Visual impact’ (C42), ‘Public acceptance’ (C33), and ‘Ecological damage’ (C43). Including these aspects supports the principle of preventive protection and enhances the comprehensiveness of wind farm site evaluation.

These criteria are critical in making specific decisions and selecting locations for wind power plants. The importance of each criterion is context-dependent, varying according to the unique goals and objectives of the decision-maker. The Fuzzy Analytic Hierarchy Process (FAHP) aids decision-makers by incorporating multiple factors into the evaluation process. This enables a more informed decision-making process through a thorough assessment of the relative significance of each criterion.

4.2.2. Ranking the Location Using the F-CoCoSo Model

The F-CoCoSo model utilizes triangular fuzzy numbers to represent the performance rating of 11 locations: Aceh (LOC-01), DKI Jakarta (LOC-06), Gorontalo (LOC-07), West Java (LOC-09), Central Java (LOC-10), Lampung (LOC-18), Maluku (LOC-19), Papua (LOC-23), West Papua (LOC-24), Riau (LOC-25), and North Sumatra (LOC-33). Figure 5 displays the decision hierarchy tree used to choose wind plant locations. In addition, the FAHP model is used to calculate the relative preferred fuzzy weight of each criterion. The F-CoCoSo model selects the most favorable option by taking into account the weighted combination of the additive and multiplicative methods, which assess and prioritize the alternatives with a high level of dependability.

In this study, the data used to evaluate and rank the 11 shortlisted locations in the F-CoCoSo model were based on subjective expert evaluations. The same group of ten domain experts involved in the FAHP process (described in Section 4.2.1 and Table 9) provided these assessments. Each expert evaluated the performance of each location with respect to the 15 sub-criteria using linguistic terms (“Very High”, “Moderate”, “Low”), which were then converted into triangular fuzzy numbers using a standardized fuzzy scale.

The fuzzy evaluation scores from all experts were then aggregated using the geometric mean method to create the integrated fuzzy decision matrix (

Table A2. The integrated fuzzy comparison matrix of the FAHP model.

