An Offshore Wind–Wave Energy Station Location Analysis by a Novel Behavioral Dual-Side Spherical Fuzzy Approach: The Case Study of Vietnam

Abstract

Despite the high capital requirements, offshore wind and wave energy integrated stations (WWS) are an emerging and potential solution to optimize efficiency in renewable energy development. Decisions about installation location significantly influence their efficiency. This study examines and determines highly efficient and sustainable locations based on quantitative indicators and qualitative criteria. For this purpose, a novel dual-side behavioral spherical fuzzy multi-criteria decision-making (MCDM) approach was developed and applied for the case study of Vietnam. In the first stage, the behavioral Data Envelopment Analysis (B-DEA) model, constructed based on prospect theory, is applied to analyze locations according to quantitative indicators under decision makers’ psychological behavior consideration. In the second stage, a spherical fuzzy extension of the integration composed of the DEMATEL (decision-making trial and evaluation laboratory) and the EDAS (evaluation based on distance from average solution) methods helped to evaluate the locations. Based on the convergence in qualitative and quantitative analysis results, efficiency–sustainability positioning maps are established. The research provides recommendations for appropriate WWS locations from that visualization. The research compared findings with current development projects, plans, and policies in Vietnam for validation.

1. Introduction

To remove the dependence on fossil energy, the development of renewable energy has been emerging rapidly on a global scale. The onshore wind energy has reached technological maturity and is cost-effective [1]. However, onshore wind energy projects are limited by the disadvantages of land use, noise, and visible impacts. Therefore, the researchers and managers of renewables have gradually turned their attention to offshore projects [2]. Offshore wind power stations allow for the deployment of larger wind turbines and alleviate transport constraints. On the other hand, ocean energy studies are also developing at an early stage. Wave or tidal energy has great potential for development. Therefore, technologies that integrate offshore wind and wave energy are being developed vigorously [3]. In 2020, a good review about the future of offshore wind–wave integrated energy conversion systems was provided by Gao et al. The key finding of this study is the potential for greater energy generation and the reduced energy dispersion of integrated conversion systems [2].

Although WWSs are a solution to simultaneously exploit the wind and wave energy potential of the ocean, this type of integrated renewable energy is limited by high installation and operation and maintenance costs. Several attempts to optimize the cost of WWSs by the researchers have been found [4,5,6]. The primary purpose of integrated wind and wave energy studies is to minimize the cost and maximize the energy yield of offshore stations [7]. In addition to technological developments, determining the appropriate location is an important decision for the efficiency and sustainability of offshore wind and wave energy stations (WWS) [8,9]. Integrated multi-criteria decision-making (MCDM) approaches are increasingly being applied to the renewable energy site selection problems [8]. However, most renewable energy site selection studies use either expert-based assessments or quantitative analyses. In addition, decision-making processes are influenced by the psychological behavior of the decision maker, such as risk aversion, opinions on gains/losses [10]. Therefore, they leave an academic research gap for methods that combine expert-based assessment and quantitative assessment that consider psycho-behavior in the problem of location selection.

According to the International Energy Agency (IEA), Vietnam is leading the growth of renewable energy capacity of ASEAN with a contribution of 40% of renewable energy capacity [1]. Vietnam’s wind power capacity is planned to share 1.5% in 2025 and 2.1% in 2030 of the total national electricity production [11]. World Bank studies forecast that Vietnam’s offshore wind power will produce between 203 TWh and 433 TWh of electricity in 2035 [12]. However, offshore wind projects, either in the early stages or already in operation, are mostly nearshore wind power projects. Therefore, there is still a practical research gap on assessing suitable locations for offshore integrated wave and wind energy projects in Vietnam.

With the aim of narrowing the academic and practical research gaps discussed, the objective of this study is to analyze and evaluate the efficiency and sustainability of WWS locations in Vietnam. For this purpose, as theoretical contribution, this study proposes a novel behavioral dual-side spherical fuzzy approach. On the one side, the efficiency of WWS locations is evaluated based on quantitative indicators by a behavioral Data Envelopment Analysis (B-DEA) model, which is refined according to prospect theory principles. On the other side, the sustainability of locations is evaluated by an integrated MCDM method. The proposed MCDM method is composed of spherical fuzzy extensions of the DEMATEL method and EDAS method. Based on efficiency and sustainability rankings, this study classifies locations for WWS along the coastline of Vietnam as the practical contribution. In addition to the practical contribution of appropriate locations to WWSs, the remarkable novelty of this study is the novel behavioral dual-side spherical fuzzy approach for decision-support problems.

The remainder of this article includes the literature review in Section 2, the proposed methodology in Section 3, numerical results for Vietnam’s WWS location selection in Section 4, and conclusions in Section 5.

2. Literature Review

First, this study provides an overview of the research available in the literature on site selection for renewable energy. Systematic review studies show that renewable energy selection studies are primarily directed towards a specific energy type dominated by solar and wind [8,9]. According to

Table 1. MCDM application for renewable energy site selection problem.

No.	Author	Year	Data Type	Approach	Energy Type	Applied Country
1	Karaaslan et al. [24]	2021	Crisp	AHP-MARCOS	Multiple	Turkey
2	Turk et al. [25]	2021	Intuitionistic fuzzy	AHP-TOPSIS	Photovoltaic solar	Turkey
3	Zambrano-Asanza et al. [26]	2021	Crisp	GIS-AHP-WLC	Photovoltaic solar	Ecuador
4	Bishnoi and Chaturvedi [27]	2021	Crisp	AHP-TOPSIS	Gas flaring renewable	India
5	Coruhlu et al. [28]	2022	Crisp	AHP-GIS	Solar	Turkey
6	Deveci et al. [29]	2022	q-rung Orthopair fuzzy	CoCoSo	Offshore wind	Norway
7	Emeksiz and Yüksel et al. [30]	2022	Crisp	MAUT-entropy	Bioenergy	Turkey
8	Gil-García et al. [31]	2022	Interval Fuzzy	GIS-AHP-TOPSIS	Offshore wind	USA
9	Noorollahi et al. [32]	2022	Multiple membership function	GIS-AHP	Photovoltaic solar	Iran
10	Zhou et al. [15]	2022	Triangular fuzzy	AHP-weighted overlay approach	Hybrid wind–wave	China
11	This study	2022	Spherical fuzzy	B-DEA and DEMATEL-EDAS	Hybrid wind–wave	Vietnam

Note: MARCOS (measurement of alternatives and ranking according to compromise solution); TOPSIS (technique for order preference by similarity to ideal solution); WLC (weighted linear combination); CoCoSo (combined compromise solution); MAUT (multi-attribute utility theory); WOA (weighted overlay approach).

, MCDM methods are used in a variety, combined, and extended with fuzzy sets in the problem of location selection. However, site selection studies for integrated renewable energy are lacking. One of the related studies was site selection for a hybrid wind and solar energy system by Wu et al. [13], in which the analytic hierarchy process (AHP) method was applied to select the location of integrated renewable energy in China. In 2017, Vasileiou et al. used the AHP method in combination with geographic information system (GIS) to identify suitable locations for an integrated wind–wave energy project [14]. Recently, a study on the selection of wind and wave integrated energy locations in China’s Hainan province was published by Zhou et al. [15]. This expert-based assessment is performed using a triangular fuzzy extension of the AHP method. In addition, several DEA-MCDM combinations for renewable energy site selection problems were found [16,17]. Besides the DEA method, different MCDM methods could be helpful. For example, Peldschus et al. used the Game Theory to assess the construction site [18]. According to Karabasevic et al., the selection of project implementation sites highly depends on the available project implementation team [19] and available contractors [20], and feasible technologies [21]. Moreover, the alternative that is suitable to determine the local and international scopes and aims in a dynamically changing business environment [22] must protect nature and cultural heritage [23], which are requirements to turn to green energy. However, quantitative assessments that consider the psychological behavior of decision makers have not been found in the literature for this problem.

In practical terms, Vietnam is one of the leading countries in wind energy development in Southeast Asia [1]. At the same time, Vietnam has a coastline along the country. Therefore, Vietnam has great potential for offshore energy projects that take advantage of the inexhaustible energy sources of both wind and waves. However, no study on offshore wind and wave integrated energy has been found for the case of Vietnam. From the above review, it can be seen that there is a lack of studies on location selection for mixed renewable energy for Vietnam that apply both qualitative and quantitative analysis, including the psychological behavior of decision makers.

3. Methodology

In order to comprehensively evaluate and rank potential locations for WWSs, this study proposes a novel integrated decision-making approach consisting of two stages as illustrated in Figure 1. The objective of stage A is to evaluate the locations’ efficiency based on quantitative indicators. These indicators contain information about energy potential, wave climate, bathymetry, distance to shore and so on. Based on the data of the indicators, a behavioral DEA model is used to determine the locations’ efficiency under consideration of decision makers’ psychosocial behavior. On the other hand, in stage B, the locations’ sustainability is evaluated based on qualitative criteria. At this stage, a group of experts and evaluation criteria are determined. Then, the spherical fuzzy DEMATEL method is applied to calculate the weights of the evaluation criteria. In the next step, the locations’ sustainability is evaluated according to the criteria using the spherical fuzzy EDAS method. Finally, the locations’ ranking, discussions, and recommendations are provided based on both efficiency and sustainability assessments.

3.1. Behavioral Data Envelopment Analysis (B-DEA)

In 1978, Charnes et al. introduced the primitive DEA model, referred to as the CCR model, to evaluate the technical efficiency of a decision-making unit (DMU) with the constant returns to scale assumption [33]. Because this assumption is unconvincing in many cases, the BCC model with the assumption of the variable returns to scale was proposed by Banker et al. [34]. Considering $M$ inputs $\left(i=1\dots M\right)$ and $T$ outputs $\left(r=1\dots T\right)$ of the $L$ DMUs $\left(j=1\dots L\right)$, the technical efficiency ${\psi }_k$ of the $kth$ DMU can be calculated by solving the following model:

$$\begin{array}{c}maximize {\psi }_k=\varphi +{\displaystyle \sum }_{r=1}^T{u}_r{f}_{rk}\\ subject to\hfill \\ {\displaystyle \sum }_{i=1}^M{v}_i{e}_{ik}=1\\ \varphi +{\displaystyle \sum }_{r=1}^T{u}_r{f}_{rj}-{\displaystyle \sum }_{i=1}^M{v}_i{e}_{ij}\le 0, j=1, \dots ,L\\ u_r, v_i\ge 0 i=1, \dots ,M;r=1,\dots ,T\\ \varphi \mathrm{is} \mathrm{free}\end{array}$$

(1)

where $u_r$ and $v_i$ represent the weight of the $rth$ output and the $ith$ input, respectively. The $e_{ij} and f_{rj}$ represent the $ith$ input value and $rth$ output value of $jth$ DMU. The $kth$ DMU is effective if the technical efficiency (${\psi }_k$) is 1.

