**1. Introduction**

Including some sports activities or watching sports events in the tourist itinerary has become one of the major development projects of the tourism industry [1]. Sports tourism is defined as "combining sports events with tourism" and can be divided into six types, including sports events, sports resorts, sports cruises, sports attractions, sports adventures and sports tours [2]. Many studies have pointed out that organizing related sports tourism in cities is conducive to the development of social image and local economy. For this reason, many cities have also set up special organizations to organize sports events to increase regional exposure and sports image [3,4]. Many countries are actively seeking viable marketing strategies to attract foreign and domestic tourists to travel there. The most typical way is to increase the number of tourists by using sports events. For example, in 2017, Taipei hosted a 13-Erlenmeyer-day Universiade and sold a total of 720,000 tickets to the sports event. This event not only attracted more foreign tourists but also promoted the local culture of Taipei. In addition, some well-known cities have been successfully transformed into sports tourism attractions and have established their image as sports cities. For example, Perth is known as the City of Sporting Events, Lausanne is known as Olympic Capital City and Lake Placid is billed as the Winter Sports Capital of the United States [2].

Due to abnormal climate change and frequent natural disasters, many international organizations (such as the World Health Organization (WHO), European Union (EU) and World Trade Organization (WTO)) have called on all industries to pay attention to "sustainable development" and formulated many regulations and agreements on environmental protection [5]. Therefore, the tourism industry is also actively moving towards the developmental vision of sustainable tourism and many kinds of research on sustainable sports tourism have been released. Gibson et al. [6] explored the cooperation between six small-scale sports events and local sports agencies (the evaluation includes economic, social and environmental protection aspects) and surveyed 447 sports event participants and spectators in terms of sports planning satisfaction. Pouder et al. [3] used expert interviews to explore how for-profit organizations can develop the market for sports tourism. Their study is particularly focused on economic development, with the goal of maximizing returns. Gil-Alana et al. [4] examined whether fluctuations in financial exchange rates have a significant impact on the returns of Brazilian sports tourism. The study used a multiple linear regression model to analyze the structure of tourism revenue structure over 20 years. Hsu et al. [7] developed an island-type sustainable tourism attitude scale focusing on the environmental protection perspective of sports attractions. Their data came from a survey of three islands in Taiwan. The results show that local culture and environmental protection are the most important factors in tourism development.

It is an important task to develop an effective urban tourism development evaluation model [8,9]. Multi-criteria decision-making (MCDM) is widely used in various evaluation and selection problems and it has excellent evaluation performance under many constraints. In contrast to statistical methods, MCDM does not need to establish basic assumptions for criteria or variables. MCDM has developed many soft calculation methods to process a variety of complex data (including data from expert interviews and data from actual surveys) and provide valuable management information to support decision-makers in formulating optimal strategies [10–13]. At present, there have been some studies using MCDM to study tourism-related issues, such as surveys of service quality in tourism [14], hotel performance evaluation and selection [15], tourism development and management [16].

According to the literature review, the evaluation system of urban sustainable sports tourism for cities has not been established yet. The purpose of this study is to propose a novel two-stage MCDM model to establish the evaluation criteria for cities to develop sustainable sports tourism and to explore the mutual influential relationships among the criteria. The evaluation framework is new, and the proposed hybrid methodology has not appeared. In summary, this model brings some contributions and innovations to sustainable tourism development for the cities:


The rest of this article is organized as follows. Section 2 briefly reviews the literature on sports tourism and presents the proposed evaluation framework for sustainable urban sports tourism development. Section 3 introduces the proposed two-stage MCDM model, including the implementation steps of Bayesian BWM and rough DEMATEL. Section 4 presents a real case in Taiwan to illustrate the feasibility and practicality of the proposed model. Section 5 includes discussions and management implications. Section 6 presents concludes with conclusions and future research.

#### **2. Literature Review for Sustainable Sports Tourism Evaluation Criteria**

Many countries promote sports tourism by joining sports, setting up specialized sports tourism agencies whether in large cities or local towns [3,18]. Sports tourism is a special type of tourism that provides tourists with an active (active participation in sports events as competitors) or passive (passive participation in sports events as spectators) experience that is different from traditional tourism. People interact with events, people and places when participating in sports tourism-related events [19]. Kim et al. [20] pointed out that large-scale sports tourism activities can attract many domestic and foreign participants and spectators; these sports events can increase local income and opportunities for urban development. On the contrary, these events also have negative impacts, that is, traffic congestion, environmental pollution, safety issues and damage to residents' rights. Therefore, the concept of sustainable development combined with research on tourism has been proposed. Nunkoo et al. [21] emphasized that the establishment of public trust and the formulation of environmental protection policies can develop excellent urban tourism. Gkoumas [22] proposes a comprehensive assessment index for sustainable tourism for the Mediterranean tourism industry; local governance is the most critical factor for the development of sports tourism. Musavengane et al. [23] explored the security of tourism in African countries, holding that cultural tolerance, local security, medical and rescue flexibility and the integrity of environmental awareness are all key items for evaluation. Yang et al. [24] first proposed a complete MCDM model of sustainable sports tourism, which established an effective evaluation system for tourist attractions in central Taiwan. Unfortunately, to our knowledge, no article has been conducted to examine the performance of sustainable sports tourism in the cities. In addition, the mutual influential relationships among evaluation criteria have not been explored.

