Sustainable Agritourism Location Investigation in Vietnam by a Spherical Fuzzy Extension of Integrated Decision-Making Approach

Abstract

For tourists in the post-COVID era, it is a popular choice to experience nature and idyllic rural life in fields, gardens, and farms instead of crowding into high-level services in modern tourist destinations. This trend has created a focus on sustainable development within tourism. Agritourism is an alternative tourism experience that demonstrates high potential for the tourism industry while positively impacting agricultural production in rural areas. A suitable location selection process is essential to effectively developing agritourism and sustainability. However, the current literature on this issue is still limited. Therefore, this study introduces a combined decision-making model for optimal agritourism destination identification in the context of sustainable development. This research highlights the use of the spherical fuzzy set (SFSs), in which the spherical fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) determines the criteria’s importance in combination with their causal relationship, and the spherical fuzzy Evaluation based on Distance from Average Solution (EDAS) finds the alternative destinations’ priority. The model’s efficiency is illustrated through an empirical study of Vietnam and by a sensitivity analysis. The resulting research found that decision-makers should consider the factors of local living conditions (ASC10), and local agriculture products (ASC3) when investigating agritourism locations. Consequently, the optimal destination for sustainable agritourism development was found to be Lam Dong (AD9), which can efficiently promote tourism activities while increasing the value of agriculture in the countryside. These findings can assist decision-makers in selecting tourism sites in other regions and other tourism development projects.

1. Introduction

In recent years, green tourism has received greater attention from tourists because they prefer learning, creating, and participating in environmental activities to engaging in traditional tourism [1]. Increasingly, the development of green tourism is diversified to attract investment and creativity from tourism developers. Agritourism is a typical alternative to traditional tourism, involving environmentally friendly activities and demonstrating great potential for sustainable development in the future [2,3]. With many unique elements, agritourism creates an open tourist space, encouraging harmony with nature, and a return to an idyllic life, where visitors can plant, care for, and harvest agricultural products by themselves [4]. In the context of the COVID-19 epidemic, this model also meets the present needs of tourists such as limiting contact between groups of people and improving both mental and physical health through experiential activities. As the Fortune Business Insights report, the agritourism market was worth USD 69.24 billion in 2019. This value is forecast to reach USD 117.37 billion in 2027, with a 7.42% compound annual growth rate (CAGR) from 2020 to 2027 [5]. It is clear that this type of tourism has become a globally sustainable and economically green growth trend based on its comprehensive development in both size and quality. Specifically, the planning of agricultural land in developed countries was initially conducted for recreational purposes, to efficiently use natural resources based on the conditions of geography, the economy, and society [6]. One example is the US, where more than USD 800 million is spent organizing many events related to agritourism every year. In Austria, agricultural development associated with tourism and traditional cuisine is professionally organized, despite farmers making up only 3% of the population. In France, the policy of countryside development has encouraged the promotion of rural tourism. As a result, this program has now become a popular tourism phenomenon in rural areas, which can help to quickly increase a region’s value [7,8]. Developing countries where the agricultural economy is predominant are now enacting plans to diversify the cultivation of land and exploit the inherent potential of agricultural products and regional culture. In Japan, the combination of agricultural products and rural landscapes is defined in the local economic development strategy [9]. The Chinese government has built more than 15 unique agritourism routes with 251 agro-ecological gardens, contributing to the effective improvement in agricultural production [8]. Thailand is applying agritourism in local communities by expanding the tourism industry and raising the incomes of local people. The advantage of this activity is that it not only helps agricultural sustainable development but also decreases pressure on crowded tourist destinations in the area [4].

In the case of Vietnam, tourism associated with new rural reconstruction has become an inevitable trend, in which agriculture is a key economic sector, accounting for 72.84% of the country’s economic structure (General Statistics Office of Vietnam, Vietnam, 2022). According to the Vietnam National Administration of Tourism, rural tourism plays an important role in overall tourism development by connecting urban areas and tourist centers, expanding the spatial scope, and extending the guests’ stay. This is an appropriate direction for the development of Vietnam’s tourism industry, especially in the wake of the COVID-19 pandemic. The countryside of Vietnam possesses rich natural and human resources, such as rice fields, fruit gardens, community identities, and traditional craft villages; these are important factors in the establishment of tourist destinations. Furthermore, these destinations create value for local products, contributing to farm income stabilization and promoting local natural values. Hence, many agricultural products, such as food, beverages, handicrafts, fruits, and confectionery, have been displayed in restaurant chains, hotels, and resorts. Many destinations have exploited different agritourism models based on specific regional features such as the Moc Chau dairy farm, the Sa Pa terraced fields, the Tra Que vegetable village, the Dong Trieu ceramic craft village, the Da Lat hydroponic vegetable and high-tech flower gardens, the Ninh Thuan vineyards and sheep farms, the Dong Nai fruit garden, and the Cai Rang floating market.

However, Vietnam’s agritourism cannot fulfill the requirements of sustainable development, leading to many challenges. Firstly, the conflict-of-interest issue in choosing local agricultural and tourism development models must be considered. In particular, the link between the agriculture and tourism sectors is an essential factor in ensuring consistency in the implementation process. This not only directly affects the direction and policies but also relates to the outcome and expectations of the local agritourism industry. Moreover, the benefit to farmers must be considered to help them improve their income and the quality of their products [10]. Next, the planning and preservation of traditional agricultural villages associated with tourism is a complicated issue, which requires a long-term vision. According to each locality’s strengths, close attention should be paid to the diversification of agricultural land due to links with the development of the commodity economy and agricultural communities such as farm, households, agricultural centers, and cooperatives [11]. Another challenge is building the assessment criteria for agritourism products. These criteria need to be established to evaluate and support agritourism models based on local characteristics. With the increasing requirements from travelers, high-quality services are notably focused. Moreover, this standardization also assists in managing travelling destinations and the continuous improvement in leisure activities [12]. Training funds are another difficulty while running this model. Despite their direct participation in production, the farmer’s skills in tourism services, including welcoming visitors, communicating, and promoting tourist products, are very limited. In addition, when the operation scale is expanded, the demand for labor resources is very large. Thus, it is necessary train human resources in the chain to provide related information, such as information on the production process, product characteristics, customs and traditions, and culture of the region, to incoming travelers [13]. Finally, tourism promotion and marketing are the main concerns in the development strategy. The variety of destination information is a highlight of this form of tourism, providing convenience and attractiveness to tourists. With the advancement of modern technology, it is extremely important to be innovative and creative in advertising strategies. Thus, an appropriate plan regarding the promotion agritourism is identified, looking at the combination of value locality and market demand [14].

Despite facing challenges in the development process, Vietnam’s agritourism has created many opportunities for innovation, breakthroughs, and sustainability. It encourages the exploitation of tourism with agricultural values in rural areas by investors and tourism developers. The selection of a suitable location is greatly important when deciding whether to invest in a project because it directly affects the business strategy, operational capability, and the surrounding environment [15]. Before deciding, tourist developers need to investigate and evaluate the destination’s characteristics linked to economic, social, and environmental resources [16]. An optimal site would result in high tourism potential and competitive advantages [17]. Furthermore, sustainability is an indispensable factor in the agritourism model, enhancing service quality, allowing for the efficient use of resources, preserving traditional values, and creating a stable income for the local people [18].