Prospect theory is a descriptive theory for individual psychological behavior, which was introduced initially by Kahneman and Tversky [10]. Prospect theory is one of the widely applied theories in behavioral decision-making problems in many fields [35,36]. According to prospect theory, there are three important principles in behavioral decision-making as follows:

• Reference dependence: Individuals’ perceptions of gains and losses depend on a reference point.
• Loss aversion: Individuals’ sensitivity to losses is greater than to equal gains.
• Diminishing sensitivity: Individuals tend to be risk-seeking for losses and risk-averse for gains.

According to these three principles, the prospective value function is an asymmetrical S-shape curve as illustrated in Figure 2, in which the principle of reference dependence divides the prospect value function into a loss domain and a gain domain. On the other hand, the value function’s slope of the gain domain is smaller than that of the loss domain according to the principle of loss aversion. In accordance with the principle of diminishing sensitivity, the prospect value function is convex in the gain domain and concave in the loss domain. The prospect value function is described in Equation (2).

$$f\left(\Delta t\right)=\left\{\begin{array}{cc}{\left(\Delta t\right)}^{\alpha }& ,\forall \Delta t\ge 0;0<\alpha <1\\ -\mu {\left(-\Delta t\right)}^{\beta }& ,\forall \Delta t<0;0<\beta <1\end{array}\right.$$

(2)

where $\Delta t$ represents the value of loss or gain relative to a reference point. The parameters $\mu , \alpha ,$ and $\beta$ represent the loss aversion, the gain risk attitude, and the loss risk attitude of decision makers, respectively.

Based on prospect theory, Chen et al. proposed a new behavioral DEA model that includes the following steps [37]:

Step 1: The normalized value of input ($x_{ij}$) and output ($y_{ij}$) are determined as Equations (3) and (4).

$$x_{ij}=\frac{e_{ij}^{max}-e_{ij}}{e_{ij}^{max}-e_{ij}^{min}} j=1,\dots ,L$$

(3)

$$y_{ij}=\frac{f_{ij}-f_{ij}^{min}}{f_{ij}^{max}-f_{ij}^{min}} j=1,\dots ,L$$

(4)

Step 2: The positive and negative reference points are determined as Equations (5) and (6).

The positive reference points ($e_i^{+} and f_r^{+})$:

$$e_i^{+}=\underset{j}{\min }\left(x_{ij}\right);f_r^{+}=\underset{r}{\max }\left(y_{ij}\right)$$

(5)

The negative reference points ($e_i^{-} and f_r^{-})$:

$$e_i^{-}=\underset{j}{\max }\left(x_{ij}\right);f_r^{-}=\underset{r}{\min }\left(y_{ij}\right)$$

(6)

Step 3: The Behavioral DEA model is constructed (7).

$$\begin{array}{c}maximize \phi =\mathsf{\Theta }\left(\varphi +{\displaystyle \sum }_{r=1}^T{u}_{rk}{\left(y_{rk}-f_r^{-}\right)}^{\alpha }+{\displaystyle \sum }_{i=1}^M{v}_{ik}{\left(e_i^{-}-x_{ik}\right)}^{\alpha }\right)\\ \hfill -\left(1-\mathsf{\Theta }\right)\left(\varphi +{\displaystyle \sum }_{r=1}^T{u}_{rk}\mu {\left(f_r^{+}-y_{rk}\right)}^{\beta }+{\displaystyle \sum }_{i=1}^M{v}_{ik}\mu {\left(x_{ik}-e_i^{+}\right)}^{\beta }\right)\\ subject to\hfill \\ {\displaystyle \sum }_{i=1}^M{v}_{ik}{e}_{ik}=1\\ \varphi +{\displaystyle \sum }_{r=1}^T{u}_{rj}{f}_{rj}-{\displaystyle \sum }_{i=1}^M{v}_{ij}{e}_{ij}\le 0 j=1, \dots ,L\\ u_{rj}, v_{ij}\ge 0 i=1, \dots ,M;r=1,\dots ,T;j=1, \dots ,L\\ \varphi \mathrm{is} \mathrm{free}\end{array}$$

(7)

where $\mathsf{\Theta }$ represents the relative degree of importance toward gains and $0<\mathsf{\Theta }<1$. If $\mathsf{\Theta }=0.5$, it implies that the decision maker considers gains and losses equally important.

3.2. Spherical Fuzzy (SF) Sets

To deal with uncertainties in decision making, fuzzy sets have been introduced, evolved, and applied over the past decades as illustrated in Figure 3 [38,39,40,41,42,43,44]. The spherical fuzzy set, which was introduced recently, has attracted the attention of researchers [45,46,47]. The definition of SFS and its basic operators are presented as follows:

Definition 1.

Spherical fuzzy set$\tilde{A}$ of the universe of discourse X is defined by

$$\tilde{A}=\left\{\left.\langle x,\left({\alpha }_{\tilde{A}}\left(x\right),{\beta }_{\tilde{A}}\left(x\right),{\gamma }_{\tilde{A}}\left(x\right)\right)\right|x\in X\right\}$$

(8)

where

$${\alpha }_{\tilde{A}},{\beta }_{\tilde{A}}, {\gamma }_{\tilde{A}}:X\to \left[0, 1\right] and 0\le {\alpha }_{\tilde{A}}^2\left(x\right)+{\beta }_{\tilde{A}}^2\left(x\right)+{\gamma }_{\tilde{A}}^2\left(x\right)\le 1 \forall x\in X$$

(9)

The numbers${\alpha }_{\tilde{A}}\left(x\right),{\beta }_{\tilde{A}}\left(x\right),$and${\gamma }_{\tilde{A}}\left(x\right)$are the membership degree, non-membership degree, and hesitancy degree of each$x$to$\tilde{A}$, respectively.

Definition 2.

Consider two universes$X_1$and$X_2$. Let$\tilde{A}=\left({\alpha }_{\tilde{A}},{\beta }_{\tilde{A}},{\gamma }_{\tilde{A}}\right)$and$\tilde{B}=\left({\alpha }_{\tilde{B}},{\beta }_{\tilde{B}},{\gamma }_{\tilde{B}}\right)$be two spherical fuzzy sets (SFS) from the universe of discourse$X_1$and$X_2$. The Basic operators are defined as follows:

Addition

$$\tilde{A}\oplus \tilde{B}=\left\{{\left({\alpha }_{\tilde{A}}^2+{\alpha }_{\tilde{A}}^2-{\alpha }_{\tilde{A}}^2{\alpha }_{\tilde{B}}^2\right)}^{\frac{1}{2}},{\beta }_{\tilde{A}}{\beta }_{\tilde{B}},{\left(\left(1-{\alpha }_{\tilde{B}}^2\right){\gamma }_{\tilde{A}}^2+\left(1-{\alpha }_{\tilde{A}}^2\right){\gamma }_{\tilde{B}}^2-{\gamma }_{\tilde{A}}^2{\gamma }_{\tilde{B}}^2\right)}^{\frac{1}{2}} \right\}$$

(10)

Multiplication

$$\tilde{A}\otimes \tilde{B}=\left\{ {\alpha }_{\tilde{A}}{\alpha }_{\tilde{B}},{\left({\beta }_{\tilde{A}}^2+{\beta }_{\tilde{B}}^2-{\beta }_{\tilde{A}}^2{\beta }_{\tilde{B}}^2\right)}^{\frac{1}{2}},{\left(\left(1-{\beta }_{\tilde{B}}^2\right){\gamma }_{\tilde{A}}^2+\left(1-{\beta }_{\tilde{A}}^2\right){\gamma }_{\tilde{B}}^2-{\gamma }_{\tilde{A}}^2{\gamma }_{\tilde{B}}^2\right)}^{\frac{1}{2}} \right\}$$

(11)

Multiplication by a scalar$(\lambda >0)$

$$\lambda \tilde{A}=\left\{{\left(1-{\left(1-{\alpha }_{\tilde{A}}^2\right)}^{\lambda }\right)}^{\frac{1}{2}},{\beta }_{\tilde{A}}^{\lambda }, {\left({\left(1-{\alpha }_{\tilde{A}}^2\right)}^{\lambda }-{\left(1-{\alpha }_{\tilde{A}}^2-{\gamma }_{\tilde{A}}^2\right)}^{\lambda }\right)}^{\frac{1}{2}} \right\}$$

(12)

Power of$\tilde{A}$ $(\lambda >0)$

$${\tilde{A}}^{\lambda }=\left\{{\alpha }_{\tilde{A}}^{\lambda },{\left(1-{\left(1-{\beta }_{\tilde{A}}^2\right)}^{\lambda }\right)}^{\frac{1}{2}},{\left({\left(1-{\beta }_{\tilde{A}}^2\right)}^{\lambda }-{\left(1-{\beta }_{\tilde{A}}^2-{\gamma }_{\tilde{A}}^2\right)}^{\lambda }\right)}^{\frac{1}{2}}\right\}$$

(13)

Definition 3.