This study proposes a novel evaluation framework to determine the evaluation criteria and their mutual influential relationships. For cities to develop sustainable sports tourism, they must receive support from local governments and the tourism industry. First, important criteria should be fully integrated into the evaluation system to reflect the characteristics and connotation of sports tourism. The initial criteria review was based on relevant academic literature [3,8,9,18,19,24] and expert interviews (a decision group was formed, including tourism industry, Taiwan Tourism Bureau, local government and environmental protection experts). The main framework includes four dimensions, namely social (S), environmental (G), economic (E) and institutional (I). Each of these four dimensions contains several criteria and a total of 30 evaluation criteria are included in the evaluation framework. The criteria, descriptions and literature are shown in Table 1.





#### **3. The Proposed Two-Stage MCDM Model**

The chosen case is Taichung City, Taiwan. The Taichung City Government actively promotes sports infrastructure and promotes the correct sports concept to implement "sports for all ages". In December 2019, the Taichung City Sports Bureau decided to organize marathons to connect the sports events with local specialties in order to serve the purpose of marketing the city and promoting culture. In 2020 alone, Taichung City has already prepared at least 35 marathon events. However, building an image of a sports city is a difficult and complex project; many factors and restrictions must be considered, including economic feasibility, social development, environmental awareness and policy support. Only through continuous review and improvement can we move towards the vision of urban sports for all ages. At present, there has not been a sustainable sports tourism evaluation system developed specifically for the cities. In addition, most studies have not examined the mutual influential relationships among criteria. Which evaluation criteria are the main factors that affect the success or failure of urban sports tourism? How do these criteria affect other criteria? These two issues are the focal points of this study.

In the study, the decision-making team consisted of ten experts, including tourism managers, members of the Ministry of Tourism and academics. These ten experts have at least 8 years of qualifications in sports events or tourism-related jobs; their current jobs are highly relevant to the development of sports tourism. The proposed evaluation framework is presented in Sections 2 and 4 dimensions with 30 criteria classified under them were identified.

**Figure 1.** The analysis procedure diagram.

Next, we describes the method used and its detailed calculation process. In the first stage, preliminary evaluation criteria were established based on the literature discussions on sports tourism and sustainable tourism. Due to the large number of evaluation criteria, screening must be performed to retain key criteria. Based on the interview data of several experts, the Bayesian BWM was used to calculate the weight of criteria and select the key criteria. Bayesian BWM—proposed by Mohammadi and Rezaei [17]—effectively integrates the judgments of multiple experts and shortens the computational procedures of the conventional BWM. In the second stage, the rough decision making trial and evaluation laboratory (rough DEMATEL) technique is used to map a cause-and-effect diagram of criteria to examine the strength of the influential relationship among the criteria. This study combines rough set theory with conventional DEMATEL. On the one hand, the consensus of the decision-making group can be known. Moreover, the interval value operation can be retained to avoid the loss of information. The analysis procedure diagram of this study is shown in Figure 1.

#### *3.1. Stage 1: Bayesian BWM*

Bayesian BWM effectively integrates the opinions of multiple experts to generate a set of optimal group criteria weights. Its survey process is simple and intuitive. Experts are asked to choose the most important and least important criteria; then they are compared pairwise with other criteria to form a structured set of two vectors. Based on the concept of statistical distribution, the optimal group criteria weights are estimated. The detailed Bayesian BWM derivation and proof can be found in the study of Mohammadi and Rezaei [17]. The implementation steps of Bayesian BWM are explained as follows:

3.1.1. Step 1. Determining the Set of Criteria in the Evaluation System

The evaluation criteria {*c*1, *c*2, ... , *cn*} were identified through literature review and multiple expert interviews.

#### 3.1.2. Step 2. Choosing the Most Important and Least Important Criteria

Based on the set of criteria, each expert chooses what s/he considers the most important and least important criteria.

3.1.3. Step 3. Comparing the Most Important Criteria with Other Criteria to Generate the BO (Best-to-Others) Vector

Each expert evaluates the relative importance of the most important criteria to other criteria to generate the BO vector. The ratings of BWM are shown in Table 2.

$$A\_{B\circ} = (a\_{B1}, a\_{B2}, \dots, a\_{Bn}) \tag{1}$$

where *aBj* indicates the importance of the most important criterion *B* relative to criterion *j*.