The location of tourism development is decided as specified by different assessment criteria. In scientific research, location selection issues are commonly clarified by the multi-criteria decision-making (MCDM) technique. Specifically, this technique is applied in renewable energy construction location selection [19,20], hotel construction selection [21], shopping center choice [17], service apartment location selection [15], logistics distribution center location decision [16], and warehouse location selection [22]. However, extensive research on choosing agritourism locations focusing on sustainability is still limited. Therefore, the authors propose a hybrid MCDM model to assist decision-makers in finding the most potential destination. The highlight of this study is the use of a spherical fuzzy set to obtain the solution, including two main steps. First, the spherical fuzzy DEMATEL calculates the assessment criteria’s importance and analyzes the causal relationship between them. Next, the spherical fuzzy EDAS method is carried out to rank the alternative destinations. The effectiveness of this model is demonstrated through the case study, and it can be applied to similar subsequent projects.

The research has the following sections: Section 2 conveys the literature review, Section 3 explains the methodology, Section 4 introduces the case study, and Section 5 displays the discussion and conclusions.

2. Literature Review

2.1. Agritourism Location Selection

Agritourism is increasingly attractive to tourists, where they can directly or indirectly learn and experience agricultural activities [18]. It is currently focused on investment, with a diversification strategy for farmers, businesses, and rural governments [23]. The benefits of this tourism are improvements in agricultural production, increases in farmers’ income, support for regional economic development, and the preservation of traditional culture [10]. As a result, an appropriate agritourism location selection is an indispensable step in exploiting the availability of valuable resources and promoting sustainable development. Many scholars have focused on discussing many aspects of this issue, as shown in Table 1. Zarei Morteza [24] presented a solution to encourage the tourism industry, which develops the sustainability of the economy and society in the Qeshm Island area. An model integrating fuzzy ANP and fuzzy TOPSIS methods was used to find a suitable tourist location based on concerns regarding ecological and socio-economic features. Similarly, Wu et al. [25] realized that Vietnam’s agritourism has many potential destinations, but is still limited in terms of policies, scale, and service quality. Through an expert evaluation process, the optimal solution for the agritourism site is shown using fuzzy AHP and TOPSIS techniques. This result assists the decision-makers in defining an appropriate strategic development to effectively exploit resources and maximize tourism potential in this country. In addition, Zhongmei Guan [26] reported that establishing a tourist location is a complicated matter for investors, and tourist destination selection is a significant step in deciding the success’s project. After identifying the evaluation factors using experts, the author applied a geographic information system (GIS) technique and spatial data measurement to solve the problem. Serafeim Polyzos et al. [27] found that urban areas largely attract the tourism industry investment, while rural areas have not been fully exploited, despite their great potential in terms of local natural and cultural resources. Tourism development in rural areas brings significant benefits, helping to improve people’s lives and preserve cultural traditions. Thereby, the author proposed the regression model to analyze the problem and encourage enterprises to invest in the countryside with diversified and high-quality tourism products. Gabrijela Popovic [28] introduced the issues surrounding hotel location decisions through a combination of SWARA and WSPLP methods. A suitable location will help increase profits, and competitiveness and reduce risks in the operating business. It also directly impacts the success of the business model, where decision-makers need to come up with the right strategy and a clear plan. Pin-Ju Juan [29] has argued that determining the location of tourist sites for a multi-function company will greatly affect its overall network. The author proposed assessment criteria to measure the risks when establishing a new tourist destination and the AHP model was used to assist tourism operators in their decision.

Table 1. The recent literature on tourist site selection.

No.	Authors	Year	Model	Region	Factor Focusing
1	Guan, Z.M. et al. [26]	2013	GIS	Global	Economic, Social, and Environment
2	Morteza, Z. et al. [24]	2016	Fuzzy ANP–Fuzzy TOPSIS	Iran	Eco-logical and socio-economic
3	Popovic, G. et al. [28]	2019	SWARA and WSPLP	Serbia	Economic
4	Batista e Silva, F.B. et al. [30]	2020	GIS and hierarchical clustering algorithm	EU	Economic
5	Gelbman, A. [31]	2021	Quantitative analysis	Israel	Geographic and environment
6	García Mestanza, J. et al. [32]	2021	Fuzzy AHP–Fuzzy MAIRCA	Spain	Economic, Social, and Environment
7	Zhang, C. et al. [33]	2021	Thermodynamic feature-based	China	Environment
8	Wu, C.K. & Wang, C.-N. et al. [25]	2022	Fuzzy AHP–Fuzzy TOPSIS	Vietnam	Economic, Social, and Environment
9	Chen, Y.C. et al. [34]	2022	GIS	Taiwan	Geographic
10	Rezvani, M. et al. [35]	2022	GIS-OWA	Iran	Economic, Social, and Environment
11	This study	2022	Spherical fuzzy DEMATEL–Spherical fuzzy EDAS	Vietnam	Economic, Social, and Environment

2.2. Sustainable Agritourism

In addition, the development of agritourism is associated with the economic, cultural, and social characteristics of the locality [36]. Therefore, sustainability should be considered in agritourism, and selecting a suitable location is the priority condition in enterprises’ long-term strategic development [37]. Many articles explained agritourism sustainability based on the triple-bottom-line research framework regarding economic, social, and environmental aspects [38]. Regarding the economic aspect, Tseng et al. [4] found that the main factors of agritourism sustainability in Thailand are commercial performances and the economic context of the countryside. The author suggested that the government should create policies promptly, establish a specific plan for the agritourism sector, and link actors in the local business value chain. Moreover, farmers continuously expand and diversify traditional agricultural activities, increasing their competitive advantage in the market [39,40]. On the other hand, Sonnino [10] recognized that the exploitation of tourism in agricultural production is directly related to daily life in the locality. Therefore, the friendly environment and connecting activities, such as enhancing exchanges and sharing traditional culture combined with the promotion of regional products, are typical ways to shape customers’ choices. The connection between urban and rural areas is formed to create opportunities for farmers’ land keeping, farmland expansion, and agricultural diversification [41]. In addition, Ramona Ciolac [12] suggested that agritourism and the environment are close relations. When natural resources are exploited effectively, they will create unique tourism products. Tourism activities are strongly deployed which promote the potential values and inherent preservation of the rural environment [42,43].

3. Methodology

The decision model of agritourism destination is implemented by integrating the SF-DEMATEL and SF-EDAS techniques with the procedure in Figure 1.

Figure 1. The flowchart of the research methodology.

3.1. Spherical Fuzzy Sets

Fuzzy sets have been introduced, evolved, and applied in recent years to deal with uncertainties in decision-making. Spherical fuzzy sets (SFS), recently defined as fuzzy set extensions developed by Gundogdu et al. [44,45,46], have attracted the attention of researchers. This theory is a combination of Pythagorean fuzzy sets and Neuromorphic sets, in which the uncertain opinion of the decision-maker is individually expressed at the level of membership and non-membership, as denoted by the conditions shown below.

Definition 1.

The SFS ${\tilde{A}}_s$ of the universe of L is described in Equation (1):

$$\tilde{A}=\left\{l,{\mu }_{\tilde{A}}(l),{\upsilon }_{\tilde{A}}(l),{\pi }_{\tilde{A}}(l)|l\in L\right\}$$

(1)

where ${\mu }_{\tilde{A}},{\upsilon }_{\tilde{A}},{\pi }_{\tilde{A}}(l):L\to \left[0,1\right]$ and $0\le {\mu }_{\tilde{A}}^2(l)+{\upsilon }_{\tilde{A}}^2(l)+{\pi }_{\tilde{A}}^2(l)\le 1,\forall l\in L$.

The numbers ${\mu }_{\tilde{A}}(l)$, ${\upsilon }_{\tilde{A}}(l)$, ${\pi }_{\tilde{A}}(l)$ are the level of membership, non-membership, and hesitance of l to $\tilde{A}$.

Definition 2.