Consider the weight vector$w=\left(w_1,w_2,\dots ,w_n\right)$, where $0\le w_i\le 1$ and ${\displaystyle \sum }_{i=1}^n{w}_i=1$. Spherical weighted arithmetic mean (SWAM) and spherical weighted geometric mean (SWGM) are defined as follows:

$$\begin{gathered} SWA{M}_w\left({\tilde{A}}_1,{\tilde{A}}_2,\dots ,{\tilde{A}}_n\right)=w_1{\tilde{A}}_1+w_2{\tilde{A}}_2+\dots +w_n{\tilde{A}}_n \\ =\left\{{\left(1-{\displaystyle \prod }_{i=1}^n{\left(1-{\alpha }_{{\tilde{A}}_i}^2\right)}^{w_i}\right)}^{\frac{1}{2}},{\displaystyle \prod }_{i=1}^n{\beta }_{{\tilde{A}}_i}^{w_i},{\left({\displaystyle \prod }_{i=1}^n{\left(1-{\alpha }_{{\tilde{A}}_i}^2\right)}^{w_i}-{\displaystyle \prod }_{i=1}^n{\left(1-{\alpha }_{{\tilde{A}}_i}^2-{\gamma }_{{\tilde{A}}_i}^2\right)}^{w_i}\right)}^{\frac{1}{2}}\right\} \end{gathered}$$

(14)

$$\begin{gathered} SWG{M}_w\left({\tilde{A}}_1,{\tilde{A}}_2,\dots ,{\tilde{A}}_n\right)={\tilde{A}}_1^{w_1}+{\tilde{A}}_2^{w_2}+\dots +{\tilde{A}}_n^{w_n} \\ =\left\{{\displaystyle \prod }_{i=1}^n{\alpha }_{{\tilde{A}}_i}^{w_i},{\left(1-{\displaystyle \prod }_{i=1}^n{\left(1-{\beta }_{{\tilde{A}}_i}^2\right)}^{w_i}\right)}^{\frac{1}{2}},{\left({\displaystyle \prod }_{i=1}^n{\left(1-{\beta }_{{\tilde{A}}_i}^2\right)}^{w_i}-{\displaystyle \prod }_{i=1}^n{\left(1-{\beta }_{{\tilde{A}}_i}^2-{\gamma }_{{\tilde{A}}_i}^2\right)}^{w_i}\right)}^{\frac{1}{2}}\right\} \end{gathered}$$

(15)

Definition 4

[45]. Consider two universes $X_1$ and $X_2$. Let $\tilde{A}=\left({\alpha }_{\tilde{A}},{\beta }_{\tilde{A}},{\gamma }_{\tilde{A}}\right)$ and $\tilde{B}=\left({\alpha }_{\tilde{B}},{\beta }_{\tilde{B}},{\gamma }_{\tilde{B}}\right)$ be two SFSs from the universe of discourse $X_1$ and $X_2$. The followings are valid under the condition $\lambda$, ${\lambda }_1$, ${\lambda }_2>0$.

$$\tilde{A}\oplus \tilde{B}=\tilde{B}\oplus \tilde{A}$$

(16)

$$\tilde{A}\otimes \tilde{B}=\tilde{B}\otimes \tilde{A}$$

(17)

$$\lambda \left(\tilde{A}\oplus \tilde{B}\right)=\lambda \tilde{A}\oplus \lambda \tilde{B}$$

(18)

$${\lambda }_1\tilde{A}\oplus {\lambda }_2\tilde{A}=({\lambda }_1+{\lambda }_2)\tilde{A}$$

(19)

$${\left(\tilde{A}\otimes \tilde{B}\right)}^{\lambda }={\tilde{A}}^{\lambda }\otimes {\tilde{B}}^{\lambda }$$

(20)

$${\tilde{A}}^{{\lambda }_1}\otimes {\tilde{A}}^{{\lambda }_2}={\tilde{A}}^{{\lambda }_1+{\lambda }_2}$$

(21)

Definition 5.

The defuzzied value (DFV) of SFS$\tilde{A}=\left({\alpha }_{\tilde{A}},{\beta }_{\tilde{A}},{\gamma }_{\tilde{A}}\right)$IS defined as follows:

$$DFV\left(\tilde{A}\right)={\left({\alpha }_{\tilde{A}}-{\gamma }_{\tilde{A}}\right)}^2+{\left({\beta }_{\tilde{A}}-{\gamma }_{\tilde{A}}\right)}^2$$

(22)

3.3. Spherical Fuzzy DEMATEL-EDAS Method

To evaluate the interrelationships of factors in complex systems, the DEMATEL method was initially proposed by Fontela and Gabus [48]. A systematic review of MCDM studies found that the DEMATEL method is increasingly used in the role of weighting criteria. In terms of prioritizing alternatives, distance-based evaluation methods, such as TOPSIS or EDAS, are applied effectively with high frequency [8]. Moreover, fuzzy variations of MCDM methods are introduced and proposed more and more widely. Therefore, this study proposes a spherical fuzzy extension of the integration approach composed by DEMATEL and EDAS, named SF DEMATEL–EDAS, for the first time. The proposed approach includes the following steps:

Step 1: Identify experts and criteria

In this step, a group of experts $\left(k=1, 2,\dots ,K\right)$ with experience and a high level of expertise in the research field is selected. Then, the evaluation criteria $\left(j=1, 2,\dots ,J\right)$ are determined according to previous studies and expert contributions.

Step 2: Prioritize experts

The weights of experts are calculated because of the difference in their experience, knowledge, and expertise level. Let the expertise of the $kth$ expert be expressed as a spherical fuzzy number (SFN) ${\tilde{A}}_k=\left({\alpha }_k, {\beta }_k,{\gamma }_k\right)$. The crisp weight of the $kth$ expert can be calculated as Equation (23) [49].

$$\begin{array}{c}{\vartheta }_k=\frac{1-\sqrt{\left(\left(1-{\alpha }_k^2\right)+{\beta }_k^2+{\gamma }_k^2\right)/3}}{{{\displaystyle \sum }}_k\left(1-\sqrt{\left(\left(1-{\alpha }_k^2\right)+{\beta }_k^2+F{\gamma }_k^2\right)/3}\right)}\hfill \\ \mathrm{where}\hfill \\ {\displaystyle \sum }_{k=1}^K{\vartheta }_k=1\\ \mathrm{and}\\ 0\le {\alpha }_k^2+{\beta }_k^2+{\gamma }_k^2\le 1\end{array}$$

(23)

Step 3: Construct the individual direct influence matrices

The experts provide linguistic pairwise comparisons of the influence between the evaluation criteria. These linguistic pairwise comparisons were then converted to the respective SFNs as shown in

Table 2. Linguistics term and respective SFNs for the SF DEMATEL method.

Linguistics Term	Notation	Spherical Fuzzy Numbers
No Influence	NI	(0, 0.3, 0.2)
Weak Influence	WI	(0.35, 0.25, 0.25)
Moderate Influence	MI	(0.6, 0.2, 0.35)
Strong Influence	SI	(0.85, 0.15, 0.45)

[50]. The individual direct influence matrix of the $kth$ expert is represented by $U^k={\left[{\tilde{u}}_{jl}^k\right]}_{JxJ}={\left[\left({\alpha }_{jl}^k,{\beta }_{jl}^k,{\gamma }_{jl}^k\right)\right]}_{JxJ}$.

Step 4: Construct the aggregated direct influence matrix

The aggregated direct influence matrix is constructed by aggregating the matrices of the experts. This aggregation process applies the spherical weight arithmetic mean SWAM according to Equation (14). The aggregated direct influence matrix of the $kth$ expert is represented by $U^{*}={\left[{\tilde{u}}_{jl}^{*}\right]}_{JxJ}={\left[\left({\alpha }_{jl}^{*},{\beta }_{jl}^{*},{\gamma }_{jl}^{*}\right)\right]}_{JxJ}.$

Step 5: Construct the initial direct influence submatrices

To normalize the aggregated direct influence matrix, it is split into three submatrices corresponding to each parameter of the SFS. These submatrices are represented by $U^{\alpha }={\left[{\alpha }_{jl}^{*}\right]}_{JxJ}$, $U^{\beta }={\left[{\beta }_{jl}^{*}\right]}_{JxJ}$, and $U^{\gamma }={\left[{\gamma }_{jl}^{*}\right]}_{JxJ}$. Then, the normalized submatrices are calculated as Equations (24)–(26).

$$V^{\alpha }=s^{\alpha }\times U^{\alpha }, \mathrm{where} s^{\alpha }=min\left(\frac{1}{\underset{j}{\max }{{\displaystyle \sum }}_{l=1}^J{\alpha }_{il}^{*}},\frac{1}{\underset{l}{\max }{{\displaystyle \sum }}_{j=1}^J{\alpha }_{il}^{*}}\right)$$

(24)

$$V^{\beta }=s^{\beta }\times U^{\beta }, \mathrm{where} s^{\beta }=min\left(\frac{1}{\underset{j}{\max }{{\displaystyle \sum }}_{l=1}^J{\beta }_{il}^{*}},\frac{1}{\underset{l}{\max }{{\displaystyle \sum }}_{j=1}^J{\beta }_{il}^{*}}\right)$$

(25)

$$V^{\gamma }=s^{\gamma }\times U^{\gamma }, \mathrm{where} s^{\gamma }=min\left(\frac{1}{\underset{j}{\max }{{\displaystyle \sum }}_{l=1}^J{\gamma }_{il}^{*}},\frac{1}{\underset{l}{\max }{{\displaystyle \sum }}_{j=1}^J{\gamma }_{il}^{*}}\right)$$

(26)

Step 6: Construct the total direct influence matrix

Firstly, the initial influence submatrices are transformed into total influence submatrices according to Equations (27)–(29) [51].

$$T^{\alpha }=V^{\alpha }{\left(I-V^{\alpha }\right)}^{-1}$$

(27)

$$T^{\beta }=V^{\beta }{\left(I-V^{\beta }\right)}^{-1}$$

(28)

$$T^{\gamma }=V^{\gamma }{\left(I-V^{\gamma }\right)}^{-1}$$

(29)

Next, the total influence submatrices are combined to form the total influence matrix, which is represented by $T={\left[{\tilde{t}}_{jl}\right]}_{JxJ}={\left[\left({\alpha }_{jl}^T,{\beta }_{jl}^T,{\gamma }_{jl}^T\right)\right]}_{JxJ}$.

Step 7: Calculate the SF row and column sums

In this step, the SF row sum $\left({\tilde{r}}_j\right)$ and the SF column sum $\left({\tilde{c}}_j\right)$ of the total influence matrix are computed according to Equations (30) and (31). The summing process utilizes the SF addition operator as shown in Equation (10).

$${\tilde{r}}_j={\displaystyle \sum }_{l=1}^J{\tilde{t}}_{jl} j=1\dots J$$

(30)

$${\tilde{c}}_l={\displaystyle \sum }_{j=1}^J{\tilde{t}}_{jl} l=1\dots J$$

(31)

Step 8: Calculate the criteria’ prominence, relation and weight

First, the SF row sum $\left({\tilde{r}}_j\right)$ and the SF column sum $\left({\tilde{c}}_j\right)$ are defuzzied according to Equation (22). Based on the results of defuzzification, the prominence, the relation, and the weight $\left(w_j\right)$ of the $jth$ criteria are determined as follows:

$$prominenc{e}_j=r_j+c_j j=1\dots J$$

(32)

$$relatio{n}_j=r_j-c_j j=1\dots J$$

(33)

$$w_j=\frac{r_j+c_j}{{{\displaystyle \sum }}_{j=1}^J\left(r_j+c_j\right)} j=1\dots J$$

(34)

Step 9: Construct the spherical fuzzy decision matrix

In this step, each expert provides the linguistic evaluation of alternatives $\left(i=1,2,\dots ,I\right)$ according to the criteria. Based on the relationships presented in

Table 3. Linguistics term and respective SFNs for the SF EDAS method.