Criteria	C11			C12			C13			C21
C11	1.0000	1.0000	1.0000	0.7319	1.0000	1.3663	0.8637	1.1802	1.5930	0.8027	1.1269	1.5397
C12	0.7319	1.0000	1.3663	1.0000	1.0000	1.0000	0.5763	0.8247	1.2221	0.6110	0.8706	1.2699
C13	0.6277	0.8473	1.1578	0.8183	1.2125	1.7351	1.0000	1.0000	1.0000	1.3299	1.8882	2.4403
C21	0.6495	0.8874	1.2457	0.7875	1.1487	1.6367	0.4098	0.5296	0.7519	1.0000	1.0000	1.0000
C22	0.6934	1.0000	1.4422	0.5921	0.8247	1.1895	0.5639	0.7725	1.0760	0.6934	1.0000	1.4422
C23	0.9221	1.3663	1.9031	1.0000	1.4198	1.9082	0.5255	0.7319	1.0845	0.8805	1.2699	1.7351
C24	1.0194	1.4587	1.9316	0.4778	0.6250	0.8874	0.8407	1.2360	1.7021	0.9733	1.3928	1.8801
C25	0.9733	1.3928	1.8801	1.0194	1.4587	1.9316	0.7813	1.1269	1.5819	1.2944	1.7811	2.2521
C31	0.5723	0.7875	1.1055	0.8805	1.3046	1.8523	1.2599	1.9031	2.5487	0.9922	1.4702	2.0317
C32	0.6371	0.8637	1.1895	0.7519	1.0194	1.3868	0.4240	0.5547	0.8091	0.4562	0.5809	0.8091
C33	0.3497	0.4757	0.7376	0.7074	1.0000	1.4137	0.3808	0.5296	0.8091	0.4440	0.5361	0.7180
C34	0.5921	0.8247	1.1895	0.5994	0.8473	1.2125	0.6988	1.0000	1.4310	0.6934	1.0000	1.4422
C41	1.0882	1.6567	2.2894	0.6934	1.0000	1.4422	0.4909	0.6673	0.9367	1.0194	1.5277	2.0784
C42	1.2599	1.7473	2.2188	0.9657	1.4702	2.0873	1.0391	1.5397	2.1596	1.0194	1.5277	2.1504
C43	0.3023	0.4109	0.6250	0.6988	0.9294	1.2457	0.3637	0.4982	0.7376	0.3866	0.4922	0.7180
Criteria	C22			C23			C24			C25
C11	0.6934	1.0000	1.4422	0.5255	0.7319	1.0845	0.5177	0.6856	0.9810	0.5319	0.7180	1.0274
C12	0.8407	1.2125	1.6888	0.5240	0.7043	1.0000	1.1269	1.5999	2.0930	0.5177	0.6856	0.9810
C13	0.9294	1.2944	1.7735	0.9221	1.3663	1.9031	0.5875	0.8091	1.1895	0.6322	0.8874	1.2799
C21	0.6934	1.0000	1.4422	0.5763	0.7875	1.1358	0.5319	0.7180	1.0274	0.4440	0.5614	0.7725
C22	1.0000	1.0000	1.0000	0.5399	0.7319	1.0556	0.5763	0.7875	1.1358	0.3971	0.5319	0.7579
C23	0.9474	1.3663	1.8523	1.0000	1.0000	1.0000	0.6988	1.0000	1.4310	0.4630	0.6201	0.8944
C24	0.8805	1.2699	1.7351	0.6988	1.0000	1.4310	1.0000	1.0000	1.0000	0.4700	0.6322	0.9189
C25	1.3195	1.8801	2.5179	1.1181	1.6125	2.1596	1.0882	1.5819	2.1277	1.0000	1.0000	1.0000
C31	0.7319	1.0968	1.5819	0.7665	1.1487	1.6252	0.6673	0.8874	1.2125	0.3637	0.4757	0.6856
C32	0.4562	0.5809	0.8091	0.4562	0.5809	0.8091	0.3866	0.4922	0.7180	0.3166	0.4368	0.6856
C33	0.3839	0.4849	0.6546	0.4098	0.5547	0.8091	1.0676	1.4986	1.9031	0.3515	0.4542	0.6371
C34	0.7813	1.1055	1.5695	0.6988	1.0000	1.4310	0.6934	1.0000	1.4422	0.6371	0.8637	1.1895
C41	0.7024	1.0194	1.3868	0.8637	1.2944	1.8444	0.7519	1.0000	1.3299	0.4630	0.6201	0.8944
C42	1.2030	1.7007	2.2521	1.2944	1.8523	2.4875	1.0391	1.5397	2.0873	1.0882	1.5930	2.2188
C43	0.3971	0.4849	0.6546	0.3866	0.5399	0.8312	0.3866	0.4922	0.7180	0.4409	0.5880	0.8091
Criteria	C31			C32			C33			C34
C11	0.9046	1.2699	1.7473	0.8407	1.1578	1.5695	1.3557	2.1020	2.8598	0.8407	1.2125	1.6888
C12	0.5399	0.7665	1.1358	0.7211	0.9810	1.3299	0.7074	1.0000	1.4137	0.8247	1.1802	1.6684
C13	0.3924	0.5255	0.7937	1.2360	1.8029	2.3586	1.2360	1.8882	2.6257	0.6988	1.0000	1.4310
C21	0.4922	0.6802	1.0079	1.2360	1.7215	2.1920	1.3928	1.8654	2.2521	0.6934	1.0000	1.4422
C22	0.6322	0.9117	1.3663	1.2360	1.7215	2.1920	1.5277	2.0621	2.6052	0.6371	0.9046	1.2799
C23	0.6153	0.8706	1.3046	1.2360	1.7215	2.1920	1.2360	1.8029	2.4403	0.6988	1.0000	1.4310
C24	0.8247	1.1269	1.4986	1.3928	2.0317	2.5869	0.5255	0.6673	0.9367	0.6934	1.0000	1.4422
C25	1.4587	2.1020	2.7499	1.4587	2.2894	3.1588	1.5695	2.2015	2.8451	0.8407	1.1578	1.5695
C31	1.0000	1.0000	1.0000	1.1487	1.6438	2.1920	1.7215	2.6693	3.5596	1.1181	1.6125	2.0873
C32	0.4562	0.6084	0.8706	1.0000	1.0000	1.0000	0.9221	1.3663	1.9031	0.9046	1.3299	1.8171
C33	0.2809	0.3746	0.5809	0.5255	0.7319	1.0845	1.0000	1.0000	1.0000	0.4791	0.6201	0.8944
C34	0.4791	0.6201	0.8944	0.5503	0.7519	1.1055	1.1181	1.6125	2.0873	1.0000	1.0000	1.0000
C41	0.6934	1.0000	1.4422	1.0391	1.5397	2.0873	0.7665	1.0968	1.5105	0.9046	1.3557	1.8949
C42	0.8805	1.2699	1.7351	1.0194	1.4587	1.9316	1.0194	1.4986	1.9931	1.0882	1.5819	2.1277
C43	0.3081	0.4222	0.6546	0.4356	0.5809	0.8473	0.4159	0.5654	0.8312	0.4159	0.5399	0.7725
Criteria	C41			C42			C43
C11	0.4368	0.6036	0.9189	0.4507	0.5723	0.7937	1.5999	2.4336	3.3082
C12	0.6934	1.0000	1.4422	0.4791	0.6802	1.0355	0.8027	1.0760	1.4310
C13	1.0676	1.4986	2.0372	0.4630	0.6495	0.9624	1.3557	2.0071	2.7499
C21	0.4811	0.6546	0.9810	0.4650	0.6546	0.9810	1.3928	2.0317	2.5869
C22	0.7211	0.9810	1.4236	0.4440	0.5880	0.8312	1.5277	2.0621	2.5179
C23	0.5422	0.7725	1.1578	0.4020	0.5399	0.7725	1.2030	1.8523	2.5869
C24	0.7519	1.0000	1.3299	0.4791	0.6495	0.9624	1.3928	2.0317	2.5869
C25	1.1181	1.6125	2.1596	0.4507	0.6277	0.9189	1.2360	1.7007	2.2679
C31	0.6934	1.0000	1.4422	0.5763	0.7875	1.1358	1.5277	2.3687	3.2453
C32	0.4791	0.6495	0.9624	0.5177	0.6856	0.9810	1.1802	1.7215	2.2957
C33	0.6621	0.9117	1.3046	0.5017	0.6673	0.9810	1.2030	1.7687	2.4042
C34	0.5277	0.7376	1.1055	0.4700	0.6322	0.9189	1.2944	1.8523	2.4042
C41	1.0000	1.0000	1.0000	1.1487	1.5695	1.9690	1.6438	2.3687	3.1206
C42	0.5079	0.6371	0.8706	1.0000	1.0000	1.0000	1.3557	2.0873	2.8374
C43	0.3204	0.4222	0.6084	0.3524	0.4791	0.7376	1.0000	1.0000	1.0000

). This matrix was used as the input for the F-CoCoSo model. The model then followed the normalization, weighting, and appraisal steps described in Equations (10)–(21) to generate the final crisp scores and rankings.

This method allows for the systematic and consistent integration of expert knowledge into the decision-making process, which is particularly useful in contexts like wind energy planning, where detailed numerical performance data for each alternative may not be readily available or comparable. The use of fuzzy linguistic evaluations is aligned with standard practices in the fuzzy MCDM literature.

Table A2 (Appendix A) shows the fuzzy aggregated decision matrix. In the next step, the matrix is normalized, referring to Equations (11) and (12).

Table A3. Aggregated Decision Matrix.

Criteria	C11			C12			C13			C21
Aceh	0.2467	0.4333	0.6333	0.3800	0.5800	0.7600	0.4733	0.6733	0.8400	0.3000	0.4800	0.6667
DKI Jakarta	0.2600	0.4600	0.6533	0.2133	0.3867	0.5800	0.3933	0.5800	0.7533	0.2267	0.4000	0.5933
Gorontalo	0.1667	0.3333	0.5267	0.2667	0.4600	0.6600	0.4067	0.6067	0.7800	0.5000	0.6867	0.8400
West Java	0.3200	0.5133	0.7000	0.3133	0.5000	0.6867	0.2667	0.4200	0.6000	0.3333	0.5267	0.7133
Central Java	0.3533	0.5533	0.7400	0.4333	0.6333	0.8133	0.3067	0.5000	0.6867	0.6200	0.7933	0.9133
Lampung	0.3667	0.5667	0.7533	0.3933	0.5933	0.7733	0.4200	0.6200	0.7933	0.2733	0.4533	0.6467
Maluku	0.2267	0.4067	0.6067	0.2867	0.4733	0.6667	0.3933	0.5933	0.7733	0.5533	0.7333	0.8733
Papua	0.2467	0.4333	0.6267	0.4467	0.6467	0.8267	0.5400	0.7200	0.8600	0.3800	0.5800	0.7600
West Papua	0.2533	0.4333	0.6333	0.5800	0.7600	0.9000	0.5267	0.7133	0.8600	0.1867	0.3400	0.5267
Riau	0.2133	0.3667	0.5533	0.1400	0.3067	0.5000	0.2733	0.4467	0.6333	0.1733	0.3267	0.5133
North Sumatra	0.2400	0.4133	0.6067	0.1333	0.2933	0.4867	0.2867	0.4667	0.6533	0.1200	0.2533	0.4333
Criteria	C22			C23			C24			C25
Aceh	0.4733	0.6667	0.8333	0.3533	0.5533	0.7400	0.3933	0.5933	0.7733	0.3800	0.5800	0.7600
DKI Jakarta	0.2600	0.4400	0.6267	0.3667	0.5667	0.7533	0.2867	0.4733	0.6667	0.2133	0.3867	0.5800
Gorontalo	0.4600	0.6600	0.8267	0.2267	0.4067	0.6067	0.4467	0.6467	0.8267	0.2667	0.4600	0.6600
West Java	0.1800	0.3200	0.5000	0.2467	0.4333	0.6267	0.5800	0.7600	0.9000	0.3133	0.5000	0.6867
Central Java	0.4067	0.6067	0.7867	0.2533	0.4333	0.6333	0.1400	0.3067	0.5000	0.4333	0.6333	0.8133
Lampung	0.3800	0.5667	0.7400	0.2133	0.3667	0.5533	0.1333	0.2933	0.4867	0.4733	0.6733	0.8400
Maluku	0.5000	0.6867	0.8400	0.2400	0.4133	0.6067	0.4733	0.6733	0.8467	0.3933	0.5800	0.7533
Papua	0.4733	0.6667	0.8267	0.4733	0.6667	0.8333	0.4600	0.6600	0.8400	0.4067	0.6067	0.7800
West Papua	0.4867	0.6733	0.8200	0.2333	0.4200	0.6200	0.3400	0.5400	0.7400	0.2667	0.4200	0.6000
Riau	0.2200	0.3800	0.5667	0.3600	0.5467	0.7200	0.1333	0.2867	0.4733	0.3067	0.5000	0.6867
North Sumatra	0.3467	0.5400	0.7200	0.6200	0.8000	0.9267	0.2467	0.4333	0.6333	0.4200	0.6200	0.7933
Criteria	C31			C32			C33			C34
Aceh	0.2667	0.4200	0.6000	0.2267	0.4000	0.5933	0.5000	0.6867	0.8400	0.6200	0.7933	0.9133
DKI Jakarta	0.3067	0.5000	0.6867	0.5000	0.6867	0.8400	0.4733	0.6667	0.8267	0.2733	0.4533	0.6467
Gorontalo	0.4200	0.6200	0.7933	0.3333	0.5267	0.7133	0.4867	0.6733	0.8200	0.5533	0.7333	0.8733
West Java	0.3933	0.5933	0.7733	0.6200	0.7933	0.9133	0.2200	0.3800	0.5667	0.3800	0.5800	0.7600
Central Java	0.2867	0.4733	0.6667	0.2733	0.4533	0.6467	0.3467	0.5400	0.7200	0.1867	0.3400	0.5267
Lampung	0.4467	0.6467	0.8267	0.5533	0.7333	0.8733	0.4733	0.6667	0.8333	0.1733	0.3267	0.5133
Maluku	0.5800	0.7600	0.9000	0.3800	0.5800	0.7600	0.2600	0.4400	0.6267	0.1200	0.2533	0.4333
Papua	0.1400	0.3067	0.5000	0.1867	0.3400	0.5267	0.4600	0.6600	0.8267	0.2267	0.4067	0.6067
West Papua	0.1333	0.2933	0.4867	0.1733	0.3267	0.5133	0.1800	0.3200	0.5000	0.4600	0.6533	0.8133
Riau	0.4733	0.6733	0.8467	0.1200	0.2533	0.4333	0.4067	0.6067	0.7867	0.2467	0.4333	0.6333
North Sumatra	0.4600	0.6600	0.8400	0.2600	0.4400	0.6267	0.3800	0.5667	0.7400	0.1000	0.2200	0.3933
Criteria	C41			C42			C43
Aceh	0.3133	0.5000	0.6867	0.3800	0.5800	0.7600	0.2267	0.4000	0.5933
DKI Jakarta	0.4333	0.6333	0.8133	0.1867	0.3400	0.5267	0.5000	0.6867	0.8400
Gorontalo	0.3933	0.5933	0.7733	0.1733	0.3267	0.5133	0.3333	0.5267	0.7133
West Java	0.2867	0.4733	0.6667	0.1200	0.2533	0.4333	0.6200	0.7933	0.9133
Central Java	0.4467	0.6467	0.8267	0.2267	0.4067	0.6067	0.2733	0.4533	0.6467
Lampung	0.5800	0.7600	0.9000	0.4600	0.6533	0.8133	0.5533	0.7333	0.8733
Maluku	0.1400	0.3067	0.5000	0.2467	0.4333	0.6333	0.3800	0.5800	0.7600
Papua	0.3200	0.5133	0.7000	0.1000	0.2200	0.3933	0.1867	0.3400	0.5267
West Papua	0.3533	0.5533	0.7400	0.2667	0.4200	0.6000	0.1733	0.3267	0.5133
Riau	0.3667	0.5667	0.7533	0.3067	0.5000	0.6867	0.1200	0.2533	0.4333
North Sumatra	0.2267	0.4067	0.6067	0.4200	0.6200	0.7933	0.2267	0.4067	0.6067

(Appendix A) indicates the fuzzy normalized decision matrix.

The fuzzy weighted comparability sequence matrix and the fuzzy exponentially weighted comparability sequence matrix for each alternative are summarized in

Table A4. Normalized Matrix.

Criteria	C11			C12			C13			C14
Aceh	0.1364	0.4545	0.7955	0.3217	0.5826	0.8174	0.0337	0.3146	0.6517	0.3109	0.5462	0.7731
DKI Jakarta	0.1591	0.5000	0.8295	0.1043	0.3304	0.5826	0.1798	0.4719	0.7865	0.4034	0.6471	0.8655
Gorontalo	0.0000	0.2841	0.6136	0.1739	0.4261	0.6870	0.1348	0.4270	0.7640	0.0924	0.2857	0.5210
West Java	0.2614	0.5909	0.9091	0.2348	0.4783	0.7217	0.4382	0.7416	1.0000	0.2521	0.4874	0.7311
Central Java	0.3182	0.6591	0.9773	0.3913	0.6522	0.8870	0.2921	0.6067	0.9326	0.0000	0.1513	0.3697
Lampung	0.3409	0.6818	1.0000	0.3391	0.6000	0.8348	0.1124	0.4045	0.7416	0.3361	0.5798	0.8067
Maluku	0.1023	0.4091	0.7500	0.2000	0.4435	0.6957	0.1461	0.4494	0.7865	0.0504	0.2269	0.4538
Papua	0.1364	0.4545	0.7841	0.4087	0.6696	0.9043	0.0000	0.2360	0.5393	0.1933	0.4202	0.6723
West Papua	0.1477	0.4545	0.7955	0.5826	0.8174	1.0000	0.0000	0.2472	0.5618	0.4874	0.7227	0.9160
Riau	0.0795	0.3409	0.6591	0.0087	0.2261	0.4783	0.3820	0.6966	0.9888	0.5042	0.7395	0.9328
North Sumatra	0.1250	0.4205	0.7500	0.0000	0.2087	0.4609	0.3483	0.6629	0.9663	0.6050	0.8319	1.0000
Criteria	C22			C23			C24			C25
Aceh	0.4444	0.7374	0.9899	0.2617	0.5234	0.8037	0.1652	0.4000	0.6609	0.1277	0.4149	0.7340
DKI Jakarta	0.1212	0.3939	0.6768	0.2430	0.5047	0.7850	0.3043	0.5565	0.8000	0.4149	0.7234	1.0000
Gorontalo	0.4242	0.7273	0.9798	0.4486	0.7290	0.9813	0.0957	0.3304	0.5913	0.2872	0.6064	0.9149
West Java	0.0000	0.2121	0.4848	0.4206	0.6916	0.9533	0.0000	0.1826	0.4174	0.2447	0.5426	0.8404
Central Java	0.3434	0.6465	0.9192	0.4112	0.6916	0.9439	0.5217	0.7739	0.9913	0.0426	0.3298	0.6489
Lampung	0.3030	0.5859	0.8485	0.5234	0.7850	1.0000	0.5391	0.7913	1.0000	0.0000	0.2660	0.5851
Maluku	0.4848	0.7677	1.0000	0.4486	0.7196	0.9626	0.0696	0.2957	0.5565	0.1383	0.4149	0.7128
Papua	0.4444	0.7374	0.9798	0.1308	0.3645	0.6355	0.0783	0.3130	0.5739	0.0957	0.3723	0.6915
West Papua	0.4646	0.7475	0.9697	0.4299	0.7103	0.9720	0.2087	0.4696	0.7304	0.3830	0.6702	0.9149
Riau	0.0606	0.3030	0.5859	0.2897	0.5327	0.7944	0.5565	0.8000	1.0000	0.2447	0.5426	0.8511
North Sumatra	0.2525	0.5455	0.8182	0.0000	0.1776	0.4299	0.3478	0.6087	0.8522	0.0745	0.3511	0.6702
Criteria	C31			C32			C33			C34
Aceh	0.1739	0.3739	0.6087	0.1345	0.3529	0.5966	0.4848	0.7677	1.0000	0.6393	0.8525	1.0000
DKI Jakarta	0.2261	0.4783	0.7217	0.4790	0.7143	0.9076	0.4444	0.7374	0.9798	0.2131	0.4344	0.6721
Gorontalo	0.3739	0.6348	0.8609	0.2689	0.5126	0.7479	0.4646	0.7475	0.9697	0.5574	0.7787	0.9508
West Java	0.3391	0.6000	0.8348	0.6303	0.8487	1.0000	0.0606	0.3030	0.5859	0.3443	0.5902	0.8115
Central Java	0.2000	0.4435	0.6957	0.1933	0.4202	0.6639	0.2525	0.5455	0.8182	0.1066	0.2951	0.5246
Lampung	0.4087	0.6696	0.9043	0.5462	0.7731	0.9496	0.4444	0.7374	0.9899	0.0902	0.2787	0.5082
Maluku	0.5826	0.8174	1.0000	0.3277	0.5798	0.8067	0.1212	0.3939	0.6768	0.0246	0.1885	0.4098
Papua	0.0087	0.2261	0.4783	0.0840	0.2773	0.5126	0.4242	0.7273	0.9798	0.1557	0.3770	0.6230
West Papua	0.0000	0.2087	0.4609	0.0672	0.2605	0.4958	0.0000	0.2121	0.4848	0.4426	0.6803	0.8770
Riau	0.4435	0.7043	0.9304	0.0000	0.1681	0.3950	0.3434	0.6465	0.9192	0.1803	0.4098	0.6557
North Sumatra	0.4261	0.6870	0.9217	0.1765	0.4034	0.6387	0.3030	0.5859	0.8485	0.0000	0.1475	0.3607
Criteria	C41			C42			C43
Aceh	0.2807	0.5263	0.7719	0.3925	0.6729	0.9252	0.4034	0.6471	0.8655
DKI Jakarta	0.1140	0.3509	0.6140	0.1215	0.3364	0.5981	0.0924	0.2857	0.5210
Gorontalo	0.1667	0.4035	0.6667	0.1028	0.3178	0.5794	0.2521	0.4874	0.7311
West Java	0.3070	0.5614	0.8070	0.0280	0.2150	0.4673	0.0000	0.1513	0.3697
Central Java	0.0965	0.3333	0.5965	0.1776	0.4299	0.7103	0.3361	0.5798	0.8067
Lampung	0.0000	0.1842	0.4211	0.5047	0.7757	1.0000	0.0504	0.2269	0.4538
Maluku	0.5263	0.7807	1.0000	0.2056	0.4673	0.7477	0.1933	0.4202	0.6723
Papua	0.2632	0.5088	0.7632	0.0000	0.1682	0.4112	0.4874	0.7227	0.9160
West Papua	0.2105	0.4561	0.7193	0.2336	0.4486	0.7009	0.5042	0.7395	0.9328
Riau	0.1930	0.4386	0.7018	0.2897	0.5607	0.8224	0.6050	0.8319	1.0000
North Sumatra	0.3860	0.6491	0.8860	0.4486	0.7290	0.9720	0.3866	0.6387	0.8655

(Appendix A) and

Table A5. Fuzzy weighted comparability Sequence matrix.

Criteria	C11			C12			C13			C21
Aceh	0.0049	0.0302	0.0994	0.0106	0.0356	0.0949	0.0013	0.0235	0.0914	0.0101	0.0328	0.0871
DKI Jakarta	0.0057	0.0332	0.1037	0.0034	0.0202	0.0677	0.0071	0.0352	0.1103	0.0132	0.0388	0.0975
Gorontalo	0.0000	0.0189	0.0767	0.0057	0.0261	0.0798	0.0053	0.0319	0.1072	0.0030	0.0171	0.0587
West Java	0.0093	0.0392	0.1136	0.0077	0.0292	0.0838	0.0173	0.0553	0.1403	0.0082	0.0292	0.0824
Central Java	0.0114	0.0438	0.1221	0.0129	0.0399	0.1030	0.0115	0.0453	0.1308	0.0000	0.0091	0.0417
Lampung	0.0122	0.0453	0.1250	0.0111	0.0367	0.0969	0.0044	0.0302	0.1040	0.0110	0.0348	0.0909
Maluku	0.0036	0.0272	0.0937	0.0066	0.0271	0.0808	0.0058	0.0335	0.1103	0.0016	0.0136	0.0511
Papua	0.0049	0.0302	0.0980	0.0134	0.0409	0.1050	0.0000	0.0176	0.0757	0.0063	0.0252	0.0757
West Papua	0.0053	0.0302	0.0994	0.0191	0.0500	0.1161	0.0000	0.0184	0.0788	0.0159	0.0433	0.1032
Riau	0.0028	0.0226	0.0824	0.0003	0.0138	0.0555	0.0150	0.0520	0.1387	0.0164	0.0443	0.1051
North Sumatra	0.0045	0.0279	0.0937	0.0000	0.0128	0.0535	0.0137	0.0495	0.1356	0.0197	0.0499	0.1127
Criteria	C22			C23			C24			C25
Aceh	0.0152	0.0464	0.1169	0.0096	0.0365	0.1059	0.0061	0.0275	0.0840	0.0065	0.0401	0.1284
DKI Jakarta	0.0041	0.0248	0.0799	0.0090	0.0352	0.1035	0.0113	0.0383	0.1017	0.0211	0.0699	0.1749
Gorontalo	0.0145	0.0458	0.1157	0.0165	0.0509	0.1293	0.0035	0.0227	0.0752	0.0146	0.0586	0.1600
West Java	0.0000	0.0134	0.0573	0.0155	0.0483	0.1256	0.0000	0.0126	0.0530	0.0124	0.0524	0.1470
Central Java	0.0117	0.0407	0.1085	0.0152	0.0483	0.1244	0.0193	0.0532	0.1260	0.0022	0.0318	0.1135
Lampung	0.0104	0.0369	0.1002	0.0193	0.0548	0.1318	0.0200	0.0544	0.1271	0.0000	0.0257	0.1023
Maluku	0.0166	0.0484	0.1181	0.0165	0.0502	0.1269	0.0026	0.0203	0.0707	0.0070	0.0401	0.1247
Papua	0.0152	0.0464	0.1157	0.0048	0.0254	0.0838	0.0029	0.0215	0.0729	0.0049	0.0360	0.1210
West Papua	0.0159	0.0471	0.1145	0.0158	0.0496	0.1281	0.0077	0.0323	0.0928	0.0195	0.0647	0.1600
Riau	0.0021	0.0191	0.0692	0.0107	0.0372	0.1047	0.0206	0.0550	0.1271	0.0124	0.0524	0.1489
North Sumatra	0.0086	0.0344	0.0966	0.0000	0.0124	0.0567	0.0129	0.0419	0.1083	0.0038	0.0339	0.1172
Criteria	C31			C32			C33			C34
Aceh	0.0071	0.0295	0.0896	0.0037	0.0174	0.0560	0.0122	0.0346	0.0865	0.0210	0.0521	0.1164
DKI Jakarta	0.0093	0.0378	0.1062	0.0131	0.0352	0.0851	0.0111	0.0332	0.0847	0.0070	0.0266	0.0782
Gorontalo	0.0154	0.0501	0.1267	0.0074	0.0253	0.0701	0.0116	0.0337	0.0839	0.0183	0.0476	0.1106
West Java	0.0139	0.0474	0.1229	0.0173	0.0419	0.0938	0.0015	0.0137	0.0507	0.0113	0.0361	0.0944
Central Java	0.0082	0.0350	0.1024	0.0053	0.0207	0.0623	0.0063	0.0246	0.0708	0.0035	0.0180	0.0610
Lampung	0.0168	0.0529	0.1331	0.0150	0.0381	0.0890	0.0111	0.0332	0.0856	0.0030	0.0170	0.0591
Maluku	0.0239	0.0645	0.1472	0.0090	0.0286	0.0757	0.0030	0.0178	0.0585	0.0008	0.0115	0.0477
Papua	0.0004	0.0179	0.0704	0.0023	0.0137	0.0481	0.0106	0.0328	0.0847	0.0051	0.0230	0.0725
West Papua	0.0000	0.0165	0.0678	0.0018	0.0129	0.0465	0.0000	0.0096	0.0419	0.0145	0.0416	0.1021
Riau	0.0182	0.0556	0.1369	0.0000	0.0083	0.0370	0.0086	0.0292	0.0795	0.0059	0.0250	0.0763
North Sumatra	0.0175	0.0542	0.1357	0.0048	0.0199	0.0599	0.0076	0.0264	0.0734	0.0000	0.0090	0.0420
Criteria	C41			C42			C43
Aceh	0.0112	0.0401	0.1089	0.0192	0.0632	0.1588	0.0080	0.0227	0.0594
DKI Jakarta	0.0046	0.0267	0.0866	0.0059	0.0316	0.1026	0.0018	0.0100	0.0357
Gorontalo	0.0067	0.0307	0.0940	0.0050	0.0298	0.0994	0.0050	0.0171	0.0501
West Java	0.0123	0.0428	0.1138	0.0014	0.0202	0.0802	0.0000	0.0053	0.0254
Central Java	0.0039	0.0254	0.0841	0.0087	0.0404	0.1219	0.0067	0.0204	0.0553
Lampung	0.0000	0.0140	0.0594	0.0247	0.0729	0.1716	0.0010	0.0080	0.0311
Maluku	0.0210	0.0595	0.1410	0.0100	0.0439	0.1283	0.0038	0.0148	0.0461
Papua	0.0105	0.0388	0.1076	0.0000	0.0158	0.0706	0.0097	0.0254	0.0628
West Papua	0.0084	0.0347	0.1015	0.0114	0.0421	0.1203	0.0100	0.0260	0.0640
Riau	0.0077	0.0334	0.0990	0.0142	0.0527	0.1411	0.0120	0.0292	0.0686
North Sumatra	0.0154	0.0494	0.1250	0.0219	0.0685	0.1668	0.0077	0.0224	0.0594

(Appendix A), respectively. By applying Equations (15)–(17), three fuzzy appraisal scores $\left(\widetilde{f_{ia}},\widetilde{f_{ib}},\widetilde{f_{ic}}\right)$ are calculated and presented in

Table 10. Utility degree and fuzzy matrix of ${\tilde{T}}_i$.

Location	$\mathbf{Fuzzy} \mathbf{Fia} \left(\widetilde{{\mathit{f}}_{\mathit{i}\mathit{a}}}\right)$			$\mathbf{Fuzzy} \mathbf{Fib} \left(\widetilde{{\mathit{f}}_{\mathit{i}\mathit{b}}}\right)$			$\mathbf{Fuzzy} \mathbf{Fic} \left(\widetilde{{\mathit{f}}_{\mathit{i}\mathit{c}}}\right)$
Aceh	0.0707	0.0916	0.1302	2.8668	7.2897	17.7998	0.7729	0.9085	0.9985
DKI Jakarta	0.0698	0.0910	0.1295	2.6430	6.8927	17.0822	0.7628	0.9024	0.9931
Gorontalo	0.0660	0.0911	0.1297	2.6269	6.9977	17.2924	0.7206	0.9031	0.9944
West Java	0.0565	0.0904	0.1290	2.4084	6.7757	16.7025	0.6171	0.8967	0.9892
Central Java	0.0654	0.0908	0.1295	2.5514	6.8878	17.1855	0.7140	0.9006	0.9933
Lampung	0.0641	0.0917	0.1304	2.8899	7.5368	18.0611	0.6998	0.9091	0.9997
Maluku	0.0688	0.0909	0.1295	2.6713	6.9359	17.1080	0.7514	0.9008	0.9927
Papua	0.0585	0.0891	0.1277	2.0406	5.9232	15.3828	0.6395	0.8834	0.9795
West Papua	0.0586	0.0911	0.1296	2.6355	7.1362	17.2868	0.6405	0.9034	0.9941
Riau	0.0655	0.0914	0.1300	2.7757	7.2593	17.6507	0.7153	0.9060	0.9969
North Sumatra	0.0581	0.0909	0.1296	2.5467	7.0618	17.2781	0.6346	0.9012	0.9937

.

Based on Equations (18)–(21), these fuzzy appraisal scores $\left(\widetilde{f_{ia}},\widetilde{f_{ib}},\widetilde{f_{ic}}\right)$ were transformed into crisp appraisal scores Crisp $\left(\widetilde{f_{ia}},\widetilde{f_{ib}},\widetilde{f_{ic}}\right)$. The final score (Fi) for each alternative is estimated by integrating all these appraisal points. The crisp appraisal scores, final scores, and rankings of each location are given in

Table 11. Utility functions and final ranking of locations.

Location	$\mathit{C}\mathit{r}\mathit{i}\mathit{s}\mathit{p}{\mathit{f}}_{\mathit{i}\mathit{a}}$	$\mathit{C}\mathit{r}\mathit{i}\mathit{s}\mathit{p}{\mathit{f}}_{\mathit{i}\mathit{b}}$	$\mathit{C}\mathit{r}\mathit{i}\mathit{s}\mathit{p}{\mathit{f}}_{\mathit{i}\mathit{c}}$	Final Score Fi	Rank
Aceh	0.0975	9.3187	0.8933	4.3694	2
DKI Jakarta	0.0968	8.8727	0.8861	4.1981	7
Gorontalo	0.0956	8.9723	0.8727	4.2214	4
West Java	0.0920	8.6288	0.8343	4.0566	10
Central Java	0.0952	8.8749	0.8693	4.1822	9
Lampung	0.0954	9.4959	0.8695	4.4104	1
Maluku	0.0964	8.9051	0.8816	4.2055	6
Papua	0.0918	7.7822	0.8341	3.7442	11
West Papua	0.0931	9.0195	0.8460	4.2119	5
Riau	0.0956	9.2286	0.8727	4.3156	3
North Sumatra	0.0929	8.9622	0.8432	4.1880	8

.

According to the study results, the top three provinces for the construction of wind power plants are Lampung (LOC-18), Aceh (LOC-01), and Riau (LOC-25). They are ranked first, second, and third, with utility function scores of 4.4104, 4.3694, and 4.3156, respectively. These locations have been identified as the most suitable for wind energy development, based on a comprehensive evaluation using the Fuzzy Combined Compromise Solution (F-CoCoSo) model. Figure 6 displays the final location ranking, while Figure 7, Figure 8, and Figure 9 illustrate the geographic positioning and characteristics of the top-ranked locations: Lampung, Aceh, and Riau.

5. Discussion

This study proposed a two-phase decision-making framework that integrates Data Envelopment Analysis (DEA), Fuzzy Analytic Hierarchy Process (FAHP), and Fuzzy Combined Compromise Solution (F-CoCoSo) to evaluate and rank optimal locations for wind energy development in Indonesia. The findings provide valuable insights into the effectiveness of hybrid MCDM techniques and the suitability of different provinces for renewable energy investment.

5.1. Methodological Contribution

The combination of DEA and fuzzy MCDM methods enables a comprehensive evaluation of both quantitative and qualitative factors. DEA effectively identified 11 efficient locations from an initial set of 33 provinces, based on objective performance metrics such as wind power density, geological conditions, land cost, and population. These shortlisted locations were further evaluated using FAHP to weight 15 criteria across technical, economic, social, and environmental dimensions. F-CoCoSo then synthesized these weights with expert evaluations to provide a robust ranking of potential sites. This approach demonstrates the value of integrating objective screening with subjective expert judgment, offering a more holistic decision-making framework than single-method models.

5.2. Interpretation of Results

Among the efficient provinces, Lampung, Aceh, and Riau consistently ranked as the most suitable locations for wind power development. Lampung scored the highest, likely due to its favorable wind power density, reasonable land costs, and strong technical and environmental performance. Aceh and Riau also displayed strategic advantages in terms of natural resource availability, public acceptance, and grid accessibility. These findings align with the spatial characteristics and energy demands of the selected provinces. For example, Lampung and Riau are located in regions with growing industrial activity and infrastructure support, making them practical for large-scale renewable energy deployment. The results are also consistent with Indonesia’s renewable energy targets and guide the narrowing down of investment zones.

5.3. Practical Implications

The findings provide useful guidance for national and regional energy planners. Prioritizing the development of wind energy in Lampung, Aceh, and Riau could accelerate Indonesia’s progress toward achieving its renewable energy targets. The methodological framework used in this study could also serve as a reference for similar site selection problems in other renewable energy sectors or regions. Policymakers and investors can use this ranking to make more informed decisions, reduce site selection risk, and allocate development resources more efficiently. This is especially important as Indonesia works toward increasing the share of renewables in its energy mix under the RUEN roadmap.

6. Conclusions

The primary objective of this study was to identify the optimal locations for the construction of wind power plants among 33 provinces in Indonesia, focusing on areas with high potential for wind energy deployment. Through expert interviews and literature reviews, essential factors influencing site suitability for wind energy projects were identified. These factors were then rigorously analyzed using multi-criteria decision-making (MCDM) methods.

The application of the Data Envelopment Analysis (DEA) model effectively pinpointed the most promising sites by evaluating quantitative factors such as land cost, wind power density, and geographical suitability. The Fuzzy Analytic Hierarchy Process (FAHP) played a crucial role in weighting qualitative criteria, including socio-economic acceptance and environmental impacts, which are subjective yet vital for the sustainable development of projects. The Fuzzy Combined Compromise Solution (F-CoCoSo) method then synthesized these evaluations to rank the sites, highlighting Lampung, Aceh, and Riau as the top provinces. These provinces were identified based on their strategic suitability for wind energy development, underscored by a balance of cost-effectiveness, community acceptance, and environmental considerations.

The findings of this study support Indonesia’s national energy transition goals outlined in the Rencana Umum Energi Nasional (RUEN), which targets a 23% renewable energy mix by 2025 and 31% by 2050. By identifying high-potential wind power sites such as Lampung, Aceh, and Riau, this research provides actionable insights for spatial energy planning and provincial investment prioritization. These locations not only show technical suitability but also align with regions that have active industrial zones and existing infrastructure, making them strategically favorable for renewable energy integration. The proposed framework can assist government agencies such as the Ministry of Energy and Mineral Resources (ESDM) in refining their regional energy blueprints and incentivizing private-sector investments through targeted subsidies or public–private partnerships. Furthermore, incorporating such location-based insights into national electricity procurement plans (RUPTL) would promote a more balanced and regionally optimized renewable energy deployment.

While this study considers “network accessibility” as a criterion for evaluating proximity to existing transmission lines, it does not include a detailed assessment of the technical integration with Indonesia’s power grid. The practical implementation of wind projects requires thorough grid feasibility studies, including capacity analysis, load-flow modeling, and infrastructure readiness. Therefore, we recommend that future research complement site prioritization with electrical grid assessments to ensure that selected locations can be reliably and efficiently connected to the national transmission system.

Regarding limitations and future research, while this study provides a robust framework for site selection, it is contingent upon the reliability of available data and the accuracy of expert inputs, which could affect its universality and scalability. Future research should consider applying this framework to other forms of renewable energy and expand the criteria to include more diverse economic and political factors that could influence the practical implementation of wind energy projects. Exploring alternative methodologies, such as stochastic DEA, could address the variability in data more effectively. Moreover, integrating advanced techniques like artificial intelligence and machine learning might significantly enhance the predictive accuracy and adaptability of the site selection models, providing a more dynamic tool for policymakers and investors in the renewable energy sector.