The SFS of two values $\tilde{A}=({\mu }_{\tilde{A}},{\upsilon }_{\tilde{A}},{\pi }_{\tilde{A}})$ and $\tilde{B}=({\mu }_{\tilde{B}},{\upsilon }_{\tilde{B}},{\pi }_{\tilde{B}})$ of the universe of $L_1$ and $L_2$ are illustrated based on some calculations, as shown by the following Equations (2)–(5):

Addition

$$\tilde{A}\oplus \tilde{B}=\left\{{({\mu }_{\tilde{A}}^2+{\mu }_{\tilde{B}}^2-{\mu }_{\tilde{A}}^2{\mu }_{\tilde{B}}^2)}^{\frac{1}{2}},{\upsilon }_{\tilde{A}}{\upsilon }_{\tilde{B}},{((1-{\mu }_{\tilde{B}}^2){\pi }_{\tilde{A}}^2+(1-{\mu }_{\tilde{A}}^2){\pi }_{\tilde{B}}^2-{\pi }_{\tilde{A}}^2{\pi }_{\tilde{B}}^2)}^{\frac{1}{2}}\right\}$$

(2)

Multiplication

$$\tilde{A}\otimes \tilde{B}=\left\{{\mu }_{\tilde{A}}{\mu }_{\tilde{B}},{({\upsilon }_{\tilde{A}}^2+{\upsilon }_{\tilde{B}}^2-{\upsilon }_{\tilde{A}}^2{\upsilon }_{\tilde{B}}^2)}^{\frac{1}{2}},{((1-{\upsilon }_{\tilde{B}}^2){\pi }_{\tilde{A}}^2+(1-{\upsilon }_{\tilde{A}}^2){\pi }_{\tilde{B}}^2-{\pi }_{\tilde{A}}^2{\pi }_{\tilde{B}}^2)}^{\frac{1}{2}}\right\}$$

(3)

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

$$\lambda \tilde{A}=\left\{{(1-{(1-{\mu }_{\tilde{A}}^2)}^{\lambda })}^{\frac{1}{2}},{\upsilon }_{\tilde{A}}^{\lambda },{({(1-{\mu }_{\tilde{A}}^2)}^{\lambda }-{(1-{\mu }_{\tilde{A}}^2-{\pi }_{\tilde{A}}^2)}^{\lambda })}^{\frac{1}{2}}\right\}$$

(4)

Power of$\tilde{A}$(λ > 0)

$${\tilde{A}}^{\lambda }=\left\{{\mu }_{\tilde{A}}^{\lambda },{(1-{(1-{\upsilon }_{\tilde{A}}^2)}^{\lambda })}^{\frac{1}{2}},{({(1-{\upsilon }_{\tilde{A}}^2)}^{\lambda }-{(1-{\upsilon }_{\tilde{A}}^2-{\pi }_{\tilde{A}}^2)}^{\lambda })}^{\frac{1}{2}}\right\}$$

(5)

Definition 3.

Spherical weighted arithmetic mean (SWAM) and spherical weighted geometric mean (SWGM) are represented through the weight vector $\omega =({\omega }_1,{\omega }_2,\dots ,{\omega }_n)$, where $0\le {\omega }_i\le 1$ and ${\displaystyle {\sum }_{i=1}^n{\omega }_i}=1$, as shown by the following Equations (6) and (7):

$$\begin{array}{l}S\mathrm{W}A{M}_{\omega }\left({\tilde{A}}_1,{\tilde{A}}_2,\dots ,{\tilde{A}}_n\right)={\omega }_1{\tilde{A}}_1+{\omega }_2{\tilde{A}}_2+\dots +{\omega }_k{\tilde{A}}_k\\ =\left\{{(1-{\displaystyle \prod _{i=1}^k}{\left(1-{\mu }_{{\tilde{A}}_i}^2\right)}^{{\omega }_i})}^{\frac{1}{2}},{\displaystyle \prod _{i=1}^k}{\upsilon }_{{\tilde{A}}_i}^{{\omega }_i},{({\displaystyle \prod _{i=1}^k}{\left(1-{\mu }_{{\tilde{A}}_i}^2\right)}^{{\omega }_i}-{\displaystyle \prod _{i=1}^k}{(1-{\mu }_{{\tilde{A}}_i}^2-{\pi }_{{\tilde{A}}_i}^2)}^{{\omega }_i})}^{\frac{1}{2}}\right\}\end{array}$$

(6)

$$\begin{array}{l}S\mathrm{WG}{M}_{\omega }\left({\tilde{A}}_1,{\tilde{A}}_2,\dots ,{\tilde{A}}_n\right)={\tilde{A}}_1{}^{{\omega }_1}+{\tilde{A}}_2{}^{{\omega }_2}+\dots +{\tilde{A}}_k{}^{{\omega }_k}\\ =\left\{{\displaystyle \prod _{i=1}^k}{\mu }_{{\tilde{A}}_i}^{{\omega }_i},{(1-{\displaystyle \prod _{i=1}^k}{\left(1-{\upsilon }_{{\tilde{A}}_i}^2\right)}^{{\omega }_i})}^{\frac{1}{2}},{({\displaystyle \prod _{i=1}^k}{\left(1-{\upsilon }_{{\tilde{A}}_i}^2\right)}^{{\omega }_i}-{\displaystyle \prod _{i=1}^k}{(1-{\upsilon }_{{\tilde{A}}_i}^2-{\pi }_{{\tilde{A}}_i}^2)}^{{\omega }_i})}^{\frac{1}{2}}\right\}\end{array}$$

(7)

Definition 4.

The SFS of two values $\tilde{A}=({\mu }_{\tilde{A}},{\upsilon }_{\tilde{A}},{\pi }_{\tilde{A}})$ and $\tilde{B}=({\mu }_{\tilde{B}},{\upsilon }_{\tilde{B}},{\pi }_{\tilde{B}})$ of the universe of $L_1$ and $L_2$ under the condition $\lambda$, ${\lambda }_1$, ${\lambda }_2>0$, are described in Equations (8)–(13):

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

(8)

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

(9)

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

(10)

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

(11)

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

(12)

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

(13)

Definition 5.

The value of defuzzification (DeF) of SFS $\tilde{A}=({\mu }_{\tilde{A}},{\upsilon }_{\tilde{A}},{\pi }_{\tilde{A}})$ is demonstrated by the following Equation (14):

$$\mathrm{DeF}(\tilde{A})={({\mu }_{\tilde{A}}-{\pi }_{\tilde{A}})}^2+{({\upsilon }_{\tilde{A}}-{\pi }_{\tilde{A}})}^2$$

(14)

To evaluate the interrelationships of factors in complex systems, the DEMATEL method was initially proposed by Fontela and Gabus. A systematic review of MCDM studies found that the DEMATEL method is increasingly used as weighting criteria. In terms of prioritizing alternatives, distance-based evaluation methods, such as TOPSIS or EDAS, are applied effectively, with high frequency. The details of the proposed method are described in the following sections.

3.2. SF DEMATEL

Decision-Making Trial and Evaluation Laboratory (DEMATEL) is a tool of the MCDM approach, which deals with complex and interdependent issues in various fields such as manufacturing [47,48], supply chain [49,50], technology [51,52], hospitality [53,54], education [55,56], services [57,58], and others [59,60]. As a result, DEMATEL has become a commonly used tool to determine the potential relationships among these factors and select the best one for the evaluation process. However, the preferences of decision-makers are not considered in the traditional DEMATEL method. Therefore, Sait Gul [61] developed the spherical fuzzy DEMATEL (SF-DEMATEL) approach, defined as an extension of DEMATEL, to support experts and increase the priority domain and independence in decision-making. In this research, SF-DEMATEL is utilized to calculate the criteria’s weight and the cause–effect relationships of these criteria, conducting nine steps as follows.