**Table 2.** BWM evaluation ratings.

3.1.4. Step 4. Comparing Other Criteria with the Least Important Criteria to Generate the OW (Others-to-Worst) Vector

Similar to Step 3, each expert evaluates the relative importance of the other criteria to the least important criteria to generate the OW vector.

$$A\_{\bar{J}W} = \begin{pmatrix} a\_{1W}, a\_{2W}, \dots, a\_{nW} \end{pmatrix}^T \tag{2}$$

where *ajW* indicates the importance of the other criterion *j* relative to the least important criterion *W*.

#### 3.1.5. Step 5. Calculating the Optimal Group Criteria Weights

Each expert follows Step 1 to Step 4 to get multiple sets of BO and OW vectors. According to the MATLAB program software provided by Mohammadi and Rezaei [17], the evaluation scores of all experts are used as input data to obtain the optimal group criteria weights.

3.1.6. Step 6. Testing Confidence for Ranking

After the weights are obtained, it must be checked whether the ranking of the weight is consistent. Assume that the two criteria in the criteria set are *ci* and *cj* and use the concept of Credal Ranking to test their confidence. Then the probability that *ci* is better than *cj* is

$$P(c\_i > c\_j) = \bigcup I(w\_i^{a \otimes \xi} > w\_j^{a \otimes \xi}) P(w^{a \otimes \xi}) \tag{3}$$

where *wagg* is the group criteria weight, *P*(*wagg*) is the posterior probability of *wagg* and *I* is the condition parameter, which can be calculated when *wagg <sup>i</sup>* <sup>&</sup>gt; *wagg j* is true, otherwise it is 0. The Markov-chain Monte Carlo (MCMC) technique is used to perform multiple simulations and the number of samples *Q* obtained by it is used to calculate its average confidence level.

$$\begin{aligned} P(c\_i > c\_j) &= \frac{1}{Q} \sum\_{q=1}^{Q} I\left(w\_i^{a\_{\xi\xi\xi q}} > w\_j^{a\_{\xi\xi q}}\right); \\ P(c\_j > c\_i) &= \frac{1}{Q} \sum\_{q=1}^{Q} I\left(w\_j^{a\_{\xi\xi q}} > w\_i^{a\_{\xi\xi q}}\right) \end{aligned} \tag{4}$$

where *waggq* represents *q wagg* s from the MCMC sample. When *P* - *ci* > *cj* > 0.5, it indicates that criterion *i* is more important than criterion *j* and the probability presented is the confidence level. In addition, the total probability is 1, *P* - *ci* > *cj* + *P* - *cj* > *ci* = 1.

#### 3.1.7. Step 7. Screening Criteria by α-cut

The α-cut is the threshold value of the screening criteria. There are *n* criteria in the criteria set, {*c*1, *c*2, ... , *cn*}. α-cut is shown below.

$$a\text{-cut} = \frac{1}{n}\tag{5}$$

This step can distinguish the relatively important and relatively unimportant criteria groups. We retain the rules that are larger than α-cut.

#### *3.2. Stage 2: Rough DEMATEL*

DEMATEL technique was proposed by Battelle Memorial Institute in 1972. This method is used to solve the problem of the complex structures in real society [25]. DEMATEL aims to establish a structure diagram that can show mutual influential relationships among the criteria. It is called a cause-and-effect diagram, which effectively supports decision-makers in understanding the interaction and influence relationships in the entire system. The conventional DEMATEL uses arithmetic average method to integrate evaluation data from multiple experts. This study combines rough set theory with DEMATEL, called rough DEMATEL or R-DEMATEL. This method not only can know the consensus degree of the decision-making group, but also retain the calculation of interval values to avoid the loss of information. The calculation steps of the rough number can be found in Lo et al. [26] and Chang et al. [27]. We use a simple example to illustrate how to integrate the rough number calculations of multiple experts. Assume that the evaluation values of the five experts in evaluating event *A* are 4, 4, 3, 2 and 2, respectively, then lower and upper bounds of rough numbers (*Lim* and *Lim*) are

$$\begin{array}{l} \underline{\dim}(4) = (4+4+3+2+2)/5 = 3, \, \overline{\dim}(4) = (4+4)/2 = 4 \\ \Rightarrow \vec{A}^{(1)} = \vec{A}^{(2)} = \vec{4} = [3, \, 4]; \\\\ \underline{\dim}(3) = (3+2+2)/3 = 2.333, \, \overline{\dim}(3) = (3+4+4)/3 = 3.667 \end{array}$$

$$\begin{array}{l} \underline{\dim}(2) = (2+2)/2 = 2, \; \overline{\dim}(2) = (4+4+3+2+2)/5 = 3\\ \Rightarrow \tilde{A}^{(4)} = \tilde{A}^{(5)} = \tilde{2} = [2, 3]. \end{array}$$

where the symbol "~" indicates that those are rough numbers. This set of scores can be obtained by averaging as follows:

$$\bar{A} = [(3+3+2.333+2+2)/5, \ (4+4+3.667+3+3)/5] = [2.467, 3.533]\_{-}$$

After screening criteria by Bayesian BWM, the rough DEMATEL procedure is further performed. The detailed steps are stated below:
