Direct-Use Geothermal Energy Location Multi-Criteria Planning for On-Site Energy Security in Emergencies: A Case Study of Malaysia

Abstract

Geothermal potential is a significant advantage in terms of renewable energy for countries located on the Pacific Ring of Fire. Studies on geothermal energy sources show that Malaysia is one of the countries possessing this inexhaustible and stable energy source. This on-site energy source is a promising solution to the problem of energy security during emergencies where the energy supply chain is disrupted. To exploit this advantage, this study proposes a novel tri-layer framework to prioritize locations for direct-use geothermal energy location (DGL) in Malaysia. First, the proposed locations are screened for feasibility to limit the impact on other natural conservation areas and stable residential areas. In the second layer, locations are evaluated for efficiency using the data envelopment analysis (DEA) model based on quantitative indicators. In the third layer, the spherical fuzzy extended combination of the analytic hierarchy process (SF AHP) and the combined compromise solution (SF CoCoSo) methods are introduced and applied to prioritize high-efficiency locations. According to the findings, costs, social acceptance, and noise impacts are the qualitative criteria of most concern for DGLs. Through the tri-layer framework, the suggested concordant locations for DGLs in Malaysia are Marudi of Sarawak, Tawau of Sabah, Serian of Sarawak, and Jeram of Selangor.

1. Introduction

In recent years, energy consumption has been increasing rapidly on a global scale. Meanwhile, humanity is still significantly dependent on fossil sources for energy supply. In addition to the depletion of reserves and instability in supply, the unsustainability of fossil energy is also reflected in the emissions it produces [1,2]. Governments have begun to review their energy strategies and policies to reduce greenhouse gases and related problems. This can be illustrated with the following examples. The UAE has targeted 50% renewable energy by 2050, lowering CO₂ emissions by 70% and cutting current energy use by 40%. Meanwhile, China and Malaysia are the leading countries in green energy supply chains. [3]. The appropriate type of renewable energy for each country is determined based on three factors, including geographical position, climatic circumstances, and renewable resource availability. Malaysia is blessed with rich natural resources that can be a potential source for sustainable clean energy generation, especially geothermal [4]. Along with that advantage, the Malaysian government has been working to mitigate global climate change by committing to increasing use of carbon-neutral energy sources, and recently raised the renewable energy target for the country from 20% to 31% by 2025 [5]. As a country located in the Pacific Ring of Fire, Malaysia’s geothermal power has the potential to become a clean, stable, and local source for electricity generation. Geothermal energy is more flexible than other renewable energy sources such as solar and wind, which are susceptible to weather variations [5]. Furthermore, among energy sources such as coal, nuclear, wind, and other renewable resources, geothermal energy requires less land use [6]. With its promising potential, many studies on the transformation and development of geothermal industry in Malaysia have been reported [7,8,9]. The majority of studies, on the other hand, are generally focused on the viability of geothermal energy extraction or well drilling techniques. Therefore, a research gap exists regarding the multi-dimensional evaluation of suitable locations for geothermal energy projects in Malaysia. The multi-criteria solution for suitable locations is even more important for direct-use geothermal energy locations (DGL) [10]. Unlike projects supplying electricity to the grid, locations of direct-use geothermal energy plants both require efficiency and ensure connectivity to the facilities they serve.

This is the essential motivation behind this study. In this paper, a multi-layer DEA-based spherical fuzzy hybrid decision making approach is proposed to identify the appropriate DGLs in Malaysia. The proposed hybrid approach is composed of data envelopment analysis (DEA), a spherical fuzzy analytic hierarchy process (SF AHP), and a spherical fuzzy combined compromise solution (SF CoCoSo). After the feasibility screening in the first layer, the high-efficiency DGLs were identified by applying the DEA model in the second layer. Later, the combination of SF AHP and SF CoCoSo method was used to determine the criteria weights and DGLs priorities. The findings on the appropriateness of DGLs in Malaysia are the primary contribution of this study. The secondary but core novelty contribution is the first application of the combination of the DEA model, SF AHP, and SF CoCoSo methods.

2. Literature Review

Geothermal energy is considered one of the most high-potential and sustainable energy sources. This energy source is receiving more and more attention around the world. Erdogdu stated that geothermal energy is an attractive option in Turkey to replace fossil fuels. It is estimated that if Turkey used all of its geothermal potentials, it could meet 14% of its total energy needs (heat and electricity) from geothermal sources [11]. Energy sources are also highly valued in Indonesia; Indonesia’s geothermal energy potential is estimated at 40% of the world’s geothermal energy potential, or about 28,617 MW. The Indonesian government is continuing efforts to increase the capacity of geothermal power plants. It is expected to install more geothermal power plants in Indonesia with a capacity of up to 9500 MW by 2025 [12]. In the study of Dalimin, the findings show that the potential for geothermal development in Malaysia is huge [13]. Recent studies often focus on the development of well drilling technology and drilling capacity calculation. As a prime example, Sien et al. studied the development of the first geothermal plant in Malaysia [14]. This paper presents previous studies on geothermal energy that have been used by other countries to their advantage and technological enhancement. Shamoushaki proposed direct estimates of both cost and drilling time be used in basic and feasibility studies for geothermal power plants applied worldwide [15]. The models include both specific correlations between different types of wells and general correlations for rough estimates. In addition, several other studies have investigated the geothermal potential in Malaysia. The findings indicate that Malaysia is a promising destination for geothermal energy investments [10,16,17], and the determination of the appropriate location is considered the most prominent topic. The MCDM methods are commonly applied for renewable energy site selection problems [18]. To deal with subjective judgments, fuzzy extensions of MCDM methods have been continuously developed in recent years [19,20]. Furthermore, researchers develop and introduce more and more combinations of MCDM methods in the fuzzy environment [21]. Method combinations are composed of traditional methods such as AHP [22], the best worst method (BWM) [23], the technique for order preference by similarity to ideal solution (TOPSIS) [24], the evaluation based on distance from average solution (EDAS) [25], VIKOR (Visekriterijumska Optimizacija i Kompromisno Resenje in Serbian, which translates to multi-criteria optimization and compromise solution) [26], the decision making trial and evaluation laboratory (DEMATEL) [27, and so on [28,29]. In several studies, quantitative techniques such as DEA [30], simulation [31], and geographic information system (GIS) [32] were also used to reinforce MCDM solutions. Inspired by this, our study proposes a spherical fuzzy extended combination of the most popular weighting method, AHP, and the emerging prioritization method, CoCoSo [22,33].

3. Materials and Methods

In order to identify both effective and efficient locations for DGLs, this study proposes a novel tri-layer framework to analyze both quantitative indicators and qualitative criteria as shown in Figure 1. In the primary phase, experts, who have experience in the field of geothermal energy and public investment, are identified for contributing to the research. In layer 1, potential locations are suggested for DGLs by the experts. Then, feasibility screening is performed to exclude potential locations that are in protected areas. The remaining locations are considered as possible locations. In layer 2, quantitative indicators are defined to evaluate the efficiency of locations. Based on these indications, the DEA model is applied to identify high-efficiency locations for DGLs. In layer 3, the priority of the experts is first determined based on their expertise and experience. After that, the qualitative assessment criteria and their weights are determined using the SF AHP method. Ultimately, the recently established SF CoCoSo method is applied to determine the effective locations among the high-efficiency locations. As a result, locations that are both effective and efficient are determined for the DGLs.

3.1. Data Envelopment Analysis

In 1978, a DEA mathematical model-based efficiency measurement tool was introduced, known as the CCR model [34]. The efficiency, in terms of decision making units (DMU), is determined based on the idea of maximizing the ratio of weighted inputs to weighted outputs. Considering the $T$ inputs and $R$ outputs of the $K$ DMUs, the relative efficiency $\left({\epsilon }_k\right)$ of $\mathrm{the} k$th DMU is determined based on the virtual variables of $t$th input ($u_t$) and $r$th output ($v_r$) using the following model:

$$Maximize {\epsilon }_k=\frac{{{\displaystyle \sum }}_{r=1}^R{v}_r{y}_{rk}}{{{\displaystyle \sum }}_{t=1}^T{u}_t{x}_{tk}}$$

(1)

subjected to

$$\frac{{{\displaystyle \sum }}_{r=1}^R{v}_r{y}_{rk}}{{{\displaystyle \sum }}_{t=1}^T{u}_t{x}_{tk}}\le 1, r=1, 2, \dots , R;t=1, 2, \dots ,T;k=1, 2, \dots ,K$$

(2)

$$u_t\ge 0, t=1, 2, \dots , T$$

(3)

$$v_r\ge 0, r=1, 2, \dots , R$$

(4)

where $x_{tk} and y_{rk}$ represent the $t$th input and $r$th output of the $k$th DMU, respectively. By solving the CCR model, $\mathrm{the} k$th DMU with a relative efficiency $\left({\epsilon }_k\right)$ of 1 is considered as an efficient DMU. However, the constant return-to-scale assumption of the CCR model is not applicable in several cases. In 1984, Banker, Charnes, and Cooper developed a DEA model for variable return-to-scale with an intercept ($\theta$) at the production frontier, known as the BBC model, as presented below [35].

$$Maximize {\epsilon }_k=\frac{{{\displaystyle \sum }}_{r=1}^R{v}_r{y}_{rk}-\theta }{{{\displaystyle \sum }}_{t=1}^T{u}_t{x}_{tk}}$$

(5)

subjected to

$$\frac{{{\displaystyle \sum }}_{r=1}^R{v}_r{y}_{rk}-\theta }{{{\displaystyle \sum }}_{t=1}^T{u}_t{x}_{tk}}\le 1 , r=1, 2, \dots , R;t=1, 2, \dots ,T;k=1, 2, \dots ,K$$

(6)

$$u_t\ge 0, t=1, 2, \dots , T$$

(7)

$$v_r\ge 0, r=1, 2, \dots , R$$

(8)

The positive value of $\theta$ at the DMU’s production frontier represents a decreasing return-to-scale, and vice versa. In 2001, Tone introduced a model that measures the efficiency of DMUs based on input slack and output slack, named the slack-based measurement (SBM) model, as shown in Equations (9)–(12) [36]. The $k$th DMU is considered as an SBM-efficient DMU if ${\beta }_r^{-}=0, {\beta }_t^{+}=0,$ and$Z_k=1$.

$$Minimize Z_k=\frac{1-\frac{1}{R}{{\displaystyle \sum }}_{r=1}^R\frac{{\beta }_r^{-}}{y_{rk}}}{1+\frac{1}{T}{{\displaystyle \sum }}_{t=1}^T\frac{{\beta }_t^{+}}{x_{tk}}}$$

(9)

subjected to

$$y_{rk}={\displaystyle \sum }_{i=1}^K{\sigma }_i{y}_{ri}+{\beta }_r^{-}, r=1, 2, \dots ,R$$

(10)

$$x_{tk}={\displaystyle \sum }_{i=1}^K{\sigma }_i{x}_{ti}+{\beta }_t^{+}, t=1, 2, \dots ,T$$

(11)

$${\sigma }_i, {\beta }_r^{-}, {\beta }_t^{+}\ge 0, r=1, 2, \dots , R;t=1, 2, \dots ,T;i=1, 2, \dots ,K$$

(12)

3.2. The Spherical Fuzzy Extension of AHP-CoCoSo Method (SF AHP-CoCoSo)

To describe the internal ambiguity of the decision makers in the decision-making process, fuzzy sets have been researched, developed, and applied in the field of decision science for many years [37,38,39,40,41,42,43]. In 2019, the spherical fuzzy sets were introduced by Fatma and Cengiz as a generalization of picture fuzzy sets [20]. The definition and operators of SFN are presented as follows:

Definition 1.

In the universe of discourse S, the spherical fuzzy set $\tilde{N}$is defined by

$$\tilde{N}=\{\langle s,\left({\vartheta }_{\tilde{N}}\left(s\right),{\mu }_{\tilde{N}}\left(s\right),{\pi }_{\tilde{N}}\left(s\right)\right)|s\in S\}$$

(13)

where

$${\vartheta }_{\tilde{N}},{\mu }_{\tilde{N}}, {\pi }_{\tilde{N}}:S\to \left[0, 1\right] and 0\le {\vartheta }_{\tilde{N}}^2\left(x\right)+{\mu }_{\tilde{N}}^2\left(x\right)+{\pi }_{\tilde{N}}^2\left(x\right)\le 1 \forall s\in S$$

(14)

The parameters${\vartheta }_{\tilde{N}}\left(s\right),{\mu }_{\tilde{N}}\left(s\right),$and${\pi }_{\tilde{N}}\left(s\right)$are the membership degree, non-membership degree, and hesitancy degree of each$s$to$\tilde{N}$, respectively.

Definition 2.

In the universe of discourse$S_1$and$S_2$, two spherical fuzzy numbers,$\tilde{N}=\left({\vartheta }_{\tilde{N}},{\mu }_{\tilde{N}}, {\pi }_{\tilde{N}}\right)$and$\tilde{M}=\left({\vartheta }_{\tilde{M}},{\mu }_{\tilde{M}}, {\pi }_{\tilde{M}}\right)$, possess the basic operators; these are defined by Equations (15)–(18):

$$\tilde{N}\oplus \tilde{M}=\left\{{({\vartheta }_{\tilde{N}}^2+{\vartheta }_{\tilde{M}}^2-{\vartheta }_{\tilde{N}}^2{\vartheta }_{\tilde{M}}^2)}^{\frac{1}{2}},{\mu }_{\tilde{N}}{\mu }_{\tilde{M}},{\left(\left(1-{\vartheta }_{\tilde{M}}^2\right){\pi }_{\tilde{N}}^2+\left(1-{\vartheta }_{\tilde{N}}^2\right){\pi }_{\tilde{M}}^2-{\pi }_{\tilde{N}}^2{\pi }_{\tilde{M}}^2\right)}^{\frac{1}{2}} \right\}$$

(15)

$$\tilde{N}\otimes \tilde{M}=\left\{ {\vartheta }_{\tilde{N}}{\vartheta }_{\tilde{M}},{\left({\mu }_{\tilde{N}}^2+{\mu }_{\tilde{M}}^2-{\mu }_{\tilde{N}}^2{\mu }_{\tilde{M}}^2\right)}^{\frac{1}{2}},{\left(\left(1-{\mu }_{\tilde{M}}^2\right){\pi }_{\tilde{N}}^2+\left(1-{\mu }_{\tilde{N}}^2\right){\pi }_{\tilde{M}}^2-{\pi }_{\tilde{N}}^2{\pi }_{\tilde{M}}^2\right)}^{\frac{1}{2}} \right\}$$

(16)

$$\alpha \tilde{N}=\left\{{\left(1-{\left(1-{\vartheta }_{\tilde{N}}^2\right)}^{\alpha }\right)}^{\frac{1}{2}},{\mu }_{\tilde{N}}^{\alpha }, {\left({\left(1-{\vartheta }_{\tilde{N}}^2\right)}^{\alpha }-{\left(1-{\vartheta }_{\tilde{N}}^2-{\pi }_{\tilde{N}}^2\right)}^{\alpha }\right)}^{\frac{1}{2}} \right\}, \forall \alpha >0$$

(17)

$${\tilde{A}}^{\alpha }=\left\{{\vartheta }_{\tilde{N}}^{\alpha },{\left(1-{\left(1-{\mu }_{\tilde{N}}^2\right)}^{\alpha }\right)}^{\frac{1}{2}},{\left({\left(1-{\mu }_{\tilde{N}}^2\right)}^{\alpha }-{\left(1-{\mu }_{\tilde{N}}^2-{\pi }_{\tilde{N}}^2\right)}^{\alpha }\right)}^{\frac{1}{2}}\right\}, \forall \alpha >0$$

(18)

Definition 3.

Consider the weight vector$\phi =\left({\phi }_1,{\phi }_2,\dots ,{\phi }_m\right)$, where$0\le {\phi }_i\le 1$and${\displaystyle \sum }_{i=1}^m{\phi }_i=1$. The spherical weighted arithmetic mean (SWAM) and spherical weighted geometric mean (SWGM) are defined by Equations (19) and (20):

$$\begin{gathered} SWA{M}_{\phi }\left({\tilde{N}}_1,{\tilde{N}}_2,\dots ,{\tilde{N}}_m\right)={\phi }_1{\tilde{N}}_1+{\phi }_2{\tilde{N}}_2+\cdots +{\phi }_m{\tilde{N}}_m \\ =\left\{{\left(1-{\displaystyle \prod }_{i=1}^m{\left(1-{\vartheta }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}\right)}^{\frac{1}{2}},{\displaystyle \prod }_{i=1}^m{\mu }_{{\tilde{N}}_i}^{{\phi }_i},{\left({\displaystyle \prod }_{i=1}^m{\left(1-{\vartheta }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}-{\displaystyle \prod }_{i=1}^m{\left(1-{\vartheta }_{{\tilde{N}}_i}^2-{\pi }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}\right)}^{\frac{1}{2}}\right\} \end{gathered}$$

(19)

$$\begin{gathered} SWG{M}_{\phi }\left({\tilde{N}}_1,{\tilde{N}}_2,\dots ,{\tilde{N}}_m\right)={\tilde{N}}_1^{{\phi }_1}+{\tilde{N}}_2^{{\phi }_2}+\cdots +{\tilde{N}}_m^{{\phi }_m} \\ =\left\{{\displaystyle \prod }_{i=1}^m{\vartheta }_{{\tilde{N}}_i}^{{\phi }_i},{\left(1-{\displaystyle \prod }_{i=1}^m{\left(1-{\mu }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}\right)}^{\frac{1}{2}},{\left({\displaystyle \prod }_{i=1}^m{\left(1-{\mu }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}-{\displaystyle \prod }_{i=1}^m{\left(1-{\mu }_{{\tilde{N}}_i}^2-{\pi }_{{\tilde{N}}_i}^2\right)}^{{\phi }_i}\right)}^{\frac{1}{2}}\right\} \end{gathered}$$

(20)

Definition 4

[20]. Let $\tilde{N}=\left({\vartheta }_{\tilde{N}},{\mu }_{\tilde{N}}, {\pi }_{\tilde{N}}\right)$ and $\tilde{M}=\left({\vartheta }_{\tilde{M}},{\mu }_{\tilde{M}}, {\pi }_{\tilde{M}}\right)$ be two spherical fuzzy numbers from the universe of discourse $S_1$ and $S_2$. The following are valid under the condition $\alpha$, ${\alpha }_1$, ${\alpha }_2>0$.

$$\tilde{N}\oplus \tilde{M}=\tilde{M}\oplus \tilde{N}$$

(21)

$$\tilde{N}\otimes \tilde{M}=\tilde{M}\otimes \tilde{N}$$

(22)

$$\alpha \left(\tilde{N}\oplus \tilde{M}\right)=\alpha \tilde{N}\oplus \alpha \tilde{M}$$

(23)

$${\alpha }_1\tilde{N}\oplus {\alpha }_2\tilde{N}=({\alpha }_1+{\alpha }_2)\tilde{N}$$

(24)

$${\left(\tilde{N}\otimes \tilde{M}\right)}^{\alpha }={\tilde{N}}^{\alpha }\otimes {\tilde{M}}^{\alpha }$$

(25)

$${\tilde{N}}^{{\alpha }_1}\otimes {\tilde{N}}^{{\alpha }_2}={\tilde{N}}^{{\alpha }_1+{\alpha }_2}$$

(26)

Definition 5

[44]. The defuzzied value (DV) of spherical fuzzy number $\tilde{N}=\left({\vartheta }_{\tilde{N}},{\mu }_{\tilde{N}}, {\pi }_{\tilde{N}}\right)$ is defined by Equation (27):

$$DV\left(\tilde{N}\right)=\sqrt{\left|{\left(3\times {\vartheta }_{\tilde{N}}-\frac{{\pi }_{\tilde{N}}}{2}\right)}^2-{\left(\frac{{\mu }_{\tilde{N}}}{2}-{\pi }_{\tilde{N}}\right)}^2\right|}$$

(27)

The AHP method was introduced by Saaty in 1970s, and is widely used as a method of determining the weight of hierarchy criteria [18,45,46]. Recently, the CoCoSo method was developed by Yazdani et al. (2019), based on the idea of compromise programming discussed by Zeleny [33,47]. The CoCoSo method validates the ranking of alternatives via three different aggregation strategies as three different measures. Many applications of this method have found MCDM problems in many different fields [48,49,50]. In this study, a spherical fuzzy extension of the integrated AHP-CoCoSo method is introduced and applied as in the following steps:

Step 1. Experts $\left(k=1\dots K\right)$ (or decision makers), who have expertise and experience in the field, are identified. Based on their expertise, the weights of the experts are determined. With the given SFN ${\tilde{E}}^k=\left({\vartheta }_{{\tilde{E}}^k},{\mu }_{{\tilde{E}}^k}, {\pi }_{{\tilde{E}}^k}\right)$ representing the expertise of the $k$th expert, the weight $\left({\omega }_k\right)$ of the $k$th expert is determined by Equation (28) [51].

$${\omega }_k=\frac{1-{\left(\left(1-{\vartheta }_{{\tilde{E}}^k}^2\right)+{\mu }_{{\tilde{E}}^k}^2+{\pi }_{{\tilde{E}}^k}^2)/3\right)}^{\frac{1}{2}}}{{{\displaystyle \sum }}_{l=1}^h\left(1-{\left(\left(1-{\vartheta }_{{\tilde{E}}^l}^2\right)+{\mu }_{{\tilde{E}}^l}^2+{\pi }_{{\tilde{E}}^l}^2)/3\right)}^{\frac{1}{2}}\right)}$$

(28)

$$\mathrm{where} {{\displaystyle \sum }}_{k=1}^K{\omega }_k=1 \mathrm{and} 0\le {\vartheta }_{{\tilde{E}}^k}^2+{\mu }_{{\tilde{E}}^k}^2+{\pi }_{{\tilde{E}}^k}^2\le 1$$

As described in

Table 1. Linguistic terms and corresponding SFN for experts’ expertise.

Linguistic Term	Spherical Fuzzy Number $\left(\mathit{\vartheta },\mathit{\mu },\mathit{\pi }\right)$
Very high (VH)	(0.85, 0.15, 0.45)
High (H)	(0.60, 0.20, 0.35)
Moderate (M)	(0.35, 0.25, 0.25)

, SFN ${\tilde{E}}^k$represents the expertise of experts, provided by analysts or higher-level decision makers in linguistic terms, based on expert attributes such as years of experience and qualifications.

Step 2. The evaluation criteria ($j=1\dots J)$, sub-criteria ($l=1\dots L)$, and their hierarchical structure are defined.

Step 3. The linguistic pairwise comparison matrices on the importance of the criteria and sub-criteria provided by the experts using the SFN scale are constructed, as shown in

Table 2. Linguistic terms and corresponding SFN for the importance of the criteria.

Linguistic Term	Spherical Fuzzy Number $\left({\mathit{\vartheta }}_{\tilde{\mathit{N}}},{\mathit{\mu }}_{\tilde{\mathit{N}}}, {\mathit{\pi }}_{\tilde{\mathit{N}}}\right)$	Score Index $\left(\mathit{S}\mathit{I}\right)$
Absolutely low importance (ALI)	(0.1, 0.9, 0.0)	1/9
Very low importance (VLI)	(0.2, 0.8, 0.1)	$1/7$
Low importance (LI)	(0.3, 0.7, 0.2)	$1/5$
Slightly low importance (SLI)	(0.4, 0.6, 0.3)	$1/3$
Equally importance (EI)	(0.5, 0.5, 0.4)	1
Slightly high importance (SHI)	(0.6, 0.4, 0.3)	3
High importance (HI)	(0.7, 0.3, 0.2)	5
Very high importance (VHI)	(0.8, 0.2, 0.1)	7
Absolutely high importance (AHI)	(0.9, 0.1, 0.0)	9

[44]. The SFN pairwise comparison matrices on the importance of the criteria provided by the $k$th expert are represented in Equation (29). Meanwhile, the SFN pairwise comparison matrices on the importance of sub-criteria belonging to the $j$th criterion provided by the $k$th expert are represented in Equation (30).

$${\tilde{S}}^k={\left[{\tilde{s}}_{jt}^k\right]}_{J\times J}, k=1\dots K$$

(29)

$${\widetilde{SS}}^{kj}={\left[{\widetilde{ss}}_{lt}^{kj}\right]}_{L\times L}, k=1\dots K,j=1\dots J$$

(30)

Step 4. The consistency of the pairwise comparison matrices is checked as in the procedure of the traditional AHP method using the scoring index in Table 2. Equation (31) presents the SI calculation for the EI, SHI, HI, VHI, and AMI linguistic terms. Meanwhile, the SI values for the SLI, LI, VLI, and ALI linguistic terms are calculated according to Equation (32). A pairwise comparison matrix is said to be consistent if the consistency ratio (CR) is less than 0.1 [45].

$$SI=\sqrt{\left|100\times ({\left({\vartheta }_{\tilde{N}}-{\pi }_{\tilde{N}}\right)}^2-{\left({\mu }_{\tilde{N}}-{\pi }_{\tilde{N}}\right)}^2)\right|}$$

(31)

$$\frac{1}{SI}=\frac{1}{\sqrt{\left|100\times ({\left({\vartheta }_{\tilde{N}}-{\pi }_{\tilde{N}}\right)}^2-{\left({\mu }_{\tilde{N}}-{\pi }_{\tilde{N}}\right)}^2)\right|}}$$

(32)

Step 5. The spherical weighted arithmetic mean is used to determine the local SF weight of the $j$th criterion provided by the $k$th expert, as defined by Equation (33).

$$\begin{gathered} {\tilde{W}}_j^k=SWA{M}_{\phi }\left({\tilde{s}}_{j1}^k,{\tilde{s}}_{j2}^k,\dots ,{\tilde{s}}_{jJ}^k\right)=\phi {\tilde{s}}_{j1}^k+\phi {\tilde{s}}_{j2}^k+\cdots +\phi {\tilde{s}}_{jJ}^k, j=1\dots J,k=1\dots K \\ \mathrm{where} \phi =\frac{1}{J} \end{gathered}$$

(33)

Step 6. The spherical weighted arithmetic mean is used to determine the local SF weight of the $l$th sub-criterion belonging to the $j$th criterion provided by the $k$th expert, as defined by Equation (34).

$$\begin{gathered} {\widetilde{SW}}_l^{kj}=SWA{M}_{\phi }\left({\widetilde{ss}}_{l1}^{kj},{\widetilde{ss}}_{l2}^{kj},\dots ,{\widetilde{ss}}_{lL}^{kj}\right)=\phi {\widetilde{ss}}_{l1}^{kj}+\phi {\widetilde{ss}}_{l2}^{kj}+\cdots +\phi {\widetilde{ss}}_{lL}^{kj}, l=1\dots L, j=1\dots J,k=1\dots K \\ \mathrm{where} \phi =\frac{1}{L} \end{gathered}$$

(34)

Step 7. The global weight of sub-criteria is calculated by multiplying the local weight of the sub-criteria and the local weight of the criteria, respectively, as defined by Equation (35).

$${\tilde{w}}_l^k={\tilde{W}}_j^k\otimes {\widetilde{SW}}_l^{kj}, l=1\dots L, j=1\dots J,k=1\dots K$$

(35)

Step 8. Based on the weights of experts (${\omega }_k)$, the aggregated global weight of the criteria is determined using the spherical weighted arithmetic mean, as defined by Equation (36).

$${\tilde{w}}_l=SWA{M}_{{\omega }_k}\left({\tilde{w}}_l^1,{\tilde{w}}_l^2,\dots ,{\tilde{w}}_l^K\right)={\omega }_1{\tilde{w}}_l^1+{\omega }_2{\tilde{w}}_l^2+\cdots +{\omega }_K{\tilde{w}}_l^K, l=1\dots L$$

(36)

Step 9. The defuzzied value ($DV$) of the aggregated global weights are calculated according to Equation (27). As shown in Equation (37), the crisp weights of the sub-criteria are determined.

$$w_l=\frac{DV\left({\tilde{w}}_l\right)}{{{\displaystyle \sum }}_{l=1}^{L}DV\left({\tilde{w}}_l\right)}, l=1\dots L$$

(37)

Step 10. Experts provide linguistic assessments of alternatives $\left(i=1\dots I\right)$ according to the sub-criteria. These linguistic assessments are then transformed into the corresponding SFNs, as shown in

Table 3. Linguistic terms and corresponding SFN for alternative assessments.

Linguistic Term	Spherical Fuzzy Number $\left({\mathit{\vartheta }}_{\tilde{\mathit{N}}},{\mathit{\mu }}_{\tilde{\mathit{N}}}, {\mathit{\pi }}_{\tilde{\mathit{N}}}\right)$
Extremely low (EL)	(0.040, 0.960, 0.040)
Very low (VL)	(0.155, 0.845, 0.155)
Low (L)	(0.270, 0.730, 0.270)
Slightly low (SL)	(0.385, 0.615, 0.385)
Moderate (M)	(0.500, 0.500, 0.500)
Slightly high (SH)	(0.615, 0.385, 0.385)
High (H)	(0.730, 0.270, 0.270)
Very high (VH)	(0.845, 0.155, 0.155)
Extremely high (EH)	(0.960, 0.040, 0.040)

, to form SF decision matrices. SF decision matrices are represented as Equation (38).

$${\tilde{N}}^k={\left[{\tilde{n}}_{il}^k\right]}_{I\times L}$$

(38)

Step 11. The aggregated decision matrix is constructed using the SWAM based on experts’ weights, as defined by Equations (39) and (40).

$$\tilde{N}={\left[{\tilde{n}}_{il}\right]}_{I\times L}$$

(39)

$$\mathrm{where} {\tilde{n}}_{il}=SWA{M}_{{\omega }_k}\left({\tilde{n}}_{il}^1,{\tilde{n}}_{il}^2,\dots ,{\tilde{n}}_{il}^K\right)={\omega }_1{\tilde{n}}_{il}^1+{\omega }_2{\tilde{n}}_{il}^1+\cdots +{\omega }_K{\tilde{n}}_{il}^K, i=1\dots I,l=1\dots L$$

(40)

Step 12. Based on the sub-criteria weight $(w_l)$, the weighted sequences of alternatives are determined using the SWAM and the SWGM according to Equations (41) and (42). They are denoted as ${\widetilde{SWA}}_i$ and ${\widetilde{SWG}}_i$, respectively.

$${\widetilde{SWA}}_i=w_1{\tilde{n}}_{i1}+w_2{\tilde{n}}_{i2}+\cdots +w_l{\tilde{n}}_{i2}+\cdots +w_L{\tilde{n}}_{iL}, i=1\dots I$$

(41)

$${\widetilde{SWG}}_i={\tilde{n}}_{i1}^{w_1}+{\tilde{n}}_{i2}^{w_2}+\cdots +{\tilde{n}}_{il}^{w_l}+\cdots +{\tilde{n}}_{iL}^{w_L}, i\dots \dots I$$

(42)

Step 13. The defuzzied values of ${\widetilde{SWA}}_i$ and ${\widetilde{SWG}}_i$ are determined and denoted as $SW{A}_i$ and $SW{G}_i$ according to Equation (27).

Step 14. The additive normalized importance (${\Phi }_i^a$) and the relative importance (${\Phi }_i^b)$ of the SWAM and the SWGM are calculated via Equations (43) and (44), respectively. In addition, the trade-off importance (${\Phi }_i^c)$ of the alternatives is determined by Equation (45), with the stability and flexibility represented by the coefficient $\delta$, which is selected by the decision makers.

$${\Phi }_i^a=\frac{SW{A}_i+SW{G}_i}{{{\displaystyle \sum }}_{i=1}^I(SW{A}_i+SW{G}_i)}, i=1\dots I$$

(43)

$${\Phi }_i^b=\frac{SW{A}_i}{\underset{i}{\min }(SW{A}_i)}+\frac{SW{G}_i}{\underset{i}{\min }(SW{G}_i)}, i=1\dots I$$

(44)

$${\Phi }_i^c=\frac{\delta SW{A}_i+\left(1-\delta \right)SW{G}_i}{\delta \underset{i}{\min }(SW{A}_i)+\left(1-\delta \right)\underset{i}{\max }\left(SW{G}_i\right)}, i=1\dots I$$

(45)

Step 15. The final evaluation score $\left({\Phi }_i\right)$ of the alternatives is determined by Equation (46). The final rank of the alternatives is in descending order of the value of ${\Phi }_i$. In other words, the best alternative has the largest value of ${\Phi }_i$.

$${\Phi }_i=\frac{\left({\Phi }_i^a+{\Phi }_i^b+{\Phi }_i^c\right)}{3}+\sqrt[3]{\left({\Phi }_i^a\times {\Phi }_i^b\times {\Phi }_i^c\right)}, i=1\dots I$$

(46)

4. Numerical Results

In this section, the proposed tri-layer methodology is applied to identify suitable locations for DGL in Malaysia. Through the layers of the proposed methodology, as a filtering system, potential locations, possible locations, high-efficiency locations, and concordant locations are determined sequentially.

4.1. Layer 1: Possibility Screening

In the beginning, a group of six experts with high-level qualifications and more than 10 years of experience in geothermal energy and public management was assembled to contribute to this study. Based on the recommendations of experts, there were 25 potential locations for geothermal energy development identified, as illustrated in Figure 2. The coordinates of these 25 potential locations are shown in

Table A2. Location coordinates.

Location	Latitude	Longitude	Location	Latitude	Longitude
DGL-1	5.388722	100.895004	DGL-14	4.825516	101.76412
DGL-2	5.43033	101.644762	DGL-15	5.492963	102.610067
DGL-3	4.516435	100.870226	DGL-16	1.227621	110.487264
DGL-4	4.702598	102.177599	DGL-17	1.408847	111.679281
DGL-5	3.853538	101.018541	DGL-18	2.034782	113.689779
DGL-6	3.288557	101.376917	DGL-19	2.704371	114.865316
DGL-7	2.899112	102.063562	DGL-20	4.535349	116.01888
DGL-8	2.311954	102.56344	DGL-21	5.049899	117.677815
DGL-9	1.79044	103.425867	DGL-22	6.427205	117.040608
DGL-10	1.639446	104.093286	DGL-23	5.312493	116.447346
DGL-11	1.856325	103.876306	DGL-24	4.3353634	117.8148853
DGL-12	2.150062	103.609823	DGL-25	2.550723	113.239338
DGL-13	4.086185	102.659506

. The possibility of potential locations was then verified based on the distribution of national and international nature reserves in Malaysia [52,53]. As shown in Figure 3, the screening results show that DGL-04, DGL-12, and DGL-21 do not guarantee the possibility due to them belonging to, or being too close to, nature conservation areas.

4.2. Layer 2: High-Efficiency Location Identification

In this layer, the efficiency of the possible locations is determined by the DEA model based on quantitative indicators. These indicators are proposed based on geothermal energy studies and experts’ opinions. Accordingly, seven indicators were defined and divided into two groups, inputs and outputs, to determine the relative efficiency of possible locations, as shown in

Table 4. DEA model’s inputs and outputs.

Location	Inputs			Outputs
	Distance to Grid (km)	Distance to the Closest Residential Area (km)	Distance to Water Supply (km)	Heat Flow (mW/m2)	Suitability Index *	Total EGS Technical Potential 2% Recovery ** (MWe/km2)	Population Density (People/km2)
DGL-1	0.70	25.53	27.59	88.50	0.09	0.05	25.23
DGL-2	17.19	36.33	19.31	87.90	0.16	0.06	35.72
DGL-3	5.58	6.32	5.15	96.57	0.12	0.05	6.01
DGL-5	4.72	9.71	5.61	97.85	0.29	0.05	9.08
DGL-6	5.46	4.80	9.29	98.56	0.29	0.05	4.48
DGL-7	9.89	4.53	14.11	98.56	0.21	0.05	4.14
DGL-8	0.82	2.93	9.11	100.00	0.16	0.06	2.55
DGL-9	0.14	4.55	19.49	100.00	0.15	0.06	4.19
DGL-10	3.60	17.73	8.78	100.00	0.21	0.06	17.25
DGL-11	14.70	17.73	17.02	100.00	0.23	0.05	12.45
DGL-13	12.92	10.30	29.20	97.20	0.37	0.05	34.60
DGL-14	19.90	36.25	61.81	96.26	0.25	0.05	21.60
DGL-15	28.48	21.91	20.85	90.42	0.20	0.05	25.64
DGL-16	0.18	6.77	21.96	87.80	0.13	0.06	6.43
DGL-17	10.46	6.77	21.26	96.48	0.00	0.06	15.32
DGL-18	86.62	15.61	29.26	96.48	0.05	0.06	131.30
DGL-19	63.31	131.96	29.83	73.34	0.06	0.05	114.98
DGL-20	64.41	115.36	77.55	68.66	0.06	0.05	44.26
DGL-22	32.21	26.94	26.98	71.80	0.43	0.05	15.75
DGL-23	22.55	16.19	72.17	64.96	0.34	0.01	5.97
DGL-24	15.26	4.62	1.16	72.28	0.29	0.05	4.31
DGL-25	71.14	50.91	49.48	62.53	0.01	0.05	50.32

* The geothermal suitability index is determined by IRENA. ** Technical potential for enhanced geothermal systems (EGS) under 2% of recovery factor.

. In the DEA model, indicators are considered as DEA inputs where the lower their value, the higher the efficiency of a particular location. In contrast, indicators, the higher the value of which, the greater the efficiency, are considered DEA outputs. In Table 4, the possible locations’ data by indicator, collected from the database of the International Renewable Energy Agency [54], are presented. Solving the DEA-SBM model using Equations (9)–(12), the relative efficiencies of the possible locations were determined, as shown in Figure 4. According to the results of the DEA model, 14 out of 22 possible locations were considered high-efficiency locations, with a relative SBM efficiency score of 1. The eight possible locations with an SBM efficiency score lower than 1 were eliminated: DGL-2, DGL-7, DGL-14, DGL-15, DGL-17, DGL-20, DGL-23, and DGL-25. The high-efficiency locations are geographically illustrated in Figure 5.

4.3. Layer 3: Concordant Location Identification

In addition to technical efficiency, other qualitative factors also need to be considered to ensure the sustainable development of direct-use geothermal energy projects. At this layer, a multi-criteria expert-based assessment is performed to make recommendations for the most suitable locations. Based on previous studies and expert recommendations, twelve criteria, which fall under three aspects, were defined to evaluate the sustainability of locations, as shown in

Table 5. List of evaluation criteria.

Aspects	Criteria	Description
Technical (C1)	Intrusive rock density (C1-1) [55,56,57]	Intrusive rock density in area.
	Drainage density (C1-2) [55,58,59]	The number of drainage routes, such as rivers and streams.
	Fault density (C1-3) [55,57,59]	The fault layer density and the distance from the faults.
	Radioactivity (C1-4) [60]	Radioactivity by interacting of radioactive elements in geothermal fluids.
	Workforce availability (C1-5) [18]	Availability of local skilled workforce.
Socioeconomic (C2)	Costs (C2-1) [18,55]	Manpower, installation, maintenance, and operation costs.
	Social acceptability (C2-2) [60]	The level of local social acceptance of DG project development.
	Noise impact (C2-3) [60,61]	Potential negative noise effects of the DG project.
	Distance to closest industrial area (C2-4) (Suggested by Experts)	Distance from possible locations to the nearest industrial area.
Environmental (C3)	Potential water contamination (C3-1) [60,62]	The corrosion and scaling can affect the geothermal energy equipment, causing potential local water contamination.
	Distance to conservation area (C3-2) (Suggested by Experts)	Distance from possible locations to the nearest conservation area.
	Geological impact (C3-3) [63,64]	Potential negative impacts on the geology of possible locations.

. In Figure 6, the hierarchy structure for the multi-criteria location selection problem is presented.

Based on the qualifications and years of experience of the experts, the SFNs representing their level of expertise are provided. Based on the SFNs, the crisp weights of the experts were determined by Equation (28), and presented in

Table 6. Expert qualification.

No.	Qualification	Years of Experience	Linguistic Term	Spherical Fuzzy Number	Weight $\left({\mathit{\omega }}_{\mathit{k}}\right)$
Expert 1	Doctoral	10	Moderate	(0.35, 0.25, 0.25)	0.146
Expert 2	Doctoral	17	Very high	(0.85, 0.15, 0.45)	0.182
Expert 3	Doctoral	11	Moderate	(0.35, 0.25, 0.25)	0.146
Expert 4	Doctoral	14	High	(0.60, 0.20, 0.35)	0.172
Expert 5	Doctoral	17	Very high	(0.85, 0.15, 0.45)	0.182
Expert 6	Doctoral	13	High	(0.60, 0.20, 0.35)	0.172

.

To determine the weights of the criteria, linguistic pairwise comparisons of the importance of the aspects and the criteria were provided by the experts. In the Appendix A,

Table A3. Linguistic pairwise comparison between aspects.

Aspects	Technical	Socioeconomic	Environment
Technical	EI	SLI	SHI
Socioeconomic	SHI	EI	HI
Environment	SLI	LI	EI

,

Table A4. Linguistic pairwise comparison between criteria of technical aspect.

Technical Aspect	C1-1	C1-2	C1-3	C1-4	C1-5
C1-1	EI	EI	SHI	HI	SHI
C1-2	EI	EI	EI	SHI	AHI
C1-3	SLI	EI	EI	SHI	HI
C1-4	LI	SLI	SLI	EI	EI
C1-5	SLI	ALI	LI	EI	EI

,

Table A5. Linguistic pairwise comparison between criteria of socioeconomic aspect.

Socioeconomic Aspect	C2-1	C2-2	C2-3	C2-4
C2-1	EI	VLI	EI	HI
C2-2	VHI	EI	HI	VHI
C2-3	EI	LI	EI	SHI
C2-4	LI	VLI	SLI	EI

and

Table A6. Linguistic pairwise comparison between criteria of environment aspect.

Environment Aspect	C3-1	C3-2	C3-3
C3-1	EI	SHI	LI
C3-2	SLI	EI	VLI
C3-3	HI	VHI	EI

illustrate the judgment of the first expert. The linguistic comparisons are converted to SFNs according to the scale shown in Table 2. As discussed in Step 4 of Section 3.1, the consistency of the pairwise comparisons was checked. The results, which are shown in

Table A7. Consistency check results.

Expert	Between Aspects	Among Technical Aspect’s Criteria	Among Socioeconomic Aspect’s Criteria	Among Environment Aspect’s Criteria
1	0.0334	0.0716	0.0883	0.0567
2	0.0251	0.0635	0.0476	0.0703
3	0.0567	0.0914	0.0985	0.0252
4	0.0703	0.0674	0.0703	0.0567
5	0.0701	0.0938	0.0911	0.0698
6	0.0252	0.0938	0.0428	0.0252

, of the pairwise comparisons show an acceptable inconsistency with CR of less than 0.1. As shown in

Table 7. The local spherical fuzzy weight of aspects and criteria.

Aspect/Criteria	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5	Expert 6
C1	(0.51, 0.49, 0.34)	(0.34, 0.58, 0.42)	(0.34, 0.49, 0.52)	(0.32, 0.47, 0.53)	(0.37, 0.33, 0.71)	(0.27, 0.45, 0.56)
C2	(0.61, 0.39, 0.30)	(0.30, 0.41, 0.59)	(0.32, 0.70, 0.31)	(0.24, 0.67, 0.34)	(0.27, 0.74, 0.27)	(0.23, 0.61, 0.39)
C3	(0.41, 0.59, 0.32)	(0.32, 0.54, 0.46)	(0.37, 0.39, 0.62)	(0.31, 0.43, 0.58)	(0.35, 0.62, 0.39)	(0.27, 0.47, 0.53)
C1-1	(0.59, 0.41, 0.32)	(0.32, 0.57, 0.44)	(0.29, 0.54, 0.46)	(0.36, 0.46, 0.56)	(0.37, 0.41, 0.59)	(0.33, 0.41, 0.59)
C1-2	(0.67, 0.35, 0.30)	(0.30, 0.46, 0.54)	(0.37, 0.63, 0.38)	(0.30, 0.53, 0.47)	(0.34, 0.44, 0.57)	(0.30, 0.44, 0.57)
C1-3	(0.56, 0.45, 0.32)	(0.32, 0.43, 0.59)	(0.34, 0.34, 0.69)	(0.26, 0.41, 0.6)	(0.33, 0.43, 0.58)	(0.29, 0.43, 0.58)
C1-4	(0.43, 0.58, 0.34)	(0.34, 0.71, 0.30)	(0.22, 0.65, 0.38)	(0.30, 0.46, 0.56)	(0.33, 0.68, 0.32)	(0.24, 0.68, 0.32)
C1-5	(0.40, 0.62, 0.32)	(0.32, 0.44, 0.57)	(0.35, 0.52, 0.49)	(0.33, 0.83, 0.18)	(0.15, 0.60, 0.40)	(0.28, 0.60, 0.40)
C2-1	(0.52, 0.49, 0.31)	(0.31, 0.45, 0.57)	(0.31, 0.54, 0.47)	(0.33, 0.51, 0.49)	(0.35, 0.63, 0.38)	(0.30, 0.54, 0.47)
C2-2	(0.73, 0.28, 0.21)	(0.21, 0.35, 0.68)	(0.28, 0.73, 0.28)	(0.23, 0.61, 0.39)	(0.30, 0.42, 0.61)	(0.34, 0.61, 0.39)
C2-3	(0.49, 0.51, 0.34)	(0.34, 0.62, 0.39)	(0.28, 0.36, 0.66)	(0.29, 0.46, 0.54)	(0.37, 0.7, 0.32)	(0.27, 0.45, 0.55)
C2-4	(0.37, 0.64, 0.29)	(0.29, 0.80, 0.21)	(0.18, 0.51, 0.50)	(0.29, 0.45, 0.55)	(0.36, 0.42, 0.59)	(0.34, 0.44, 0.57)
C3-1	(0.49, 0.52, 0.32)	(0.32, 0.43, 0.58)	(0.35, 0.49, 0.52)	(0.32, 0.70, 0.31)	(0.24, 0.64, 0.37)	(0.30, 0.49, 0.52)
C3-2	(0.39, 0.62, 0.31)	(0.31, 0.47, 0.53)	(0.37, 0.76, 0.25)	(0.21, 0.39, 0.62)	(0.31, 0.54, 0.46)	(0.37, 0.76, 0.25)
C3-3	(0.70, 0.31, 0.24)	(0.24, 0.67, 0.34)	(0.27, 0.38, 0.65)	(0.31, 0.49, 0.52)	(0.32, 0.39, 0.62)	(0.31, 0.38, 0.65)