Step 1: Identifying related evaluating criteria

It is assumed that a group discussion has k decision-maker, who contributes to and decides on the project’s investment, and n criteria, which affect the assessment and decision.

Step 2: Creating direct influence matrices based on the expert’s evaluation

The linguistic terms of SF-DEMATEL [61], as shown in Table 2, are developed to illustrate the expert’s judgment on the influence criteria assessment, denoted as the score index (SI) value, using Equation (15).

$$SI=\sqrt{|100\ast \left[{\left(\mu -\pi \right)}^2-{\left(\upsilon -\pi \right)}^2\right]|}$$

(15)

Table 2. SF-DEMATEL linguistics term.

Linguistic Scale	Notation	$\mathit{\mu }$	$\mathit{\upsilon }$	$\mathit{\pi }$	SI
No Influence	NI	0	0.3	0.2	0
Weak Influence	WI	0.35	0.25	0.25	1
Moderate Influence	MI	0.6	0.2	0.35	2
Strong Influence	SI	0.85	0.15	0.45	3

According to the pairwise comparisons from experts, the direct influence matrix form ($D^e$) is constructed in Equation (16).

$$D^e={\left[d_{\mathrm{ij}}^e\right]}_{n\times n}={\left[{\mu }_{\mathrm{ij}}^e,{\upsilon }_{\mathrm{ij}}^e,{\pi }_{\mathrm{ij}}^e\right]}_{n\times n} i, j=1,\dots ,n and e=1,\dots , k$$

(16)

where $D^e$ is the direct influence matrix, $d_{\mathrm{ij}}^e=\left({\mu }_{\mathrm{ij}}^e,{\upsilon }_{\mathrm{ij}}^e,{\pi }_{\mathrm{ij}}^e\right)$ is the spherical fuzzy value of the impact of criterion ith to jth by $e^{th}$ decision-maker.

Step 3: Calculating the decision-makers weights

The decision-maker’s weights in the decision group reflect the importance of the participants and their experiences. Let $A_e=({\mu }_e,{\upsilon }_e,{\pi }_e)$ is provided as the spherical fuzzy value by e^th decision-makers, and the decision-maker’s weights (${\omega }_e$) can be defined by Liu et al. [62], as in Equation (17).

$${\omega }_e=\frac{1-\sqrt{\left\{{\left(1-{\mu }_e\right)}^2+{\upsilon }_e^2+{\pi }_e^2\right\}/3}}{{\sum }_e\left(1-\sqrt{\left\{{\left(1-{\mu }_e\right)}^2+{\upsilon }_e^2+F{\pi }_e^2\right\}/3}\right)}({\mu }_e,{\upsilon }_e^2,{\pi }_e^2) e=1, \dots , k$$

(17)

where ${\sum }_{e=1}^k{\omega }_e=1$, $0\le {\mu }_e^2+{\upsilon }_e^2+{\pi }_e^2\le 1$.

Step 4: Establishing aggregated direct influence matrix ( $D^{agg}$)

In this step, individual comparisons are collected from the decision-makers to synthesize all the evaluations. The aggregated direct influence matrix ($D^{agg}$) is constructed through the SWAM process from Equation (6), as shown in Equation (18).

$$D^{agg}=\left[\begin{array}{cccc}0& \left({\mu }_{12}^{agg},{\upsilon }_{12}^{agg},{\pi }_{12}^{agg}\right)& \cdots & \left({\mu }_{1n}^{agg},{\upsilon }_{1n}^{agg},{\pi }_{1n}^{agg}\right)\\ \left({\mu }_{21}^{agg},{\upsilon }_{21}^{agg},{\pi }_{21}^{agg}\right)& 0& \cdots & \left({\mu }_{2n}^{agg},{\upsilon }_{2n}^{agg},{\pi }_{2n}^{agg}\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({\mu }_{n1}^{agg},{\upsilon }_{n1}^{agg},{\pi }_{n1}^{agg}\right)& \left({\mu }_{n2}^{agg},{\upsilon }_{n2}^{agg},{\pi }_{n2}^{agg}\right)& \cdots & 0\end{array}\right]$$

(18)

where $\left({\mu }_{\mathrm{ij}}^{agg},{\upsilon }_{\mathrm{ij}}^{agg},{\pi }_{\mathrm{ij}}^{agg}\right)$ is the aggregated SF value of the impact of criterion ith to jth.

Step 5: Creating the initial direct influence matrix (X)

The SF value of each comparison contains three dimensions, including membership ($\mu$), non-membership ($\upsilon$), and hesitancy level ($\pi$). After separating these into three submatrices, the normalization of matrix (D) will be performed to create the initial direct influence matrix (X), as defined in Equation (19). The final matrix form in this stage is described as in Equation (20).

$$X=sD \mathrm{where} s=\min \left[\frac{1}{\underset{i}{\max }{\sum }_{j=1}^n\left|d_{\mathrm{ij}}\right|},\frac{1}{\underset{j}{\max }{\sum }_{i=1}^n\left|d_{\mathrm{ij}}\right|}\right]$$

(19)

where s is the normalization index.

$$X^{\mu }=\left[\begin{array}{cccc}0& {\mu }_{12}& \cdots & {\mu }_{1n}\\ {\mu }_{21}& 0& \cdots & {\mu }_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\mu }_{n1}& {\mu }_{n2}& \cdots & 0\end{array}\right], X^{\upsilon }=\left[\begin{array}{cccc}0& {\upsilon }_{12}& \cdots & {\upsilon }_{1n}\\ {\upsilon }_{21}& 0& \cdots & {\upsilon }_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\upsilon }_{n1}& {\upsilon }_{n2}& \cdots & 0\end{array}\right], X^{\pi }=\left[\begin{array}{cccc}0& {\pi }_{12}& \cdots & {\pi }_{1n}\\ {\pi }_{21}& 0& \cdots & {\pi }_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\pi }_{n1}& {\pi }_{n2}& \cdots & 0\end{array}\right]$$

(20)

Step 6: Defining the total influence matrix (T)

The submatrices of T are transformed from the submatrices of X by utilizing Equation (21). Then, these matrices are merged into the T matrix shown in Equation (22).

$$T=X+X^{\prime }=X{(1-X)}^{-1}=\left[\begin{array}{ccc}{t}_{11}& \cdots & t_{1n}\\ ⋮& \ddots & ⋮\\ t_{n1}& \cdots & t_{nn}\end{array}\right] i, j=1, \dots , n$$

(21)

$$T=\left[\begin{array}{cccc}\left({\mu }_{11}^T,v_{11}^T,{\pi }_{11}^T\right)& \left({\mu }_{12}^T,v_{12}^T,{\pi }_{12}^T\right)& \cdots & \left({\mu }_{1n}^T,v_{1n}^T,{\pi }_{1n}^T\right)\\ \left({\mu }_{21}^T,v_{21}^T,{\pi }_{21}^T\right)& \left({\mu }_{22}^T,v_{22}^T,{\pi }_{22}^T\right)& \cdots & \left({\mu }_{2n}^T,v_{2n}^T,{\pi }_{2n}^T\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({\mu }_{n1}^T,v_{n1}^T,{\pi }_{n1}^T\right)& \left({\mu }_{n2}^T,v_{n2}^T,{\pi }_{n2}^T\right)& \cdots & \left({\mu }_{nn}^T,v_m^T,{\pi }_m^T\right)\end{array}\right]$$

(22)

where T is the total influence matrix, X is the direct influence matrix, $X^{\prime }$ is the indirect influence matrix, $\left({\mu }_{\mathrm{ij}}^T,{\upsilon }_{\mathrm{ij}}^T,{\pi }_{\mathrm{ij}}^T\right)$ and is the SF value of the T matrix corresponding to the impact from criterion ith to jth.