Linguistics Term	Notation	Spherical Fuzzy Numbers
Absolutely Low	AL	(0.1, 0.9, 0.1)
Very Low	VL	(0.2, 0.8, 0.2)
Low	L	(0.3, 0.7, 0.3)
Slightly Low	SL	(0.4, 0.6, 0.4)
Medium	M	(0.5, 0.5, 0.5)
Slightly High	SH	(0.6, 0.4, 0.4)
High	H	(0.7, 0.3, 0.3)
Very High	VH	(0.8, 0.2, 0.2)
Absolutely High	AH	(0.9, 0.1, 0.1)

, the linguistic evaluations are transformed into the corresponding SFNs. Using the SWAM, the SF decision matrix ($\tilde{X}={\left[{\tilde{x}}_{ij}\right]}_{IxJ}$) is constructed as Equation (35).

$${\tilde{x}}_{ij}=SWA{M}_{\vartheta }\left({\tilde{x}}_{ij}^1,{\tilde{x}}_{ij}^2,\dots ,{\tilde{x}}_{ij}^k\right)={\vartheta }_1{\tilde{x}}_{ij}^1+{\vartheta }_2{\tilde{x}}_{ij}^2+\dots +{\vartheta }_k{\tilde{x}}_{ij}^k i=1\dots I;j=1\dots J$$

(35)

Step 10: Identify the spherical fuzzy average solution

Based on the SF decision matrix, the SF average solution is determined by SWAM as Equation (34). The average solution represented by $\widetilde{AV}={\left[{\widetilde{av}}_j\right]}_J$.

$${\widetilde{av}}_j=SWAM\left({\tilde{x}}_{1j},{\tilde{x}}_{2j},\dots ,{\tilde{x}}_{Ij}\right)=\frac{1}{I}{\tilde{x}}_{1j}+\frac{1}{I}{\tilde{x}}_{2j}+\dots +\frac{1}{I}{\tilde{x}}_{Ij} j=1\dots J$$

(36)

Step 11: Identify the crisp decision matrix and the crisp average solution

The crisp decision matrix and crisp average solution are constructed by defuzzification process according to Equation (22).

Step 12: Identify the positive distance from average matrix and the negative distance from average matrix

Based on the crisp decision matrix and the crisp average solution, the positive distance from average matrix $\left(PDA={\left[d_{ij}^{+}\right]}_{IxJ}\right)$ and the negative distance from average matrix $\left(NDA={\left[d_{ij}^{-}\right]}_{IxJ}\right)$ are defined as Equations (37) and (38).

$$d_{ij}^{+}=\frac{\max \left(0,x_{ij}-a{v}_j\right)}{a{v}_j}$$

(37)

$$d_{ij}^{-}=\frac{\max \left(0,a{v}_j-x_{ij}\right)}{a{v}_j}$$

(38)

Step 13: Calculate the weighted sum positive distance and the weighted sum negative distance

In this step, the weighted sum positive distance $\left(s_i^{+}\right)$ and the weighted sum negative distance $\left(s_i^{-}\right)$ are computed as Equations (39) and (40), respectively, in which the criteria weights ($w_j$) are determined in Step 8.

$$s_i^{+}={\displaystyle \sum }_{j=1}^J{w}_j{d}_{ij}^{+}$$

(39)

$$s_i^{-}={\displaystyle \sum }_{j=1}^J{w}_j{d}_{ij}^{-}$$

(40)

Next, the normalized weighted sum of positive distance $\left(n{s}_i^{+}\right)$ and the normalized weighted sum of negative distance $\left(n{s}_i^{-}\right)$ are determined as follows.

$$n{s}_i^{+}=\frac{s_i^{+}}{\underset{i}{\max }\left(s_i^{+}\right)}$$

(41)

$$n{s}_i^{-}=1-\frac{s_i^{-}}{\underset{i}{\max }\left(s_i^{-}\right)}$$

(42)

Step 14: Calculate the alternatives’ appraisal score

Ultimately, the appraisal score $\left(a{s}_i\right)$ of alternatives is calculated as Equation (43). The alternative with a larger appraisal score is better. In other words, the alternatives are ranked in descending order of the appraisal score.

$$a{s}_i=\frac{1}{2}\left(n{s}_i^{+}+n{s}_i^{-}\right)$$

(43)

4. Case Study

4.1. Location Identification

In this section, the proposed approach is applied to evaluate and select locations for WWS in Vietnam. After excluding military and conservation areas, this study considered twenty feasible locations along the coast, numbered in ascending order from north to south as illustrated in Figure 4. In addition, the distance to the shore of these locations was greater than 25 km to avoid negative impacts on other economic and social activities [14]. The locations’ geographical coordinates are presented in

Table A1. The proposed locations’ coordinates.

Location	Latitude	Longitude	Location	Latitude	Longitude
WWS-1	20.591686	108.202101	WWS-11	12.380291	110.120526
WWS-2	20.097773	107.519992	WWS-12	11.200562	109.896527
WWS-3	19.594143	106.968776	WWS-13	10.503389	109.167185
WWS-4	18.903735	106.745225	WWS-14	9.862731	108.192441
WWS-5	18.116894	107.173398	WWS-15	9.118867	107.530793
WWS-6	17.393742	107.965662	WWS-16	8.443364	106.337667
WWS-7	16.727761	108.872040	WWS-17	8.092894	105.506814
WWS-8	15.643628	109.700175	WWS-18	8.247452	103.944320
WWS-9	14.734740	109.899698	WWS-19	9.257728	103.199160
WWS-10	13.583723	110.107265	WWS-20	10.029545	103.346960

.

4.2. Stage A: Efficiency Evaluation by B-DEA Model

To evaluate the efficiency of locations, this stage applied the B-DEA model discussed in Section 3.1. First, ten experts with at least eight years of experience in renewable energy, marine climate and public policy development were selected to contribute to this study. There are seven quantitative indicators defined by relevant research and expert opinion [17,52,53,54]. These indicators are divided into two groups as inputs and outputs of the B-DEA model. The inputs include bathymetry (m), distance to shore (km), and distance to the grid (km). These factors directly affect the cost of installation and maintenance and transmission power loss. Therefore, the smaller value of these metrics, the higher efficiency of WWS. Meanwhile, the population density in the adjacent residential area (people/km²) as well as the energy potential related indicators of locations, such as average wind speed (m/s), annual average power density (W/m²), and wave height (m), are outputs. As shown in

Table 4. The quantitative indicators of the B-DEA model.

Location	Bathymetry (m)	Distance to Shore (km)	Distance to Grid (km)	Average Wind Speed (m/s)	Annual Average Power Density (W/m2)	Wave Height (m)	Population Density of the Adjacent Residential Area (People/km2)
WWS-1	40	77.34	99.44	7.40	447.14	0.9	99.62
WWS-2	25	90.80	91.94	7.61	454.05	1.1	99.37
WWS-3	44	90.20	118.39	7.61	454.05	1.1	87.67
WWS-4	52	98.40	98.47	7.61	454.05	1.1	96.78
WWS-5	69	73.63	86.49	7.27	376.72	1.1	80.88
WWS-6	91	96.12	112.63	7.27	376.72	1.2	97.99
WWS-7	99	99.02	99.10	6.85	318.33	1.4	94.66
WWS-8	535	67.66	100.24	6.85	318.33	1.4	66.62
WWS-9	439	90.01	132.21	7.07	344.87	1.4	88.70
WWS-10	2057	89.88	96.00	7.07	344.87	1.4	90.46
WWS-11	2152	85.55	96.82	6.17	248.00	1.4	96.19
WWS-12	635	100.76	109.07	6.17	248.00	1.6	93.16
WWS-13	131	23.70	98.01	6.17	248.00	1.5	91.90
WWS-14	43	104.08	105.50	6.19	219.74	1.3	98.50
WWS-15	40	98.02	121.95	6.19	219.74	1.3	126.72
WWS-16	23	31.95	117.76	6.19	219.74	0.7	102.65
WWS-17	24	76.49	129.76	6.19	219.74	0.8	78.75
WWS-18	24	94.23	161.85	6.38	261.99	0.8	97.35
WWS-19	42	78.83	158.20	6.38	261.99	0.7	123.08
WWS-20	26	65.16	71.59	6.38	261.99	0.3	66.34

, the data of inputs and outputs were collected from online renewable energy databases, such as the International Renewable Energy Agency database [55,56].

Based on the collected data, the procedure of the B-DEA model, as mentioned in Section 3.1, was applied. This study assumed that experts are more concerned with gains than losses $(\mathsf{\Theta }>0.5)$, and $\mu =2.25$, $\alpha =0.85$, $\beta =0.92$ in the B-DEA model [10]. Then, the B-DEA model (7) was solved with a different value of $\mathsf{\Theta }$ by Lingo solver 19.0.53. The results of B-DEA’s model are presented in

Table A2. The results of the B-DEA model.

Location	$\mathbf{Value} \mathbf{of} \mathsf{\Theta }$
	0.51	0.55	0.60	0.65	0.70	0.75	0.80	0.85	0.90	0.95	0.99
WWS-1	0.027	0.071	0.126	0.182	0.237	0.293	0.394	0.495	0.596	0.696	0.797
WWS-2	0.046	0.089	0.143	0.201	0.288	0.375	0.462	0.549	0.636	0.723	0.810
WWS-3	0.046	0.089	0.143	0.201	0.288	0.375	0.462	0.549	0.636	0.723	0.810
WWS-4	0.047	0.090	0.144	0.202	0.289	0.376	0.463	0.550	0.637	0.724	0.810
WWS-5	0.016	0.061	0.117	0.198	0.286	0.373	0.461	0.548	0.635	0.723	0.810
WWS-6	0.021	0.079	0.161	0.242	0.324	0.406	0.488	0.569	0.651	0.733	0.814
WWS-7	0.102	0.160	0.234	0.307	0.380	0.453	0.526	0.600	0.673	0.746	0.819
WWS-8	0.096	0.155	0.228	0.301	0.375	0.449	0.523	0.597	0.671	0.745	0.819
WWS-9	0.100	0.159	0.232	0.306	0.379	0.452	0.526	0.599	0.673	0.746	0.819
WWS-10	0.100	0.159	0.232	0.306	0.379	0.452	0.526	0.599	0.673	0.746	0.819
WWS-11	0.099	0.158	0.231	0.305	0.378	0.452	0.525	0.599	0.672	0.746	0.819
WWS-12	0.174	0.227	0.293	0.359	0.425	0.491	0.557	0.624	0.690	0.756	0.822
WWS-13	0.128	0.184	0.254	0.324	0.394	0.464	0.534	0.605	0.675	0.745	0.815
WWS-14	0.062	0.123	0.201	0.278	0.355	0.432	0.509	0.586	0.663	0.740	0.817
WWS-15	0.061	0.122	0.200	0.277	0.354	0.431	0.508	0.586	0.663	0.740	0.817
WWS-16	0.008	0.048	0.099	0.150	0.201	0.252	0.303	0.404	0.525	0.646	0.767
WWS-17	0.009	0.050	0.101	0.152	0.203	0.254	0.347	0.457	0.567	0.677	0.787
WWS-18	0.013	0.054	0.104	0.155	0.206	0.257	0.349	0.458	0.568	0.677	0.787
WWS-19	0.014	0.055	0.105	0.156	0.207	0.257	0.308	0.407	0.529	0.650	0.771
WWS-20	0.006	0.047	0.098	0.149	0.201	0.252	0.303	0.355	0.406	0.464	0.524

in Appendix A. Based on efficiency corresponding to different values of $\mathsf{\Theta }$, locations were ranked as shown in Figure 5.

The first finding from the ranking results is that WWS-12 has the highest efficiency without being affected by $\mathsf{\Theta }$. Meanwhile, at the bottom of the rankings, the performance of WWS-12 and WWS-14 positions is also unchanged by the psychological behavior of the decision maker. Meanwhile, at the bottom of the rankings, the efficiency of WWS-16 and WWS-20 positions remained unchanged as decision makers place more emphasis on gains. As decision makers began to prioritize gains over losses $(0.5<\mathsf{\Theta }\le 0.65)$, the rankings of WWS-9, WWS-6, WWS-4, and WWS-5 improved, while WWS-10, WWS-1, and WWS-3 deteriorated. When the importance degree of gains against losses is moderate $(0.65<\mathsf{\Theta }\le 0.85)$, the change in rank mainly occurs at the bottom of the chart between WWS-17, WWS-18, and WWS-19. When decision makers are mostly concerned with gains $(0.85<\mathsf{\Theta }<1)$, the efficiency rankings are fraught with volatility. The most notable phenomenon is the severe ranking drop of WWS-13 from 2nd to 9th and the rise of WWS-8 from 7th to 3rd. In the middle of the rankings, the drop in WWS-4’s ranking led to an increase in WWS-2 and WWS-3. At the bottom of the rankings, WWS-17 and WWS-18 swap positions.

4.3. Stage B: Sustainability Evaluation by SF DEMATEL-EDAS Method

4.3.1. Evaluation Criteria Identification and Weighting

On the other hand, this study implemented a multi-criteria evaluation of sustainability for the proposed locations. The evaluation criteria are recommended by experts and previous studies as shown in

Table 5. List of evaluation criteria.

Notation	Evaluation Criteria
EC1	Vessel density
EC2	Costs
EC3	Military activities
EC4	Geopolitical issues
EC5	Proximity to conservation area
EC6	Proximity to Seaports
EC7	Proximity to Industrial Area
EC8	Potential tourism impact
EC9	Potential fisheries impact
EC10	Social acceptability

[8,17,57,58,59]. Next, the experts provide linguistic pairwise comparisons of the influence between the criteria as illustrated in

Table A3. Linguistic pairwise comparison of criteria by Expert 1.

Criteria	EC1	EC2	EC3	EC4	EC5	EC6	EC7	EC8	EC9	EC10
EC1	NI	WI	NI	SI	WI	WI	WI	SI	MI	NI
EC2	SI	NI	MI	NI	SI	SI	WI	NI	MI	SI
EC3	NI	MI	NI	WI	NI	WI	WI	WI	SI	WI
EC4	WI	NI	NI	NI	NI	WI	WI	MI	NI	WI
EC5	SI	SI	NI	SI	NI	MI	MI	MI	SI	SI
EC6	WI	MI	MI	SI	WI	NI	SI	SI	WI	MI
EC7	MI	WI	SI	SI	MI	WI	NI	WI	MI	SI
EC8	SI	MI	NI	MI	WI	WI	SI	NI	NI	SI
EC9	NI	SI	MI	WI	SI	NI	SI	NI	NI	SI
EC10	MI	WI	MI	SI	MI	SI	MI	MI	WI	NI

. Under the assumption of experts’ equally weights, the aggregated SF direct influence matrix is established according to Equation (14) and presented in

Table 6. Aggregated spherical fuzzy direct influence matrix.

Criteria	EC1	EC2	EC3	EC4	EC5
EC1	(0.00, 0.30, 0.20)	(0.73, 0.19, 0.49)	(0.62, 0.22, 0.48)	(0.65, 0.21, 0.47)	(0.59, 0.22, 0.44)
EC2	(0.66, 0.21, 0.49)	(0.00, 0.30, 0.20)	(0.52, 0.23, 0.39)	(0.59, 0.22, 0.44)	(0.61, 0.22, 0.48)
EC3	(0.54, 0.24, 0.44)	(0.70, 0.19, 0.48)	(0.00, 0.30, 0.20)	(0.57, 0.23, 0.44)	(0.67, 0.21, 0.49)
EC4	(0.38, 0.25, 0.27)	(0.49, 0.24, 0.38)	(0.36, 0.26, 0.27)	(0.00, 0.30, 0.20)	(0.52, 0.23, 0.39)
EC5	(0.66, 0.21, 0.49)	(0.69, 0.20, 0.49)	(0.57, 0.23, 0.44)	(0.64, 0.21, 0.47)	(0.00, 0.30, 0.20)
EC6	(0.30, 0.27, 0.25)	(0.65, 0.20, 0.47)	(0.57, 0.22, 0.44)	(0.68, 0.20, 0.49)	(0.62, 0.21, 0.44)
EC7	(0.72, 0.19, 0.49)	(0.65, 0.20, 0.47)	(0.69, 0.20, 0.49)	(0.63, 0.22, 0.47)	(0.46, 0.25, 0.38)
EC8	(0.77, 0.17, 0.48)	(0.57, 0.22, 0.44)	(0.64, 0.21, 0.47)	(0.70, 0.19, 0.48)	(0.71, 0.20, 0.50)
EC9	(0.59, 0.22, 0.44)	(0.70, 0.20, 0.50)	(0.59, 0.21, 0.40)	(0.55, 0.23, 0.44)	(0.58, 0.22, 0.44)
EC10	(0.64, 0.21, 0.47)	(0.56, 0.22, 0.40)	(0.72, 0.19, 0.49)	(0.53, 0.23, 0.39)	(0.59, 0.22, 0.44)
Criteria	EC6	EC7	EC8	EC9	EC10
EC1	(0.70, 0.19, 0.48)	(0.65, 0.2, 0.44)	(0.61, 0.21, 0.44)	(0.63, 0.21, 0.44)	(0.49, 0.24, 0.38)
EC2	(0.65, 0.21, 0.47)	(0.57, 0.22, 0.44)	(0.46, 0.25, 0.38)	(0.69, 0.20, 0.49)	(0.69, 0.20, 0.48)
EC3	(0.60, 0.21, 0.44)	(0.60, 0.21, 0.44)	(0.45, 0.25, 0.38)	(0.46, 0.25, 0.38)	(0.45, 0.25, 0.38)
EC4	(0.35, 0.26, 0.27)	(0.38, 0.25, 0.27)	(0.38, 0.26, 0.28)	(0.27, 0.27, 0.23)	(0.44, 0.24, 0.30)
EC5	(0.48, 0.23, 0.31)	(0.40, 0.25, 0.29)	(0.61, 0.21, 0.44)	(0.57, 0.22, 0.44)	(0.52, 0.23, 0.39)
EC6	(0.00, 0.30, 0.20)	(0.65, 0.22, 0.50)	(0.64, 0.22, 0.50)	(0.59, 0.23, 0.48)	(0.53, 0.23, 0.39)
EC7	(0.63, 0.22, 0.47)	(0.00, 0.30, 0.20)	(0.46, 0.25, 0.38)	(0.60, 0.22, 0.44)	(0.69, 0.20, 0.48)
EC8	(0.67, 0.20, 0.49)	(0.78, 0.18, 0.49)	(0.00, 0.30, 0.20)	(0.69, 0.20, 0.48)	(0.77, 0.17, 0.48)
EC9	(0.36, 0.26, 0.27)	(0.68, 0.20, 0.49)	(0.64, 0.21, 0.47)	(0.00, 0.30, 0.20)	(0.65, 0.20, 0.47)
EC10	(0.61, 0.21, 0.44)	(0.62, 0.21, 0.44)	(0.61, 0.22, 0.48)	(0.48, 0.23, 0.31)	(0.00, 0.30, 0.20)

. As shown in

Table 7. Spherical fuzzy total influence matrix.

Criteria	EC1	EC2	EC3	EC4	EC5
EC1	(0.45, 0.79, 0.87)	(0.59, 0.71, 0.98)	(0.54, 0.76, 0.93)	(0.56, 0.74, 0.98)	(0.54, 0.75, 0.95)
EC2	(0.53, 0.77, 0.93)	(0.47, 0.78, 0.93)	(0.51, 0.79, 0.92)	(0.54, 0.77, 0.97)	(0.52, 0.78, 0.96)
EC3	(0.48, 0.81, 0.89)	(0.53, 0.76, 0.95)	(0.40, 0.84, 0.84)	(0.50, 0.80, 0.94)	(0.50, 0.80, 0.93)
EC4	(0.35, 0.89, 0.63)	(0.39, 0.85, 0.68)	(0.35, 0.89, 0.63)	(0.30, 0.89, 0.64)	(0.37, 0.88, 0.67)
EC5	(0.50, 0.79, 0.88)	(0.54, 0.76, 0.92)	(0.49, 0.80, 0.87)	(0.52, 0.78, 0.92)	(0.41, 0.83, 0.84)
EC6	(0.46, 0.81, 0.86)	(0.54, 0.76, 0.96)	(0.50, 0.80, 0.91)	(0.53, 0.77, 0.96)	(0.51, 0.79, 0.93)
EC7	(0.54, 0.76, 0.93)	(0.57, 0.73, 0.98)	(0.53, 0.76, 0.94)	(0.55, 0.76, 0.98)	(0.51, 0.78, 0.94)
EC8	(0.60, 0.69, 0.98)	(0.62, 0.69, 0.99)	(0.59, 0.71, 0.98)	(0.62, 0.69, 0.99)	(0.60, 0.70, 0.99)
EC9	(0.51, 0.78, 0.90)	(0.56, 0.74, 0.96)	(0.51, 0.78, 0.89)	(0.53, 0.77, 0.95)	(0.52, 0.78, 0.93)
EC10	(0.52, 0.77, 0.90)	(0.54, 0.75, 0.93)	(0.53, 0.77, 0.90)	(0.52, 0.77, 0.93)	(0.52, 0.78, 0.92)
Criteria	EC6	EC7	EC8	EC9	EC10
EC1	(0.53, 0.75, 0.89)	(0.54, 0.74, 0.91)	(0.50, 0.78, 0.90)	(0.52, 0.77, 0.89)	(0.52, 0.76, 0.89)
EC2	(0.51, 0.78, 0.89)	(0.52, 0.77, 0.91)	(0.47, 0.82, 0.89)	(0.51, 0.79, 0.90)	(0.53, 0.77, 0.91)
EC3	(0.47, 0.81, 0.85)	(0.49, 0.08, 0.88)	(0.44, 0.85, 0.86)	(0.45, 0.84, 0.85)	(0.46, 0.82, 0.86)
EC4	(0.33, 0.90, 0.60)	(0.35, 0.88, 0.62)	(0.33, 0.93, 0.61)	(0.32, 0.91, 0.60)	(0.35, 0.88, 0.62)
EC5	(0.46, 0.81, 0.80)	(0.47, 0.80, 0.82)	(0.47, 0.83, 0.85)	(0.47, 0.81, 0.84)	(0.48, 0.80, 0.84)
EC6	(0.40, 0.84, 0.81)	(0.51, 0.79, 0.90)	(0.47, 0.83, 0.89)	(0.48, 0.82, 0.88)	(0.49, 0.80, 0.88)
EC7	(0.51, 0.78, 0.89)	(0.44, 0.80, 0.86)	(0.47, 0.81, 0.89)	(0.50, 0.79, 0.90)	(0.53, 0.76, 0.92)
EC8	(0.57, 0.71, 0.94)	(0.61, 0.69, 0.97)	(0.46, 0.77, 0.90)	(0.57, 0.72, 0.95)	(0.60, 0.69, 0.96)
EC9	(0.46, 0.81, 0.83)	(0.53, 0.77, 0.90)	(0.49, 0.81, 0.88)	(0.41, 0.83, 0.82)	(0.52, 0.77, 0.89)
EC10	(0.50, 0.79, 0.85)	(0.52, 0.77, 0.88)	(0.48, 0.81, 0.88)	(0.48, 0.80, 0.84)	(0.42, 0.81, 0.82)

, the SF total influence matrix is established by Steps 5 and 6, which were mentioned in Section 3.3.

Table A4. Spherical fuzzy DEMATEL results.

Criteria	$\tilde{\mathit{R}}$	R	$\tilde{\mathit{C}}$	C	Prominence	Relation	Weight
EC1	(0.981, 0.060, 0.193)	0.639	(0.972, 0.090, 0.236)	0.562	1.201	0.077	0.109
EC2	(0.975, 0.086, 0.223)	0.584	(0.984, 0.058, 0.178)	0.664	1.248	−0.080	0.114
EC3	(0.960, 0.126, 0.281)	0.484	(0.972, 0.093, 0.237)	0.561	1.045	−0.077	0.095
EC4	(0.847, 0.311, 0.530)	0.148	(0.980, 0.074, 0.200)	0.624	0.773	−0.476	0.070
EC5	(0.964, 0.106, 0.264)	0.516	(0.974, 0.090, 0.227)	0.577	1.092	−0.061	0.099
EC6	(0.968, 0.107, 0.252)	0.534	(0.963, 0.104, 0.270)	0.508	1.042	0.026	0.095
EC7	(0.977, 0.076, 0.212)	0.605	(0.973, 0.080, 0.232)	0.571	1.176	0.034	0.107
EC8	(0.993, 0.031, 0.122)	0.767	(0.953, 0.145, 0.303)	0.447	1.214	0.319	0.110
EC9	(0.974, 0.087, 0.228)	0.576	(0.961, 0.116, 0.277)	0.493	1.069	0.082	0.097
EC10	(0.973, 0.083, 0.229)	0.576	(0.970, 0.086, 0.242)	0.555	1.131	0.021	0.103

and Figure 6 illustrate the results of Steps 7, 8, and 9 in the SF DEMATEL–EDAS procedure mentioned above. From Figure 6, it can be seen that experts are most concerned with the costs (11.34%) and potential tourism impacts (11.04%) of WWSs. The costs such as installation, operation, maintenance, and local labor are significantly dependent on the location of the WWS. In addition, the potential effects of WWS on the tourism industry are of great concern to experts because it contributes more than six percent to Vietnam’s economy [60]. The social acceptability (10.29%), proximity to industrial area (10.70%), and vessel density (10.93%) are approximately equally weighted groups of criteria. The next lower weighted group includes potential fisheries impact (9.73%), proximity to seaports (9.48%), vessel density (9.51%), and military activities (9.51%). Although the western Pacific region has many sovereignty issues, experts consider geopolitical factor (7.03%) with the lowest weight to assess the sustainability of WWSs.

4.3.2. Sustainability Ranking

After determining the weights of the evaluation criteria, the next calculations are to evaluate and rank the locations according to the criteria. First, individual linguistic assessments were provided by each expert as illustrated in Table A3. In the expert survey, the higher linguistic terms, the better the potential of locations for the criteria. In other words, the evaluation criteria are considered as benefit criteria. Then, the individual spherical fuzzy decision matrices are formed by the SFN transformation according to Table 3. By using SWAM, individual spherical fuzzy decision matrices are synthesized to form a spherical fuzzy decision matrix as shown in

Table A6. Spherical fuzzy decision matrix.

Location	EC1	EC2	EC3	EC4	EC5
WWS-1	(0.73, 0.28, 0.31)	(0.66, 0.37, 0.29)	(0.70, 0.33, 0.33)	(0.62, 0.41, 0.33)	(0.66, 0.35, 0.31)
WWS-2	(0.58, 0.46, 0.30)	(0.56, 0.46, 0.36)	(0.40, 0.64, 0.31)	(0.57, 0.47, 0.35)	(0.57, 0.48, 0.32)
WWS-3	(0.66, 0.37, 0.29)	(0.68, 0.33, 0.31)	(0.50, 0.56, 0.34)	(0.74, 0.27, 0.30)	(0.66, 0.38, 0.27)
WWS-4	(0.61, 0.42, 0.30)	(0.69, 0.33, 0.25)	(0.61, 0.44, 0.25)	(0.68, 0.35, 0.27)	(0.56, 0.49, 0.31)
WWS-5	(0.63, 0.42, 0.27)	(0.62, 0.41, 0.31)	(0.67, 0.37, 0.27)	(0.72, 0.29, 0.28)	(0.60, 0.45, 0.26)
WWS-6	(0.57, 0.46, 0.31)	(0.63, 0.39, 0.31)	(0.70, 0.33, 0.29)	(0.70, 0.35, 0.24)	(0.68, 0.35, 0.28)
WWS-7	(0.79, 0.22, 0.24)	(0.52, 0.53, 0.33)	(0.66, 0.37, 0.28)	(0.66, 0.36, 0.30)	(0.62, 0.40, 0.34)
WWS-8	(0.63, 0.40, 0.31)	(0.61, 0.43, 0.31)	(0.57, 0.48, 0.29)	(0.68, 0.36, 0.26)	(0.55, 0.51, 0.30)
WWS-9	(0.54, 0.49, 0.37)	(0.67, 0.37, 0.24)	(0.64, 0.39, 0.31)	(0.65, 0.39, 0.27)	(0.65, 0.38, 0.31)
WWS-10	(0.51, 0.53, 0.31)	(0.49, 0.54, 0.34)	(0.59, 0.44, 0.36)	(0.49, 0.56, 0.31)	(0.71, 0.33, 0.24)
WWS-11	(0.77, 0.25, 0.21)	(0.55, 0.50, 0.31)	(0.64, 0.39, 0.30)	(0.65, 0.38, 0.29)	(0.64, 0.40, 0.28)
WWS-12	(0.67, 0.35, 0.32)	(0.62, 0.41, 0.32)	(0.64, 0.39, 0.28)	(0.70, 0.32, 0.24)	(0.69, 0.35, 0.23)
WWS-13	(0.70, 0.32, 0.31)	(0.71, 0.33, 0.20)	(0.64, 0.38, 0.29)	(0.67, 0.37, 0.26)	(0.48, 0.53, 0.40)
WWS-14	(0.66, 0.36, 0.29)	(0.70, 0.32, 0.28)	(0.60, 0.44, 0.28)	(0.63, 0.40, 0.28)	(0.61, 0.42, 0.35)
WWS-15	(0.76, 0.26, 0.20)	(0.51, 0.53, 0.29)	(0.68, 0.35, 0.28)	(0.72, 0.31, 0.24)	(0.57, 0.47, 0.35)
WWS-16	(0.69, 0.33, 0.28)	(0.59, 0.44, 0.39)	(0.69, 0.34, 0.28)	(0.73, 0.30, 0.22)	(0.58, 0.45, 0.34)
WWS-17	(0.60, 0.44, 0.30)	(0.60, 0.44, 0.32)	(0.66, 0.40, 0.22)	(0.60, 0.45, 0.28)	(0.46, 0.57, 0.37)
WWS-18	(0.55, 0.47, 0.37)	(0.56, 0.49, 0.28)	(0.68, 0.35, 0.31)	(0.67, 0.36, 0.30)	(0.79, 0.22, 0.20)
WWS-19	(0.55, 0.48, 0.34)	(0.58, 0.46, 0.31)	(0.42, 0.60, 0.34)	(0.78, 0.23, 0.21)	(0.58, 0.47, 0.28)
WWS-20	(0.67, 0.35, 0.31)	(0.63, 0.39, 0.35)	(0.74, 0.29, 0.20)	(0.63, 0.4, 0.28)	(0.66, 0.38, 0.28)
Location	EC6	EC7	EC8	EC9	EC10
WWS-1	(0.64, 0.38, 0.30)	(0.65, 0.38, 0.31)	(0.51, 0.54, 0.32)	(0.53, 0.48, 0.39)	(0.75, 0.27, 0.20)
WWS-2	(0.67, 0.34, 0.35)	(0.69, 0.33, 0.28)	(0.64, 0.39, 0.28)	(0.64, 0.39, 0.32)	(0.70, 0.35, 0.20)
WWS-3	(0.59, 0.46, 0.30)	(0.62, 0.43, 0.30)	(0.63, 0.39, 0.32)	(0.60, 0.45, 0.26)	(0.53, 0.53, 0.29)
WWS-4	(0.50, 0.56, 0.29)	(0.57, 0.45, 0.36)	(0.63, 0.40, 0.30)	(0.52, 0.51, 0.38)	(0.59, 0.45, 0.33)
WWS-5	(0.66, 0.35, 0.33)	(0.62, 0.44, 0.22)	(0.49, 0.55, 0.33)	(0.51, 0.53, 0.32)	(0.65, 0.39, 0.29)
WWS-6	(0.68, 0.35, 0.32)	(0.47, 0.55, 0.37)	(0.60, 0.43, 0.34)	(0.57, 0.47, 0.28)	(0.57, 0.46, 0.35)
WWS-7	(0.60, 0.45, 0.27)	(0.59, 0.45, 0.32)	(0.79, 0.22, 0.18)	(0.66, 0.36, 0.32)	(0.51, 0.50, 0.36)
WWS-8	(0.61, 0.44, 0.25)	(0.64, 0.40, 0.28)	(0.52, 0.52, 0.30)	(0.67, 0.36, 0.31)	(0.58, 0.47, 0.26)
WWS-9	(0.74, 0.28, 0.24)	(0.62, 0.41, 0.29)	(0.57, 0.46, 0.34)	(0.65, 0.38, 0.27)	(0.72, 0.31, 0.23)
WWS-10	(0.56, 0.46, 0.38)	(0.52, 0.50, 0.37)	(0.6, 0.43, 0.32)	(0.63, 0.40, 0.29)	(0.58, 0.47, 0.31)
WWS-11	(0.68, 0.35, 0.26)	(0.71, 0.32, 0.27)	(0.63, 0.40, 0.30)	(0.70, 0.33, 0.26)	(0.68, 0.35, 0.25)
WWS-12	(0.57, 0.49, 0.27)	(0.68, 0.34, 0.24)	(0.49, 0.54, 0.37)	(0.57, 0.48, 0.28)	(0.27, 0.76, 0.28)
WWS-13	(0.67, 0.36, 0.28)	(0.71, 0.33, 0.24)	(0.70, 0.33, 0.26)	(0.58, 0.47, 0.32)	(0.64, 0.39, 0.33)
WWS-14	(0.59, 0.44, 0.39)	(0.69, 0.34, 0.24)	(0.55, 0.48, 0.36)	(0.76, 0.27, 0.23)	(0.53, 0.49, 0.36)
WWS-15	(0.59, 0.44, 0.30)	(0.72, 0.31, 0.24)	(0.52, 0.51, 0.35)	(0.65, 0.38, 0.25)	(0.55, 0.49, 0.35)
WWS-16	(0.58, 0.44, 0.31)	(0.47, 0.56, 0.36)	(0.51, 0.52, 0.34)	(0.62, 0.41, 0.34)	(0.52, 0.52, 0.35)
WWS-17	(0.70, 0.35, 0.21)	(0.54, 0.47, 0.41)	(0.53, 0.51, 0.35)	(0.53, 0.52, 0.30)	(0.63, 0.39, 0.34)
WWS-18	(0.57, 0.46, 0.33)	(0.59, 0.45, 0.30)	(0.65, 0.42, 0.23)	(0.57, 0.46, 0.36)	(0.64, 0.39, 0.30)
WWS-19	(0.61, 0.42, 0.30)	(0.47, 0.60, 0.28)	(0.61, 0.42, 0.30)	(0.60, 0.44, 0.32)	(0.55, 0.48, 0.32)
WWS-20	(0.57, 0.47, 0.32)	(0.64, 0.39, 0.28)	(0.61, 0.43, 0.34)	(0.49, 0.55, 0.34)	(0.53, 0.53, 0.28)

. Based on the spherical fuzzy decision matrix, the average spherical fuzzy solution was determined according to Equation (34) and as shown in

Table A7. Spherical fuzzy average solution.

Criteria	EC1	EC2	EC3	EC4	EC5
Average solution	(0.66, 0.37, 0.30)	(0.62, 0.42, 0.31)	(0.63, 0.41, 0.29)	(0.67, 0.36, 0.28)	(0.63, 0.41, 0.30)
Criteria	EC6	EC7	EC8	EC9	EC10
Average solution	(0.62, 0.41, 0.31)	(0.62, 0.42, 0.30)	(0.60, 0.44, 0.31)	(0.61, 0.43, 0.31)	(0.60, 0.44, 0.30)

. The defuzzification process for the spherical fuzzy decision matrix and the spherical fuzzy averaging solution was performed and is illustrated as shown in

Table A8. Defuzzied decision matrix and average solution.

Location	EC1	EC2	EC3	EC4	EC5	EC6	EC7	EC8	EC9	EC10
WWS-1	0.182	0.140	0.135	0.093	0.128	0.126	0.120	0.083	0.028	0.315
WWS-2	0.106	0.052	0.122	0.062	0.090	0.101	0.171	0.142	0.103	0.267
WWS-3	0.145	0.137	0.076	0.192	0.165	0.107	0.119	0.108	0.153	0.114
WWS-4	0.110	0.197	0.160	0.178	0.092	0.115	0.055	0.115	0.037	0.082
WWS-5	0.149	0.106	0.167	0.195	0.147	0.112	0.210	0.071	0.081	0.145
WWS-6	0.089	0.109	0.162	0.221	0.165	0.125	0.044	0.080	0.117	0.058
WWS-7	0.304	0.075	0.152	0.131	0.083	0.135	0.091	0.372	0.117	0.044
WWS-8	0.111	0.103	0.114	0.191	0.104	0.165	0.145	0.094	0.130	0.150
WWS-9	0.043	0.202	0.115	0.161	0.120	0.249	0.126	0.067	0.161	0.243
WWS-10	0.093	0.059	0.059	0.091	0.223	0.038	0.040	0.094	0.135	0.100
WWS-11	0.306	0.090	0.124	0.135	0.139	0.187	0.196	0.121	0.198	0.191
WWS-12	0.128	0.098	0.137	0.219	0.227	0.142	0.206	0.041	0.129	0.226
WWS-13	0.152	0.271	0.129	0.181	0.023	0.156	0.231	0.196	0.089	0.100
WWS-14	0.141	0.177	0.133	0.138	0.075	0.045	0.210	0.051	0.280	0.045
WWS-15	0.326	0.104	0.164	0.238	0.062	0.102	0.233	0.052	0.180	0.059
WWS-16	0.170	0.042	0.173	0.261	0.067	0.095	0.049	0.063	0.084	0.056
WWS-17	0.109	0.098	0.225	0.131	0.047	0.258	0.021	0.053	0.097	0.084
WWS-18	0.043	0.120	0.136	0.137	0.354	0.074	0.107	0.213	0.057	0.122
WWS-19	0.066	0.102	0.079	0.325	0.124	0.111	0.141	0.113	0.090	0.083
WWS-20	0.130	0.078	0.305	0.140	0.158	0.086	0.139	0.080	0.062	0.127
Average solution	0.135	0.108	0.129	0.164	0.120	0.113	0.118	0.099	0.106	0.110

.

Table A9. Positive distance from average solution.

Location	EC1	EC2	EC3	EC4	EC5	EC6	EC7	EC8	EC9	EC10
WWS-1	0.346	0.301	0.053	0	0.063	0.115	0.022	0	0	1.866
WWS-2	0	0	0	0	0	0	0.449	0.432	0	1.43
WWS-3	0.075	0.277	0	0.169	0.371	0	0.011	0.088	0.449	0.042
WWS-4	0	0.833	0.248	0.083	0	0.02	0	0.159	0	0
WWS-5	0.1	0	0.296	0.191	0.224	0	0.779	0	0	0.319
WWS-6	0	0.013	0.26	0.348	0.368	0.108	0	0	0.101	0
WWS-7	1.251	0	0.182	0	0	0.197	0	2.749	0.107	0
WWS-8	0	0	0	0.166	0	0.464	0.23	0	0.227	0.366
WWS-9	0	0.876	0	0	0	1.208	0.072	0	0.516	1.213
WWS-10	0	0	0	0	0.859	0	0	0	0.279	0
WWS-11	1.265	0	0	0	0.154	0.663	0.664	0.217	0.87	0.742
WWS-12	0	0	0.066	0.334	0.892	0.262	0.748	0	0.219	1.058
WWS-13	0.127	1.522	0.003	0.107	0	0.381	0.964	0.977	0	0
WWS-14	0.046	0.648	0.032	0	0	0	0.778	0	1.648	0
WWS-15	1.413	0	0.278	0.452	0	0	0.979	0	0.699	0
WWS-16	0.256	0	0.342	0.594	0	0	0	0	0	0
WWS-17	0	0	0.752	0	0	1.291	0	0	0	0
WWS-18	0	0.112	0.057	0	1.942	0	0	1.151	0	0.113
WWS-19	0	0	0	0.985	0.035	0	0.199	0.137	0	0
WWS-20	0	0	1.369	0	0.314	0	0.181	0	0	0.159

and

Table A10. Negative distance from average solution.