, the local spherical fuzzy weights of the aspects and criteria were calculated according to Equations (33) and (34). In

Table 8. The global spherical fuzzy weight of criteria.

Criteria	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5	Expert 6
C1-1	(0.30, 0.61, 0.40)	(0.33, 0.58, 0.39)	(0.27, 0.65, 0.40)	(0.21, 0.71, 0.42)	(0.14, 0.82, 0.30)	(0.19, 0.74, 0.38)
C1-2	(0.34, 0.58, 0.40)	(0.27, 0.64, 0.42)	(0.31, 0.61, 0.38)	(0.25, 0.67, 0.42)	(0.14, 0.82, 0.29)	(0.20, 0.73, 0.37)
C1-3	(0.29, 0.63, 0.40)	(0.25, 0.68, 0.40)	(0.17, 0.78, 0.31)	(0.19, 0.74, 0.39)	(0.14, 0.82, 0.29)	(0.19, 0.74, 0.36)
C1-4	(0.22, 0.70, 0.39)	(0.41, 0.50, 0.37)	(0.32, 0.61, 0.38)	(0.22, 0.71, 0.40)	(0.22, 0.75, 0.30)	(0.30, 0.62, 0.38)
C1-5	(0.20, 0.73, 0.37)	(0.26, 0.67, 0.41)	(0.26, 0.66, 0.38)	(0.39, 0.55, 0.39)	(0.20, 0.77, 0.31)	(0.27, 0.65, 0.39)
C2-1	(0.32, 0.60, 0.38)	(0.19, 0.75, 0.35)	(0.37, 0.54, 0.37)	(0.34, 0.58, 0.4)	(0.47, 0.45, 0.36)	(0.33, 0.58, 0.39)
C2-2	(0.44, 0.47, 0.34)	(0.14, 0.81, 0.31)	(0.51, 0.41, 0.31)	(0.41, 0.50, 0.37)	(0.31, 0.64, 0.37)	(0.37, 0.53, 0.38)
C2-3	(0.30, 0.61, 0.40)	(0.25, 0.67, 0.36)	(0.25, 0.70, 0.32)	(0.31, 0.61, 0.4)	(0.52, 0.41, 0.34)	(0.28, 0.64, 0.40)
C2-4	(0.23, 0.71, 0.34)	(0.33, 0.62, 0.34)	(0.36, 0.57, 0.34)	(0.30, 0.62, 0.39)	(0.31, 0.63, 0.37)	(0.27, 0.65, 0.39)
C3-1	(0.20, 0.73, 0.36)	(0.23, 0.70, 0.41)	(0.19, 0.74, 0.35)	(0.30, 0.64, 0.38)	(0.40, 0.52, 0.37)	(0.23, 0.69, 0.40)
C3-2	(0.16, 0.78, 0.34)	(0.25, 0.66, 0.43)	(0.30, 0.65, 0.34)	(0.17, 0.77, 0.36)	(0.34, 0.58, 0.40)	(0.36, 0.57, 0.39)
C3-3	(0.29, 0.64, 0.35)	(0.36, 0.55, 0.41)	(0.15, 0.80, 0.32)	(0.21, 0.72, 0.38)	(0.25, 0.69, 0.35)	(0.18, 0.76, 0.37)

, the global spherical fuzzy weights of the criteria were determined by multiplying their local spherical fuzzy weights by the local spherical fuzzy weights of the respective aspects according to Equation (35). In the next step, SWAM was applied to aggregate the global spherical fuzzy weights of the criteria based on the weights of the experts. The aggregated spherical fuzzy weight was converted to a crisp weight according to equation (27). The results of the aggregation and defuzzification process are presented in

Table 9. The aggregated spherical fuzzy weight and defuzzied weight of criteria.

Criteria	Spherical Fuzzy Weight	Defuzzied Weight
Intrusive rock density (C1-1)	(0.30, 0.61, 0.40)	0.068
Drainage density (C1-2)	(0.34, 0.58, 0.40)	0.071
Fault density (C1-3)	(0.29, 0.63, 0.40)	0.055
Radioactivity (C1-4)	(0.22, 0.70, 0.39)	0.086
Workforce availability (C1-5)	(0.20, 0.73, 0.37)	0.077
Costs (C2-1)	(0.32, 0.60, 0.38)	0.105
Social acceptability (C2-2)	(0.44, 0.47, 0.34)	0.118
Noise impact (C2-3)	(0.30, 0.61, 0.40)	0.103
Distance to closest industrial area (C2-4)	(0.23, 0.71, 0.34)	0.090
Potential water contamination (C3-1)	(0.20, 0.73, 0.36)	0.078
Distance to conservation area (C3-2)	(0.16, 0.78, 0.34)	0.079
Geological impact (C3-3)	(0.29, 0.64, 0.35)	0.070

.

To prioritize possible locations, firstly, the experts provided linguistic judgments for each location according to the criteria. Afterward, linguistic judgments were converted into SFNs according to Table 3 to form SF decision matrices. The individual SF decision matrix provided by the first expert is illustrated in

Table A8. Spherical fuzzy decision matrix provided by expert 1.

Location	C1-1	C1-2	C1-3	C1-4	C1-5	C2-1
DGL-1	(0.39, 0.62, 0.39)	(0.73, 0.27, 0.27)	(0.73, 0.27, 0.27)	(0.04, 0.96, 0.04)	(0.16, 0.85, 0.16)	(0.5, 0.5, 0.5)
DGL-3	(0.62, 0.39, 0.39)	(0.5, 0.5, 0.5)	(0.16, 0.85, 0.16)	(0.73, 0.27, 0.27)	(0.62, 0.39, 0.39)	(0.85, 0.16, 0.16)
DGL-5	(0.27, 0.73, 0.27)	(0.96, 0.04, 0.04)	(0.62, 0.39, 0.39)	(0.5, 0.5, 0.5)	(0.04, 0.96, 0.04)	(0.04, 0.96, 0.04)
DGL-6	(0.96, 0.04, 0.04)	(0.62, 0.39, 0.39)	(0.27, 0.73, 0.27)	(0.73, 0.27, 0.27)	(0.39, 0.62, 0.39)	(0.04, 0.96, 0.04)
DGL-8	(0.96, 0.04, 0.04)	(0.39, 0.62, 0.39)	(0.96, 0.04, 0.04)	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)	(0.27, 0.73, 0.27)
DGL-9	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)	(0.16, 0.85, 0.16)	(0.39, 0.62, 0.39)	(0.96, 0.04, 0.04)	(0.39, 0.62, 0.39)
DGL-10	(0.04, 0.96, 0.04)	(0.62, 0.39, 0.39)	(0.62, 0.39, 0.39)	(0.27, 0.73, 0.27)	(0.5, 0.5, 0.5)	(0.85, 0.16, 0.16)
DGL-11	(0.62, 0.39, 0.39)	(0.62, 0.39, 0.39)	(0.73, 0.27, 0.27)	(0.62, 0.39, 0.39)	(0.5, 0.5, 0.5)	(0.62, 0.39, 0.39)
DGL-13	(0.04, 0.96, 0.04)	(0.5, 0.5, 0.5)	(0.04, 0.96, 0.04)	(0.62, 0.39, 0.39)	(0.39, 0.62, 0.39)	(0.62, 0.39, 0.39)
DGL-16	(0.39, 0.62, 0.39)	(0.5, 0.5, 0.5)	(0.16, 0.85, 0.16)	(0.62, 0.39, 0.39)	(0.27, 0.73, 0.27)	(0.96, 0.04, 0.04)
DGL-18	(0.5, 0.5, 0.5)	(0.39, 0.62, 0.39)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)	(0.96, 0.04, 0.04)	(0.5, 0.5, 0.5)
DGL-19	(0.39, 0.62, 0.39)	(0.5, 0.5, 0.5)	(0.85, 0.16, 0.16)	(0.5, 0.5, 0.5)	(0.16, 0.85, 0.16)	(0.16, 0.85, 0.16)
DGL-22	(0.16, 0.85, 0.16)	(0.16, 0.85, 0.16)	(0.62, 0.39, 0.39)	(0.96, 0.04, 0.04)	(0.04, 0.96, 0.04)	(0.96, 0.04, 0.04)
DGL-24	(0.27, 0.73, 0.27)	(0.5, 0.5, 0.5)	(0.62, 0.39, 0.39)	(0.96, 0.04, 0.04)	(0.27, 0.73, 0.27)	(0.27, 0.73, 0.27)
Location	C2-2	C2-3	C2-4	C3-1	C3-2	C3-3
DGL-1	(0.62, 0.39, 0.39)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)	(0.62, 0.39, 0.39)	(0.5, 0.5, 0.5)	(0.96, 0.04, 0.04)
DGL-3	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)
DGL-5	(0.73, 0.27, 0.27)	(0.96, 0.04, 0.04)	(0.73, 0.27, 0.27)	(0.39, 0.62, 0.39)	(0.16, 0.85, 0.16)	(0.73, 0.27, 0.27)
DGL-6	(0.04, 0.96, 0.04)	(0.39, 0.62, 0.39)	(0.5, 0.5, 0.5)	(0.39, 0.62, 0.39)	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)
DGL-8	(0.39, 0.62, 0.39)	(0.62, 0.39, 0.39)	(0.96, 0.04, 0.04)	(0.73, 0.27, 0.27)	(0.96, 0.04, 0.04)	(0.96, 0.04, 0.04)
DGL-9	(0.39, 0.62, 0.39)	(0.62, 0.39, 0.39)	(0.27, 0.73, 0.27)	(0.85, 0.16, 0.16)	(0.27, 0.73, 0.27)	(0.73, 0.27, 0.27)
DGL-10	(0.27, 0.73, 0.27)	(0.16, 0.85, 0.16)	(0.5, 0.5, 0.5)	(0.73, 0.27, 0.27)	(0.16, 0.85, 0.16)	(0.96, 0.04, 0.04)
DGL-11	(0.85, 0.16, 0.16)	(0.04, 0.96, 0.04)	(0.5, 0.5, 0.5)	(0.27, 0.73, 0.27)	(0.39, 0.62, 0.39)	(0.62, 0.39, 0.39)
DGL-13	(0.27, 0.73, 0.27)	(0.04, 0.96, 0.04)	(0.73, 0.27, 0.27)	(0.04, 0.96, 0.04)	(0.85, 0.16, 0.16)	(0.04, 0.96, 0.04)
DGL-16	(0.16, 0.85, 0.16)	(0.27, 0.73, 0.27)	(0.96, 0.04, 0.04)	(0.5, 0.5, 0.5)	(0.85, 0.16, 0.16)	(0.39, 0.62, 0.39)
DGL-18	(0.16, 0.85, 0.16)	(0.5, 0.5, 0.5)	(0.39, 0.62, 0.39)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)	(0.39, 0.62, 0.39)
DGL-19	(0.85, 0.16, 0.16)	(0.27, 0.73, 0.27)	(0.85, 0.16, 0.16)	(0.16, 0.85, 0.16)	(0.62, 0.39, 0.39)	(0.73, 0.27, 0.27)
DGL-22	(0.85, 0.16, 0.16)	(0.96, 0.04, 0.04)	(0.16, 0.85, 0.16)	(0.39, 0.62, 0.39)	(0.5, 0.5, 0.5)	(0.16, 0.85, 0.16)
DGL-24	(0.27, 0.73, 0.27)	(0.96, 0.04, 0.04)	(0.27, 0.73, 0.27)	(0.16, 0.85, 0.16)	(0.85, 0.16, 0.16)	(0.96, 0.04, 0.04)

in the Appendix A. For aggregation, SWAM was applied based on the weights of experts to form the aggregated SF decision matrix, as shown in

Table A9. The aggregated decision matrix.

Location	C1-1	C1-2	C1-3	C1-4	C1-5	C2-1
DGL-1	(0.81, 0.22, 0.16)	(0.57, 0.45, 0.36)	(0.69, 0.33, 0.27)	(0.51, 0.56, 0.25)	(0.64, 0.44, 0.26)	(0.79, 0.24, 0.24)
DGL-3	(0.72, 0.31, 0.24)	(0.80, 0.23, 0.23)	(0.63, 0.46, 0.19)	(0.72, 0.33, 0.22)	(0.72, 0.3, 0.24)	(0.59, 0.47, 0.26)
DGL-5	(0.68, 0.36, 0.24)	(0.68, 0.41, 0.14)	(0.84, 0.16, 0.22)	(0.53, 0.49, 0.41)	(0.40, 0.67, 0.23)	(0.78, 0.26, 0.19)
DGL-6	(0.87, 0.14, 0.19)	(0.78, 0.26, 0.17)	(0.75, 0.28, 0.22)	(0.65, 0.39, 0.23)	(0.62, 0.41, 0.33)	(0.70, 0.33, 0.24)
DGL-8	(0.62, 0.46, 0.28)	(0.71, 0.33, 0.25)	(0.89, 0.11, 0.15)	(0.75, 0.27, 0.30)	(0.30, 0.77, 0.24)	(0.72, 0.35, 0.17)
DGL-9	(0.48, 0.57, 0.27)	(0.77, 0.27, 0.22)	(0.67, 0.38, 0.29)	(0.72, 0.35, 0.17)	(0.71, 0.34, 0.24)	(0.55, 0.50, 0.27)
DGL-10	(0.59, 0.46, 0.29)	(0.78, 0.27, 0.15)	(0.47, 0.54, 0.37)	(0.49, 0.53, 0.41)	(0.40, 0.64, 0.35)	(0.75, 0.29, 0.23)
DGL-11	(0.73, 0.28, 0.28)	(0.57, 0.47, 0.33)	(0.81, 0.21, 0.20)	(0.38, 0.66, 0.35)	(0.42, 0.64, 0.29)	(0.65, 0.38, 0.28)
DGL-13	(0.75, 0.28, 0.27)	(0.48, 0.59, 0.29)	(0.54, 0.51, 0.27)	(0.53, 0.54, 0.26)	(0.76, 0.26, 0.28)	(0.73, 0.29, 0.32)
DGL-16	(0.64, 0.45, 0.20)	(0.70, 0.34, 0.29)	(0.22, 0.80, 0.22)	(0.82, 0.22, 0.16)	(0.77, 0.28, 0.18)	(0.71, 0.33, 0.26)
DGL-18	(0.75, 0.30, 0.23)	(0.62, 0.39, 0.36)	(0.48, 0.59, 0.24)	(0.82, 0.18, 0.20)	(0.77, 0.27, 0.21)	(0.55, 0.50, 0.35)
DGL-19	(0.67, 0.38, 0.27)	(0.84, 0.17, 0.19)	(0.53, 0.53, 0.31)	(0.68, 0.36, 0.34)	(0.68, 0.36, 0.26)	(0.73, 0.31, 0.20)
DGL-22	(0.48, 0.54, 0.37)	(0.67, 0.41, 0.20)	(0.76, 0.26, 0.24)	(0.78, 0.25, 0.22)	(0.60, 0.45, 0.32)	(0.73, 0.30, 0.28)
DGL-24	(0.68, 0.36, 0.22)	(0.67, 0.38, 0.30)	(0.45, 0.58, 0.41)	(0.81, 0.22, 0.24)	(0.64, 0.41, 0.24)	(0.64, 0.41, 0.23)
Location	C2-2	C2-3	C2-4	C3-1	C3-2	C3-3
DGL-1	(0.88, 0.14, 0.17)	(0.72, 0.31, 0.28)	(0.86, 0.15, 0.14)	(0.83, 0.19, 0.21)	(0.79, 0.23, 0.22)	(0.72, 0.32, 0.21)
DGL-3	(0.58, 0.46, 0.31)	(0.46, 0.60, 0.27)	(0.65, 0.38, 0.28)	(0.69, 0.33, 0.26)	(0.68, 0.35, 0.27)	(0.75, 0.29, 0.26)
DGL-5	(0.68, 0.37, 0.22)	(0.72, 0.31, 0.28)	(0.74, 0.29, 0.23)	(0.57, 0.47, 0.34)	(0.63, 0.41, 0.29)	(0.60, 0.44, 0.32)
DGL-6	(0.67, 0.39, 0.28)	(0.67, 0.39, 0.30)	(0.60, 0.48, 0.25)	(0.34, 0.71, 0.28)	(0.63, 0.40, 0.29)	(0.74, 0.30, 0.17)
DGL-8	(0.68, 0.36, 0.31)	(0.52, 0.55, 0.25)	(0.62, 0.46, 0.22)	(0.71, 0.31, 0.22)	(0.77, 0.26, 0.20)	(0.73, 0.29, 0.29)
DGL-9	(0.63, 0.39, 0.32)	(0.79, 0.23, 0.26)	(0.59, 0.44, 0.31)	(0.78, 0.26, 0.18)	(0.67, 0.38, 0.26)	(0.60, 0.44, 0.33)
DGL-10	(0.73, 0.31, 0.25)	(0.64, 0.45, 0.20)	(0.41, 0.62, 0.37)	(0.43, 0.62, 0.33)	(0.62, 0.47, 0.18)	(0.73, 0.28, 0.33)
DGL-11	(0.82, 0.21, 0.13)	(0.73, 0.33, 0.18)	(0.53, 0.52, 0.31)	(0.38, 0.66, 0.33)	(0.52, 0.53, 0.30)	(0.75, 0.26, 0.28)
DGL-13	(0.43, 0.62, 0.29)	(0.79, 0.23, 0.22)	(0.44, 0.59, 0.35)	(0.78, 0.27, 0.17)	(0.72, 0.35, 0.22)	(0.37, 0.72, 0.20)
DGL-16	(0.77, 0.28, 0.19)	(0.49, 0.59, 0.24)	(0.89, 0.12, 0.10)	(0.31, 0.74, 0.33)	(0.84, 0.18, 0.20)	(0.72, 0.32, 0.25)
DGL-18	(0.47, 0.56, 0.30)	(0.58, 0.43, 0.40)	(0.67, 0.39, 0.27)	(0.78, 0.25, 0.18)	(0.84, 0.18, 0.11)	(0.53, 0.48, 0.43)
DGL-19	(0.64, 0.38, 0.31)	(0.82, 0.20, 0.17)	(0.75, 0.28, 0.22)	(0.77, 0.28, 0.21)	(0.83, 0.18, 0.20)	(0.76, 0.26, 0.26)
DGL-22	(0.77, 0.25, 0.21)	(0.79, 0.25, 0.15)	(0.64, 0.44, 0.19)	(0.67, 0.35, 0.28)	(0.48, 0.56, 0.37)	(0.31, 0.72, 0.33)
DGL-24	(0.57, 0.45, 0.37)	(0.82, 0.19, 0.21)	(0.82, 0.20, 0.19)	(0.46, 0.61, 0.27)	(0.75, 0.29, 0.22)	(0.79, 0.22, 0.24)