Step 7: Computing the sum of spherical fuzzy column ( $c_i$) and row ( $r_i$)

The spherical fuzzy of row sum ($r_i$) and column sum ($c_i$) are calculated by Equations (23) and (24), respectively.

$$r_i={\displaystyle \sum _{i=1}^n\left({\mu }_{\mathrm{ij}}^T,{\upsilon }_{\mathrm{ij}}^T,{\pi }_{\mathrm{ij}}^T\right)} i, j=1, \dots , n$$

(23)

$$c_i={\displaystyle \sum _{j=1}^n\left({\mu }_{\mathrm{ij}}^T,{\upsilon }_{\mathrm{ij}}^T,{\pi }_{\mathrm{ij}}^T\right)}$$

(24)

where $\left({\mu }_{\mathrm{ij}}^T,{\upsilon }_{\mathrm{ij}}^T,{\pi }_{\mathrm{ij}}^T\right)$ is the SF value of the T matrix corresponding to the influence of criterion ith on criterion jth.

Step 8: Determining the value of prominence and relation

In this step, the values of prominence and relation are found through the defuzzification into real numbers, illustrated as score values by utilizing Equation (25).

$$Score={\left(2\mu -\pi \right)}^2-{\left(\upsilon -\pi \right)}^2$$

(25)

The term “Prominence” describes the importance level of the criteria ith through the calculus of “$r_i+c_i$”. The calculation of “$r_i-c_i$” is called “Relation”, which divided these criteria into two groups, as shown. This identification of values in the group of cause and effect plays a significant role in evaluating the degree of effect and ranking the criteria.

• $r_i-c_i⟩0$: the impact of the criteria ith on other criteria, participating in the “cause” group.
• $r_i-c_i⟨0$: the criteria ith is affected by others, and is defined as the “effect” group.

The weight (${\alpha }_j$) of the jth criteria is presented in Equation (26):

$${\alpha }_j=\frac{r_j+c_j}{{\displaystyle {\sum }_{j=1}^n(r_j+c_j)}}$$

(26)

Step 9: Painting network relations map (NRM)

In the final step, the casual dependence relationship and the important level among criteria are displayed by the network relations map, in which prominence values illustrate on horizontal axes and relation values define the vertical axes. Specifically, the member of the cause group is drawn on the above, and the remaining member of the relation group expresses the graph below.

3.3. SF EDAS

Evaluation based on distance from average solution (EDAS) is another tool of the multi-criteria decision-making method, which typically solves optimal selection problems based on the preferences of alternatives or attributes. This technique has been applied in many ways, such as finding the most suitable location for solid waste disposition [63], choosing a sustainable appropriate location for the third-party reverse logistics suppliers based on the combination of fuzzy Critic [64], identifying optimal alternative energy sources to invest in as new renewable energy by using the fuzzy AHP-EDAS-FMEA approach [65], finding optimal solutions for health emergencies systems by integrating spherical linguistics [66], determining the most efficient strategy to improve business performance in the railway industry by applying for trapezoidal fuzzy number EDAS PIPRECIA method [67], and selecting the best alternative teaching tools in terms of distance learning by incorporating spherical fuzzy AHP EDAS [68]. This study applies spherical fuzzy EDAS to compute the priority of alternative destinations, following a sequence of steps.

Step 1: Creating SF decision matrix

The evaluation of the linguistics of alternatives among the expert criteria are converted into SF values, as shown in Table 3. The SF decision matrix $D^e={\left[d_{\mathrm{ij}}^e\right]}_{n\times n}$ is established by Equation (27):

$$D^e=S\mathrm{W}A{M}_{\omega }\left(D^1,D^2,\dots ,D^k\right)={\omega }_1{D}^1+{\omega }_2{D}^2+\dots +{\omega }_k{D}^k i=1, \dots , k;j=1, \dots , n$$

(27)

Table 3. SF-EDAS linguistics term.

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)

Step 2: Determining the spherical fuzzy average solution

According to Equations (26) and (27), the SF average solution is found in Equation (28):

$$A{D}_j=S\mathrm{W}AM\left(d_{1j},d_{2j},\dots ,d_{kj}\right)=\frac{1}{k}{d}_{1j}+\frac{1}{k}{d}_{2j}+\dots +\frac{1}{k}{d}_{kj} j=1, \dots , n$$

(28)

Step 3: Converting to the crisp decision matrix and the crisp average solution

Next, the crisp decision matrix and the crisp average are converted by the defuzzification process, as shown in Equation (14).

Step 4: Calculating the value of the positive distance and the negative distance from the average matrix

Based on Equations (27) and (28), the positive and negative distances from the average matrix are identified in Equations (29) and (30).

$$x_{ij}^{+}=\frac{\max (0,d_{\mathrm{ij}}-A{D}_j)}{A{D}_j}$$

(29)

$$x_{ij}^{-}=\frac{\max (0,A{D}_j-d_{\mathrm{ij}})}{A{D}_j}$$

(30)

Step 5: Computing the value of weighted sum positive distance and negative distance

According to Equation (26), the weighted sum positive distance and the weighted sum negative distance are calculated in Equations (31) and (32).

$$s_i^{+}={\displaystyle \sum _{j=1}^n{\alpha }_j}{x}_{\mathrm{ij}}^{+}$$

(31)

$$s_i^{-}={\displaystyle \sum _{j=1}^n{\alpha }_j}{x}_{\mathrm{ij}}^{-}$$

(32)

Then, the normalization of weighted sum positive distance and negative distance are computed in Equations (33) and (34).

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

(33)

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

(34)

Step 6: Finding the appraisal score of alternatives

Finally, the alternative’s appraisal score is defined in Equation (35), in which the priority is based on a better score.

$${\mathrm{as}}_i=\frac{1}{2}(n{s}_i^{+}+n{s}_i^{-})$$

(35)

4. Case Study

For more than 80% of the population living on agriculture, with rich tropical fruits, rice, tea, and coffee products, Vietnam has good conditions to build and develop agritourism. This type of tourism is developing throughout the country and tourism products from agriculture have become a highlight when promoting the growth in domestic and foreign tourism. Agricultural culture is diverse, and each region has its own specific forms, such as the agricultural village experience in the Red River Delta, ecotourism in the Mekong Delta, high-tech farm activities in the Central Highlands, and sightseeing tours in the Northern Mountain region. This illustrates that the potential of agritourism in Vietnam is huge, which motivates the government to formulate mechanisms and create favorable conditions for the agritourism sector through mobilizing social resources, transport infrastructure, electricity, water, and investment capital. According to the Ministry of Culture, Sports, and Tourism, the project “Rural tourism development associated with new rural construction” was developed as a premise for specific solutions and rural policies in the coming period. As a result, the advantages of the agriculture sector were greatly promoted, and the value chain of agritourism was effectively built, contributing to sustainable development for the new type of tourism in the area [69].

For this study, a combination of SF-DEMATEL and SF-EDAS was proposed to select the optimal agritourism destination for sustainable development in Vietnam. The structure of the research framework was represented by four elements, including objective, elements, criteria, and alternatives, as shown in Figure 2. The results of the proposed model were found by following these steps: (1) assessment criteria analysis by SF-DEMATEL, (2) agritourism destination evaluation by SF-EDAS, and (3) sensitivity analysis and validation.

Figure 2. The agritourism destination selection network.

4.1. Criteria Analysis by SF-DEMATEL

According to the expert’s judgments and related documents, a set of relevant factors, including four key elements and ten criteria, was presented to assess the location decisions described in Table 4. These criteria were investigated by focusing on many aspects related to the economy (accessibility, surrounding activities), society (local regulation and policy, the awareness of local people, culture and custom), natural resources (local agriculture product, scenic resources, land use), and environment (waste management, local living condition). The importance level of the proposed criteria and relations between them were found by applying the SF- DEMATEL method. To conduct the evaluation process, the discussion group was established, which contains ten decision-makers who are experts in a relevant field or investors in this project. The linguistic judgment of decision-makers’ influences is illustrated in Table A1 in the Appendix A.

Table 4. The assessment criteria for agritourism selection.

Element		Criteria	Description	Sources
Economy	ASC1	Accessibility	Availability of roads network and public transport: airports, seaports, riverboats, railway networks, buses, taxis, and the ease of accessibility in tourist information and communication	[26,28,70,71,72]
	ASC2	Surrounding activities	Proximity to competitors and other recreational activities	[28,71,72]
Natural resource	ASC3	Local agriculture product	The number of plants (crops, industrial plants, medicinal plants), livestock (cow, goat, fish, etc.), and agricultural processed products	[24,27,73]
	ASC4	Scenic resource	The natural beauty from the sea, rivers, lakes, mountains, and beautiful scenery from agricultural production	[26,27,71,72,74]
	ASC5	Land use	The capacity of land use for cultivation, husbandry, and tourism exploitation	[24,26,71,72,75]
Society	ASC6	Local regulation and policy	Regulations and policies for the development of the agriculture and tourism sectors	[27,72,73,75]
	ASC7	The awareness of local people	Satisfaction and participation of the local community in agritourism activities	[26,71,72,73,75]
	ASC8	Culture and custom	Availability of custom habits, traditional cultures, traditional craft villages, local cuisine, festivals, and arts	[24,27,71,74,75]
Environment	ASC9	Waste management	The degree of garbage, emissions, and wastewater in agritourism	[24,73,74]
	ASC10	Local living condition	The effects on natural landscape and ecosystem, the local people’s life, agricultural production	[24,71,72,73]

In the next step, combined with the evaluated comparisons of decision-makers, the aggregated direct influence matrix ($D^{agg}$), following Equations (6) and (7), is represented in Table 5. Next, three submatrices of three SF values, including $D^{\mu }$, $D^{\upsilon }$, $D^{\pi }$, were separated from the aggregated matrix (D), as denoted in Table A2, Table A3 and Table A4 in the Appendix A.

Table 5. The aggregated direct influence matrix ($D^{agg}$).

Criteria	ASC1	ASC2	ASC3	ASC4	ASC5
ASC1	(0, 0.3, 0.2)	(0.51, 0.235, 0.389)	(0.549, 0.221, 0.393)	(0.471, 0.241, 0.379)	(0.627, 0.217, 0.474)
ASC2	(0.581, 0.22, 0.44)	(0, 0.3, 0.2)	(0.714, 0.196, 0.497)	(0.528, 0.226, 0.389)	(0.642, 0.212, 0.472)
ASC3	(0.561, 0.22, 0.396)	(0.695, 0.198, 0.484)	(0, 0.3, 0.2)	(0.47, 0.236, 0.312)	(0.541, 0.225, 0.393)
ASC4	(0.5, 0.239, 0.389)	(0.612, 0.222, 0.476)	(0.569, 0.216, 0.396)	(0, 0.3, 0.2)	(0.702, 0.201, 0.501)
ASC5	(0.407, 0.243, 0.28)	(0.528, 0.226, 0.389)	(0.491, 0.228, 0.315)	(0.557, 0.217, 0.392)	(0, 0.3, 0.2)
ASC6	(0.573, 0.224, 0.441)	(0.532, 0.229, 0.393)	(0.496, 0.236, 0.385)	(0.704, 0.204, 0.502)	(0.601, 0.218, 0.443)
ASC7	(0.648, 0.208, 0.47)	(0.519, 0.23, 0.389)	(0.425, 0.242, 0.291)	(0.588, 0.216, 0.439)	(0.561, 0.22, 0.396)
ASC8	(0.693, 0.195, 0.483)	(0.554, 0.229, 0.44)	(0.659, 0.214, 0.495)	(0.454, 0.237, 0.303)	(0.51, 0.235, 0.389)
ASC9	(0.541, 0.225, 0.393)	(0.412, 0.247, 0.288)	(0.437, 0.238, 0.293)	(0.378, 0.253, 0.274)	(0.519, 0.23, 0.389)
ASC10	(0.584, 0.223, 0.443)	(0.46, 0.245, 0.379)	(0.604, 0.207, 0.401)	(0.573, 0.224, 0.441)	(0.636, 0.216, 0.474)
Criteria	ASC6	ASC7	ASC8	ASC9	ASC10
ASC1	(0.385, 0.256, 0.283)	(0.541, 0.225, 0.393)	(0.537, 0.222, 0.389)	(0.491, 0.228, 0.315)	(0.75, 0.187, 0.495)
ASC2	(0.519, 0.23, 0.389)	(0.454, 0.237, 0.303)	(0.471, 0.241, 0.379)	(0.251, 0.274, 0.229)	(0.659, 0.201, 0.466)
ASC3	(0.51, 0.235, 0.389)	(0.598, 0.215, 0.44)	(0.662, 0.203, 0.468)	(0.554, 0.229, 0.44)	(0.541, 0.225, 0.393)
ASC4	(0.528, 0.226, 0.389)	(0.598, 0.23, 0.479)	(0.665, 0.211, 0.493)	(0.442, 0.242, 0.301)	(0.557, 0.217, 0.392)
ASC5	(0.501, 0.224, 0.316)	(0.43, 0.246, 0.299)	(0.449, 0.25, 0.379)	(0.492, 0.232, 0.38)	(0.449, 0.25, 0.379)
ASC6	(0, 0.3, 0.2)	(0.612, 0.222, 0.476)	(0.399, 0.252, 0.286)	(0.437, 0.238, 0.293)	(0.588, 0.216, 0.439)
ASC7	(0.587, 0.212, 0.398)	(0, 0.3, 0.2)	(0.363, 0.257, 0.271)	(0.561, 0.22, 0.396)	(0.553, 0.224, 0.397)
ASC8	(0.532, 0.229, 0.393)	(0.662, 0.203, 0.468)	(0, 0.3, 0.2)	(0.454, 0.237, 0.303)	(0.584, 0.223, 0.443)
ASC9	(0.393, 0.248, 0.277)	(0.378, 0.253, 0.274)	(0.608, 0.214, 0.441)	(0, 0.3, 0.2)	(0.7, 0.194, 0.482)
ASC10	(0.584, 0.223, 0.443)	(0.591, 0.219, 0.441)	(0.605, 0.211, 0.439)	(0.412, 0.264, 0.377)	(0, 0.3, 0.2)

The initial direct influence submatrices of X were determined by normalizing the submatrices of D by using Equations (8) and (9). According to Equations (10) and (11), this transforms into the matrices (T) consisting of $T^{\mu }$, $T^{\upsilon }$, $T^{\pi }$, as displayed in Table A5, Table A6 and Table A7 in the Appendix A. Then, matrices were synthesized to build the total influence matrix of T, as shown in Table 6.

Table 6. The total influence matrix (T).