Location	EC1	EC2	EC3	EC4	EC5	EC6	EC7	EC8	EC9	EC10
WWS-1	0	0	0	0.43	0	0	0	0.16	0.74	0
WWS-2	0.215	0.52	0.048	0.624	0.248	0.106	0	0	0.028	0
WWS-3	0	0	0.405	0	0	0.049	0	0	0	0
WWS-4	0.188	0	0	0	0.237	0	0.535	0	0.647	0.249
WWS-5	0	0.015	0	0	0	0.006	0	0.286	0.235	0
WWS-6	0.342	0	0	0	0	0	0.626	0.192	0	0.47
WWS-7	0	0.305	0	0.203	0.306	0	0.231	0	0	0.604
WWS-8	0.181	0.043	0.117	0	0.136	0	0	0.048	0	0
WWS-9	0.682	0	0.105	0.016	0.006	0	0	0.328	0	0
WWS-10	0.309	0.448	0.538	0.443	0	0.663	0.658	0.055	0	0.088
WWS-11	0	0.168	0.036	0.176	0	0	0	0	0	0
WWS-12	0.053	0.087	0	0	0	0	0	0.583	0	0
WWS-13	0	0	0	0	0.807	0	0	0	0.155	0.092
WWS-14	0	0	0	0.159	0.379	0.605	0	0.487	0	0.588
WWS-15	0	0.035	0	0	0.483	0.09	0	0.473	0	0.46
WWS-16	0	0.614	0	0	0.441	0.16	0.588	0.363	0.203	0.491
WWS-17	0.191	0.089	0	0.2	0.605	0	0.818	0.462	0.087	0.239
WWS-18	0.682	0	0	0.165	0	0.339	0.09	0	0.462	0
WWS-19	0.515	0.049	0.385	0	0	0.017	0	0	0.147	0.24
WWS-20	0.038	0.272	0	0.146	0	0.239	0	0.194	0.413	0

present the positive distances from the average solution and the negative distance from the average solution as Equations (37) and (38). Continuing to perform the calculations according to Step 13 and Step 14 as mentioned in Section 3.3, the results of assessing the sustainability of the locations are presented in

Table 8. Spherical fuzzy EDAS results.

Location	${\mathit{s}}_{\mathit{i}}^{+}$	${\mathit{s}}_{\mathit{i}}^{-}$	$\mathit{n}{\mathit{s}}_{\mathit{i}}^{+}$	$\mathit{n}{\mathit{s}}_{\mathit{i}}^{-}$	$\mathit{a}{\mathit{s}}_{\mathit{i}}$	Location	${\mathit{s}}_{\mathit{i}}^{+}$	${\mathit{s}}_{\mathit{i}}^{-}$	$\mathit{n}{\mathit{s}}_{\mathit{i}}^{+}$	$\mathit{n}{\mathit{s}}_{\mathit{i}}^{-}$	$\mathit{a}{\mathit{s}}_{\mathit{i}}$
WWS-1	0.288	0.120	0.593	0.62	0.606	WWS-11	0.472	0.035	0.97	0.889	0.930
WWS-2	0.243	0.168	0.499	0.466	0.482	WWS-12	0.353	0.080	0.726	0.746	0.736
WWS-3	0.147	0.043	0.303	0.863	0.583	WWS-13	0.442	0.105	0.907	0.668	0.788
WWS-4	0.143	0.190	0.295	0.398	0.346	WWS-14	0.325	0.220	0.668	0.301	0.485
WWS-5	0.191	0.057	0.392	0.82	0.606	WWS-15	0.385	0.160	0.792	0.492	0.642
WWS-6	0.107	0.174	0.221	0.449	0.335	WWS-16	0.102	0.302	0.21	0.042	0.126
WWS-7	0.487	0.166	1	0.473	0.736	WWS-17	0.194	0.277	0.399	0.122	0.260
WWS-8	0.140	0.055	0.288	0.827	0.557	WWS-18	0.350	0.173	0.719	0.452	0.585
WWS-9	0.397	0.122	0.815	0.612	0.713	WWS-19	0.109	0.139	0.224	0.559	0.392
WWS-10	0.112	0.315	0.231	0	0.116	WWS-20	0.197	0.130	0.405	0.589	0.497

. According to the ranking results, WWS-11, WWS-13, and WWS-7 ranked first three in terms of sustainability. In contrast, at the bottom of the sustainability rankings are WWS-17, WWS-16, and WWS-10, respectively.

4.4. Dual-Side Analysis

To evaluate the potential of locations in terms of both efficiency and sustainability, the quantitative results of the B-DEA model and the qualitative results of the SF DEMATEL–EDAS approach were compiled as shown in

Table A11. The efficiency–sustainability rank of the WWS locations.

Location	Sustainability Aspect	$\mathbf{Efficiency} \mathbf{Aspect} \mathbf{with} \mathbf{the} \mathbf{Given} \mathbf{Value} \mathbf{of} \mathsf{\Theta }$
		0.55	0.60	0.65	0.70	0.75	0.80	0.85	0.90	0.95	1.00
WWS-1	8	14	14	15	15	15	15	15	15	15	15
WWS-2	14	11	12	12	12	12	12	12	12	12	11
WWS-3	10	12	13	13	13	13	13	13	13	13	12
WWS-4	16	10	11	11	11	11	11	11	11	11	13
WWS-5	7	15	15	14	14	14	14	14	14	14	14
WWS-6	17	13	10	10	10	10	10	10	10	10	10
WWS-7	3	3	3	3	3	3	3	3	3	2	2
WWS-8	11	7	7	7	7	7	7	7	7	6	3
WWS-9	5	4	4	4	4	4	4	4	4	3	4
WWS-10	20	5	5	5	5	5	5	5	5	4	5
WWS-11	1	6	6	6	6	6	6	6	6	5	6
WWS-12	4	1	1	1	1	1	1	1	1	1	1
WWS-13	2	2	2	2	2	2	2	2	2	7	9
WWS-14	13	8	8	8	8	8	8	8	8	8	7
WWS-15	6	9	9	9	9	9	9	9	9	9	8
WWS-16	19	19	19	19	19	19	19	19	19	19	19
WWS-17	18	18	18	18	18	18	17	17	17	16	16
WWS-18	9	17	17	17	17	16	16	16	16	17	17
WWS-19	15	16	16	16	16	17	18	18	18	18	18
WWS-20	12	20	20	20	20	20	20	20	20	20	20

. Considering the two factors of sustainability and efficiency, Figure 7 below illustrates the positioning maps for the potential of locations under different decision makers’ psychological behavior. From Figure 7, the positioning maps are divided into four quadrants. The lower left quadrant implies locations that rank high in both sustainability and efficiency. The lower right quadrant includes locations with high sustainability but low efficiency. In contrast, locations in the upper left quadrant have high efficiency but low sustainability. Finally, the upper right quadrant includes locations that rank low in both sustainability and efficiency. As the psychological behavior of decision makers changes in favor of gains versus losses, locations’ positions of on the positioning map change. However, recognized position changes do not extend beyond its original quadrant. The exception is the position change of WWS-4 and WWS-6. As the importance degree towards gains increases, WWS-4 moves into quadrant IV. Meanwhile, WWS-6 tends to move towards the origin of quadrant III. Based on the positioning maps, this study classifies the potential of locations into four groups of recommended, sustainable, efficient, and considered as shown in

Table 9. Location classification for WWS.

Group	Locations
Recommended locations	WWS-7, WWS-9, WWS-11, WWS-12, WWS-13, WWS-15
Sustainable locations	WWS-1, WWS-3, WWS-5, WWS-18
Efficient locations	WWS-6, WWS-8, WWS-10, WWS-14
Considered locations	WWS-2, WWS-4, WWS-16, WWS-17, WWS-19

.

4.5. Managerial Implications

According to statistics, the current offshore wind energy projects of Vietnam are mainly concentrated in the Southeast region as illustrated in Figure 8 [61]. As illustrated in Figure 9, the recommended locations for the installation of WWSs are distributed from Quang Tri province in the central region to Soc Trang province in the Mekong Delta. Meanwhile, the marine coordinates in the north of Vietnam mainly belong to the group of locations with high sustainability. Thus, the suggestions on both efficient and sustainable locations in this study are useful references for managers and investors to design and develop integrated wind and wave energy projects in the future.

The proposed dual-site approach allows for independent evaluation of both efficiency and sustainability of locations. Moreover, this approach both ensures the objectivity of the data and synthesizes subjective expert opinions in the evaluation process. This novel behavioral approach could be applied to decision-making problems in other areas that are influenced by human nature.

5. Conclusions

5.1. Contributions and Findings

Harnessing the potential of energy from the ocean in terms of both wind and waves through integrated offshore renewable energy stations is a promising solution for the sustainable development of many countries. With the continuous evolution of integrated energy conversion technology, the necessity of choosing both sustainable and efficient locations for WWSs is great. Vietnam’s offshore wind energy development roadmap has been studied in recent years. However, wind and wave integrated stations have not been sufficiently analyzed and evaluated. Therefore, this study proposed a novel dual-side behavioral spherical fuzzy multi-criteria decision-making approach to accomplish that purpose.

As for the practical contribution, a comprehensive assessment of the sustainability and efficiency of locations along the coast of Vietnam was provided. Accordingly, locations are classified into recommended, sustainable, efficient, and considered groups. Renewable energy investors and developers can refer to this classification in their future decisions. As for the theoretical contribution, this study proposed a dual-side approach, which has novelties on each side. To perform the quantitative evaluation, a BDEA model, which is extended according to prospect theory, was used to evaluate the efficiency of alternatives under the consideration of the decision makers’ psychological behavior. In parallel, an MCDM method combining the SF DEMATEL and SF EDAS methods was used for the multi-criteria qualitative evaluation. Then, the qualitative and quantitative evaluation results were aggregated to provide the overall evaluation results.

The practical findings of this study indicate that the recommended locations, whose efficiency and sustainability are high, for the installation of WWSs are distributed from Quang Tri province in the central region to Soc Trang province in the Mekong Delta. Meanwhile, the marine coordinates in the north of Vietnam mainly belong to the group of locations with high sustainability.

5.2. Limitations and Futher Research Recommendations

The main limitation of this study is that it has not fully explored other behavioral parameters, such as loss aversion $\left(\mu \right)$ and attitudes towards gains $\left(\alpha \right)$ and losses $\left(\beta \right)$ in the B-DEA model. The lack of more complex sensitivity analyzes of the weights of the evaluation criteria are another limitation of this study. Therefore, further studies are suggested to perform complex sensitivity analyzes for behavioral parameters. Moreover, further assessments of wave climates could enhance the ranking results of this study.