. According to Equations (41) and (42), the weighted SF sequences (${\widetilde{SWA}}_i and {\widetilde{SWG}}_i$) of locations were determined using the SWAM and the SWGM. In the next step of the SF CoCoSo procedure, the weighted SF sequences were defuzzied. Based the crisp values of the locations’ weighted sequences, the additive normalized importance (${\Phi }_i^a$), the relative importance (${\Phi }_i^b)$, and the trade-off importance (${\Phi }_i^c)$ of locations were determined by Equations (43)–(45), as shown in

Table 10. Spherical fuzzy CoCoSo results.

Location	${\widetilde{\mathit{S}\mathit{W}\mathit{A}}}_{\mathit{i}}$	${\widetilde{\mathit{S}\mathit{W}\mathit{G}}}_{\mathit{i}}$	$\mathit{S}\mathit{W}{\mathit{A}}_{\mathit{i}}$	$\mathit{S}\mathit{W}{\mathit{G}}_{\mathit{i}}$	${\Phi }_{\mathit{i}}^{\mathit{a}}$	${\Phi }_{\mathit{i}}^{\mathit{b}}$	${\Phi }_{\mathit{i}}^{\mathit{c}}$
DGL-1	(0.769, 0.262, 0.226)	(0.733, 0.324, 0.240)	21.930	20.768	0.082	2.578	1.000
DGL-3	(0.667, 0.373, 0.260)	(0.646, 0.406, 0.263)	18.708	18.052	0.070	2.220	1.856
DGL-5	(0.679, 0.367, 0.262)	(0.646, 0.411, 0.273)	19.038	18.006	0.071	2.236	0.136
DGL-6	(0.689, 0.360, 0.250)	(0.651, 0.414, 0.261)	19.406	18.225	0.072	2.271	1.934
DGL-8	(0.693, 0.356, 0.248)	(0.642, 0.434, 0.251)	19.523	18.015	0.072	2.265	1.940
DGL-9	(0.677, 0.367, 0.263)	(0.655, 0.396, 0.270)	18.991	18.292	0.071	2.252	1.914
DGL-10	(0.628, 0.430, 0.286)	(0.578, 0.481, 0.309)	17.386	15.778	0.063	2.000	1.837
DGL-11	(0.655, 0.393, 0.265)	(0.591, 0.472, 0.290)	18.301	16.269	0.066	2.084	1.881
DGL-13	(0.653, 0.401, 0.269)	(0.591, 0.483, 0.273)	18.221	16.374	0.066	2.086	1.877
DGL-16	(0.728, 0.325, 0.215)	(0.631, 0.453, 0.241)	20.744	17.726	0.074	2.317	1.999
DGL-18	(0.683, 0.357, 0.278)	(0.637, 0.413, 0.302)	19.065	17.566	0.070	2.210	1.918
DGL-19	(0.743, 0.291, 0.243)	(0.724, 0.321, 0.255)	21.058	20.410	0.079	2.505	2.014
DGL-22	(0.686, 0.362, 0.257)	(0.637, 0.423, 0.281)	19.280	17.684	0.071	2.230	1.928
DGL-24	(0.708, 0.329, 0.260)	(0.667, 0.387, 0.278)	19.928	18.612	0.074	2.326	1.960

. Ultimately, the final evaluation scores of the locations were calculated according to Equation (46). The rank of the locations is presented in descending order of the final evaluation scores, as illustrated in Figure 7.

Based on the ranking results of the SF AHP-CoCoSo approach, there are four possible locations at the top of the ranking that are considered as concordant locations for the development of direct-use geothermal energy projects in Malaysia. As shown Figure 8, these concordant locations are in the areas of Marudi of Sarawak, Tawau of Sabah, Serian of Sarawak, and Jeram of Selangor in Malaysia. However, locations in the middle of the rankings can also be considered because of the insignificant differences in evaluation scores.

4.4. Managerial Implications

Investigation into renewable energy projects requires a suitable roadmap to minimize resources and optimize efficiency. Although feasible locations are proposed throughout the territory, the energy potentials and other qualitative influences are different. Therefore, the results of prioritizing locations in this study assist renewable energy planners in Malaysia in formulating long-term investment plans for sustainable development. In other words, locations with higher ranks can be considered as investment priorities earlier and with larger design capacity.

The results of this study reflect the sustainability of efficient locations. However, the location of reinjection wells is also an important part of geothermal energy projects. Previous studies have shown that the relative location of the production well and the reinjection well can be a determining factor in the success of a geothermal project [65,66]. According to the findings of the study by Diaz et al., the mean distance of the reinjection wells should be 1.13 km from the locations evaluated in this study [67].

5. Conclusions

Geothermal energy is one of the most reliable and stable sources of renewable energy for both direct use at facilities and supplied to the power grid. It can be said that investment to develop geothermal energy sources can contribute to promoting the economy, environment, and society towards sustainable development. Among strategic decisions, prioritizing the appropriate locations is the one that has a significant impact on sustainable development. With geothermal energy potential proven by many studies, Malaysia is a promising destination for investments in this technology. However, suitable location investigation for geothermal energy projects in Malaysia is still lacking. The sustainability of geothermal energy projects depends not only on the potential of the energy source, but also on other qualitative factors. Factors such as cost, noise, distance to residential areas, etc., can be considered as criteria for assessing the sustainability of projects. To assist in exploring the geothermal energy potential of Malaysia, this study proposes the novel tri-layer MCDM framework to prioritize DGLs. As a first step in the proposed framework, DEA models are used to analyze efficient indicators to identify highly efficient locations. The efficiency of locations is determined based on quantitative indicators such as heat flow, suitability index, population density, etc., which are measured or collected from reliable databases. Next, the qualitative criteria, which are determined based on the literature and expert opinion, are weighted using the SF AHP method in the second layer. At the third and ultimate layer, the SF CoCoSo method is applied to prioritize locations for DGLs in Malaysia.

Our research findings seem to suggest that the renewable energy experts in Malaysia place more concern on social acceptability, costs, and noise impact among the qualitative criteria for evaluating DGLs. On the other hand, the results of the tri-layer MCDM framework suggest that Marudi, Tawau, and Jeram should be preferred in the investment of DGLs in Malaysia. However, the remaining positions may be considered with lower priority. This finding constitutes the primary and most important contribution of this research. The secondary contribution of this study is the proposal of a combination of both quantitative and qualitative assessments based on the most modern and robust methods.

The main limitation relates to the fact that solutions are significantly influenced by the subjective judgments of experts. Therefore, future studies should expand the size of the expert group. In addition, the construction and analysis of scenarios using simulation tools can also be considered. Additionally, the proposed framework can be applied for the geothermal energy location selection problems in other countries in the Pacific Ring of Fire.