Criteria	ASC1	ASC2	ASC3	ASC4	ASC5
ASC1	(0.533, 0.564, 0.458)	(0.592, 0.553, 0.489)	(0.61, 0.536, 0.473)	(0.577, 0.554, 0.468)	(0.659, 0.528, 0.537)
ASC2	(0.624, 0.536, 0.516)	(0.509, 0.579, 0.457)	(0.633, 0.528, 0.502)	(0.585, 0.55, 0.477)	(0.66, 0.528, 0.545)
ASC3	(0.651, 0.526, 0.522)	(0.645, 0.53, 0.529)	(0.549, 0.556, 0.453)	(0.602, 0.543, 0.473)	(0.675, 0.523, 0.542)
ASC4	(0.646, 0.536, 0.531)	(0.638, 0.542, 0.539)	(0.644, 0.528, 0.505)	(0.531, 0.57, 0.46)	(0.703, 0.517, 0.577)
ASC5	(0.544, 0.56, 0.435)	(0.542, 0.567, 0.449)	(0.547, 0.555, 0.419)	(0.538, 0.562, 0.431)	(0.501, 0.576, 0.436)
ASC6	(0.633, 0.537, 0.525)	(0.604, 0.552, 0.506)	(0.611, 0.542, 0.486)	(0.621, 0.541, 0.509)	(0.665, 0.53, 0.549)
ASC7	(0.629, 0.529, 0.507)	(0.587, 0.551, 0.481)	(0.585, 0.543, 0.445)	(0.589, 0.544, 0.473)	(0.643, 0.53, 0.514)
ASC8	(0.668, 0.519, 0.541)	(0.623, 0.545, 0.522)	(0.651, 0.527, 0.516)	(0.599, 0.547, 0.474)	(0.668, 0.53, 0.544)
ASC9	(0.571, 0.551, 0.456)	(0.53, 0.572, 0.426)	(0.546, 0.556, 0.412)	(0.517, 0.573, 0.405)	(0.591, 0.548, 0.474)
ASC10	(0.646, 0.536, 0.544)	(0.605, 0.558, 0.521)	(0.637, 0.53, 0.507)	(0.612, 0.548, 0.513)	(0.681, 0.528, 0.573)
Criteria	ASC6	ASC7	ASC8	ASC9	ASC10
ASC1	(0.547, 0.566, 0.432)	(0.601, 0.547, 0.484)	(0.589, 0.548, 0.48)	(0.518, 0.571, 0.413)	(0.677, 0.509, 0.535)
ASC2	(0.566, 0.557, 0.461)	(0.587, 0.553, 0.473)	(0.578, 0.557, 0.486)	(0.481, 0.59, 0.402)	(0.662, 0.516, 0.537)
ASC3	(0.59, 0.548, 0.472)	(0.635, 0.534, 0.513)	(0.632, 0.532, 0.516)	(0.549, 0.562, 0.456)	(0.676, 0.515, 0.537)
ASC4	(0.597, 0.549, 0.483)	(0.64, 0.543, 0.533)	(0.637, 0.538, 0.532)	(0.536, 0.57, 0.437)	(0.682, 0.515, 0.548)
ASC5	(0.513, 0.571, 0.402)	(0.53, 0.572, 0.424)	(0.523, 0.576, 0.439)	(0.472, 0.591, 0.391)	(0.575, 0.55, 0.469)
ASC6	(0.491, 0.583, 0.428)	(0.62, 0.547, 0.517)	(0.577, 0.561, 0.474)	(0.517, 0.576, 0.422)	(0.663, 0.521, 0.54)
ASC7	(0.57, 0.548, 0.448)	(0.507, 0.575, 0.435)	(0.557, 0.561, 0.448)	(0.523, 0.568, 0.423)	(0.642, 0.523, 0.508)
ASC8	(0.592, 0.55, 0.475)	(0.643, 0.533, 0.521)	(0.526, 0.572, 0.461)	(0.534, 0.569, 0.43)	(0.68, 0.518, 0.548)
ASC9	(0.503, 0.577, 0.392)	(0.529, 0.572, 0.417)	(0.553, 0.56, 0.45)	(0.397, 0.613, 0.352)	(0.619, 0.526, 0.488)
ASC10	(0.594, 0.554, 0.495)	(0.628, 0.545, 0.527)	(0.617, 0.544, 0.523)	(0.523, 0.585, 0.454)	(0.58, 0.552, 0.51)

The row sum and column sum calculations were carried out according to Equations (12) and (13), and the Prominence and Relation values were computed by Equation (14) through defuzzification into the score numbers, assuming i = j, as obtained in Table 7. The ranking of criteria, combined with the identification of cause-and-effect groups, is presented in Table 8. The significance level of the criteria is as follows: ASC10 > ASC3 > ASC1 > ASC4 > ASC8 > ASC2 > ASC7 > ASC6 > ASC5 > ASC9. The finding is that local living conditions (ASC10) were the most important factor for decision-makers when evaluating tourist destinations. In addition, these criteria were divided into two groups to clearly show the interactional relations between them in the problem. The criteria belonging to the cause group include surrounding activities (ASC2), local agriculture product (ASC3), scenic resource (ASC4), culture and custom (ASC8), local regulation and policy (ASC6), waste management (ASC9), and the ordering of these factors, defined as ASC3 > ASC4 > ASC8 > ASC2 > ASC6 > ASC9. The remaining criteria form the effect group, including accessibility (ASC1), land use (ASC5), the awareness of local people (ASC7), local living conditions (ASC10), and the priority members are determined as ASC10 > ASC1 > ASC7 > ASC5. This means that the six criteria in the cause group have a high level of importance during the evaluation process, and these criteria directly affect the rest of the criteria. Therefore, the decision-makers should consider and focus on factors such as surrounding activities, local agriculture products, scenic resources, culture and custom, local regulation and policy, and waste management when making decisions regarding investment.

Table 7. The prominence and relation of criteria.

Criteria	r	Defuzzied Score	c	Defuzzied Score	Prominence (r + c)	Relation (r − c)
ASC1	(0.994, 0.002, 0.112)	0.765	(0.996, 0.002, 0.09)	0.813	1.578	−0.048
ASC2	(0.994, 0.003, 0.113)	0.763	(0.993, 0.003, 0.117)	0.755	1.519	0.008
ASC3	(0.996, 0.002, 0.085)	0.824	(0.995, 0.002, 0.103)	0.785	1.609	0.039
ASC4	(0.997, 0.002, 0.080)	0.835	(0.992, 0.003, 0.129)	0.729	1.564	0.107
ASC5	(0.981, 0.004, 0.188)	0.595	(0.998, 0.002, 0.065)	0.867	1.463	−0.272
ASC6	(0.995, 0.002, 0.102)	0.787	(0.988, 0.003, 0.152)	0.677	1.464	0.110
ASC7	(0.993, 0.002, 0.121)	0.746	(0.994, 0.003, 0.111)	0.768	1.514	−0.022
ASC8	(0.996, 0.002, 0.085)	0.823	(0.992, 0.003, 0.126)	0.734	1.557	0.089
ASC9	(0.984, 0.003, 0.174)	0.628	(0.974, 0.004, 0.218)	0.527	1.154	0.101
ASC10	(0.996, 0.002, 0.093)	0.807	(0.998, 0.002, 0.065)	0.865	1.673	−0.058

Table 8. The overall results of the SF-DEMATEL model.

Assessment Criteria	Influence Group	Weight	Rank
ASC1	Effect	0.10451	3
ASC2	Cause	0.1006	6
ASC3	Cause	0.10662	2
ASC4	Cause	0.10362	4
ASC5	Effect	0.0969	9
ASC6	Cause	0.09701	8
ASC7	Effect	0.10029	7
ASC8	Cause	0.10313	5
ASC9	Cause	0.07648	10
ASC10	Effect	0.11083	1

After finding and classifying the values of (r + c) and (r − c), the relationships between the assessment criteria are represented by the network relation map’s given threshold value, as shown in Figure 3. The cause-and-effect graph is separated into four parts, from I to IV. Specifically, members of part I, including surrounding activities (ASC2), local agriculture products (ASC3), scenic resources (ASC4), and culture and custom (ASC8), are the causal criteria that have the largest effect on the assessment of tourist destinations. Local regulation and policy and waste management are other criteria, located in part II and defined as low prominence and high relation. In part III, accessibility and local living condition factors are independent of the system due to their low prominence and relation values. Lastly, the land-use factor located in Part IV is indicated to be highly influenced by other factors.

Figure 3. Network relations map of evaluating criteria.

4.2. Agritourism Destination Evaluation by SF-EDAS

At this stage, the spherical fuzzy EDAS calculates the priority of proposed alternative destinations after defining the criteria weights. Some computations are implemented to identify the results as follows. In the beginning, the linguistics evaluation from an expert is presented in Table A8. Next, the expert’s linguistics are transformed to build the initial spherical fuzzy decision matrix from Table 2, and these matrices are consolidated to create a spherical fuzzy decision matrix, as defined in Table A9. According to Equation (28), the spherical fuzzy average solution is established as presented in Table A10. Based on Equation (14), the defuzzied value of the SF decision matrix and the average solution is displayed in Table A11. Then, the results of the positive distances and negative distances from the average solution are demonstrated in Table A12 and Table A13, respectively. Following Step 4 and Step 5 in Section 3.3, the final ranking of destinations in sustainable development assessment is shown in Table 9. It shows that Lam Dong (AD9), Lai Chau (AD2), and Dong Thap (AD7) are the top-priority alternative destinations in agritourism development. In the lower ranks, the destinations are Nghe An (AD1), Phu Yen (AD8), and Tuyen Quang (AD5).

Table 9. The overall results of the SF-EDAS model.

Alternative Destination		ASi	Rank
AD1	Nghe An	0.240	10
AD2	Lai Chau	0.642	2
AD3	Gia Lai	0.409	5
AD4	Ninh Thuan	0.376	7
AD5	Tuyen Quang	0.365	8
AD6	Quang Ninh	0.392	6
AD7	Dong Thap	0.562	3
AD8	Phu Yen	0.335	9
AD9	Lam Dong	0.704	1
AD10	Ben Tre	0.485	4

4.3. Sensitivity Analysis and Validation

The stability of the agritourism destinations’ development order, based on the results of the proposed model, was tested through a sensitivity analysis, with the aim of reaching sustainable development. To conduct the analysis, scenarios were generated by varying the weights of the assessment criteria. Specifically, scenario 1 assumes that all factors have the same influence. In scenario 2, the importance of natural resources in agritourism is emphasized. The impact of social and environmental aspects is more concentrated in developing tourist sites in rural areas, based on scenarios 3 and 4, respectively. Finally, scenario 5 is more concerned to the effect of local economic development on the agritourism activities. After running five scenarios, the priority of ten potential tourism destinations is not changed, as shown in Figure 4. Lam Dong (AD9), Lai Chau (AD2), and Dong Thap (AD7) maintain the top ranking among potential alternative locations. This testing indicates the feasibility and high applicability of the model, even with fluctuations in the surrounding elements.

Figure 4. The result of scenarios testing.

5. Discussion and Conclusions

At present, agritourism is becoming a promising alternative for the tourism industry. By both promoting and preserving the value of the natural environment, this model seems to be a key business strategy for sustaining tourism by attracting the interest of many countries worldwide. After the COVID-19 pandemic, ensuring the demand for sustainable tourism is essential. A sustainable tourist destination is an extremely important factor influencing tourists’ choice, and it simultaneously ensures the long-term business operation of the enterprise. Based on the diversity of the agricultural industry, many models combining tourism and agriculture have been implemented in Vietnam. However, efficient exploitation in current agritourism destinations is still limited, and sustainability operations have not been fully developed. Therefore, this study developed a combination of spherical fuzzy MCDM approaches to determine an appropriate destination for sustainable development in agritourism in Vietnam. The SF-DEMATEL technique determines the assessment criteria’s influence and causal relationships, and the SF-EDAS method ranks potential tourist destinations.

In the model’s development, ten assessment criteria, related to aspects such as the economy, environment, society, and natural resources, were suggested. The results from the SF-DEMATEL method illustrate that the most important assessment criteria are local living conditions (ASC10), local agriculture product (ASC3), and accessibility (ASC1). This shows that environmental factors are increasingly focused on agritourism development, which directly impacts natural conditions such as agricultural value, natural landscapes, and ecosystems [26]. When natural resources are utilized, tourism activities are shown to have potential. Moreover, agritourism also improves the lives of local people, increasing their understanding, and generating additional income for farmers on their land [76]. In addition, the advantages of various special agriculture products are an important factor, attracting tourists to visit, learn about and experience the area. However, ease of accessibility is also an indispensable criterion in the tourism development strategy. The variety of public transport, convenient transportation, and easy access to information and communication will increase satisfaction and can adapt to customer requirements [70]. The model results show a causal dependence relationship between the evaluating factors. Local agricultural product (ASC3), scenic resource (ASC4), culture and custom (ASC8), local regulation and policy (ASC6), and waste management (ASC9) are the criteria in the cause group, and the remaining criteria, including accessibility (ASC1), land use (ASC5), awareness of local people (ASC7), and local living conditions (ASC10), belong to the effect group. Local agricultural product (ASC3), scenic resource (ASC4), and culture and custom (ASC8) were found to have a high significance level in the cause group, and changes or improvements in these criteria will greatly influence the criteria in the effect group. Therefore, natural resources play an important role in sustainable agritourism development [18]. The scale and capacity of agricultural products will extensively impact attempts to expand tourism products. The more distinctive and high-quality the agricultural products are, the better their competitiveness in the market [25]. Moreover, the rich natural beauty combined with a unique traditional culture, can be properly used as a highlight to influence the customer’s choice [77]. Consequently, decision-makers should consider these factors when selecting sustainable agritourism locations.

After determining the criteria’s weights, potential alternatives were evaluated and selected performed using the SF-EDAS method. The model’s results indicate that Lam Dong (AD9) is the optimal agritourism destination for sustainable development. Lam Dong has many advantages in terms of natural and ecological conditions combined with a temperate climate, providing a chance for the long-term promotion of agricultural production. This area is now leading the country in terms of high-tech production applications, which are conducted to expand high-quality production activities and attract further investment. Based on those strengths, the combination of agriculture and tourism is an appropriate direction in sustainable development, bringing significant value to both sectors, contributing to product diversification, and improving the local economy. Lai Chau (AD2) and Dong Thap (AD7) are some other priority agritourism destinations in terms of sustainability, based on the results shown in the method.

In conclusion, this study presented a research framework for the assessment and selection of sustainable agritourism destinations. It is an original study, which used a fuzzy multi-criteria decision model combining SF-DEMATEL and SF-EDAS methods to make decisions on agritourism sites. The model’s outcome can undergo practical application in Vietnam, and the model’s stability was considered using a sensitivity analysis. The advantage of this work is its use of previous studies and experts’ opinions to determine the assessment criteria for tourist destinations, and the results show that the environment is a significant factor, matching the current green tourism trend. The proposed research can be a valuable guide when implementing a new type of Vietnam tourism, adapting to actual market needs in the global sustainable development context. Moreover, the proposed model will assist decision-makers and tourism developers in the exploitation of natural resource efficiency and the long-term sustainability of the other tourism projects. However, this study is still limited by the significant influence of qualitative expert judgment on the evaluation results and the scenario development process.