3.2.3. Step 3. Deriving the Rough Total Influence Matrix *T*˜

The normalized rough influence relation matrix *D*˜ uses Equation (9) to calculate the degree of each direct influence relationship and indirect influence relationship (*I* is the identity matrix) and finally integrates a rough total influence matrix *T*˜ as shown in Equation (10).

$$\begin{split} \tilde{T} \quad &= \tilde{D} + \tilde{D}^2 + \cdots + \tilde{D}^{\Theta} = \tilde{D} \big( I + \tilde{D} + \tilde{D}^2 + \cdots + \tilde{D}^{\Theta - 1} \big) \\ &= \tilde{D} \big( I - \tilde{D}^{\Theta} \big) \big( I - \tilde{D} \big)^{-1} = \tilde{D} \big( I - \tilde{D} \big)^{-1}, \text{ when } \Theta \to \infty, \tilde{D}^{\Theta} = \big( 0 \big)\_{n^\* \times n^\*} \end{split} \tag{9}$$

$$\mathcal{T} = \left[ \overline{t}\_{\overline{i}\overline{j}} \right]\_{n^\* \times n^\*} \tag{10}$$

where ˜*tij* = *t L ij*, *t U ij* .

#### 3.2.4. Step 4. Establishing the Cause-and-Effect Diagram

The rough total influence matrix *T*˜ can obtain the degree of rough affecting relationship (*s*˜*i*) and the degree of rough affected relationship ( ˜*oi*) of each criterion through Equations (11) and (12).

$$\tilde{\mathbf{s}} = [\tilde{\mathbf{s}}\_{\bar{i}}]\_{n^\* \times 1} \tag{11}$$

$$\begin{bmatrix} \bar{\sigma} = [\delta\_j]\_{1 \times \mathbf{n}^\*}^T = [\delta\_i]\_{\mathbf{n}^\* \times \mathbf{1}} \end{bmatrix} \tag{12}$$

where the symbol "*T*" stands for transpose. In addition, *s*˜*<sup>i</sup>* = ⎡ ⎢⎢⎢⎢⎣ *n j*=1 *t L ij*, *n j*=1 *t U ij* ⎤ ⎥⎥⎥⎥⎦ and *o*˜*<sup>j</sup>* = *n i*=1 *t L ij*, *n i*=1 *t U ijT* .

The *s*˜*<sup>i</sup>* + *o*˜*<sup>i</sup>* represents the rough total influence of the criterion within the evaluation system, and is called the prominence. *s*˜*<sup>i</sup>* − *o*˜*<sup>i</sup>* represents the rough net influence of the criterion within the evaluation system and is called the net cause-effect. If *s*˜*<sup>i</sup>* − *o*˜*<sup>i</sup>* > 0, it represents the degree of rough net influence of the criterion on other criteria; on the contrary, if *s*˜*<sup>i</sup>* − *o*˜*<sup>i</sup>* < 0 it represents the degree of rough net influence of the criterion by other criteria. The detailed cause-and-effect diagram results are presented in Section 4.2.

#### **4. Empirical Example**

Participating in sports activities not only can promote the physical health of people of all ages, but also bring social benefits and improve people's happiness. Healthy people will be the biggest asset of a country; the physical fitness of the people will be the foundation of the country's competitiveness. Moderate exercise promotes physiological metabolism and helps to resist stress. In order to enhance the country's sports competitiveness and protect people's sports rights, the promotion of sports has become the focal policy of advanced countries to learn and observe from each other. In Taiwan, the most common sports activities include outdoor leisure sports, ball sports, stretching, dancing, water sports and so on. Among them, outdoor leisure sports account for more than 80% of total sports events [28]. Therefore, the sports projects that this study explores to promote sustainable sports tourism are mainly outdoor leisure sports. This section introduces the background of the case, as well as the practical application of Bayesian BWM and rough DEMATEL.

#### *4.1. Screening the Criteria by Using Bayesian BWM*

Based on the Bayesian BWM calculation described in Section 3.1, first, each expert was required to make pairwise comparisons of the criteria in each dimension. A total of four BWM questionnaires needed to be filled out. Since the function of Bayesian BWM at this stage is for screening criterion, there is no need to perform pairwise comparisons for the dimensions. Consistency ratio (CR) was performed on the recovered BWM questionnaires to check the logic of the experts in the response process. Based on the consistency test formula proposed by Rezaei [29], the average CR value in the study is 0.014 (with high consistency). Table 4 lists the optimal group criteria weights. According to the judgment of the threshold (α-cut), 16 relatively important criteria were identified, which are important factors for the sustainable development of urban tourism, including S6, S7, S8, G1, G2, G4, G6, G8, E4, E5, E6, E7, I1, I2, I4 and I7. The mutual influential relationships of these criteria included in the evaluation system were analyzed by the rough DEMATEL technique.


**Table 4.** Criteria weights obtained through Bayesian BWM.

Note: The "\*" symbol represents the criteria that exceed the threshold value. These criteria would be calculated by DEMATEL.

In order to check whether the weights obtained, and the ranking are reliable, a ranking confidence test is performed. Among the four dimensions, their confidence levels of ranking are 0.926, 0.871, 0.868 and 0.904, respectively. It represents the criteria ranking in each dimension is highly confident. Next, rough DEMATEL analysis was performed on the criteria incorporated in the evaluation system.

This study also compared the criteria screening results of AHP, conventional BWM and Bayesian BWM, as shown in Table 5.

**Table 5.** Criterion screening results for three different methods.


AHP and BWM have fewer screening criteria than Bayesian BWM (without G8 and I2). This is because AHP and BWM use arithmetic averages when integrating experts' opinions. This method is vulnerable to the influence of extreme values, resulting in the loss of some information. In contrast, Bayesian BWM, which pays extra consideration for G8 and I2, makes the influential relationship system

of the criteria more complete. It must be noted here that I2 and G8 are important affecting and affected factors in the analysis of rough DEMATEL.

#### *4.2. Obtaining the Cause-and-E*ff*ect Diagram by Using Rough DEMATEL*

The implementation process of rough DEMATEL is explained in Section 3.2. The data of 10 experts' surveys are calculated according to this process to obtain the rough influence degree of each criterion, as shown in Table 6.


**Table 6.** Sum of the defuzzification of rough influences given and received by criteria.

The consensus degree of the experts can be viewed by average sample gap index ((*n*(*<sup>n</sup>* <sup>−</sup> <sup>1</sup>))−<sup>1</sup> <sup>×</sup> *n i*=1 *n j*=1 *t p ij* − *t p*−1 *ij* /*t p ij* × 100%), where *n* is the number of samples, *p* is the number of experts and *t* is the evaluation value in the matrix. Based on this index, the average gap of the 10 experts is 4.8%, which means the confidence level is 95.2%, indicating that these experts have a high degree of consensus.

Table 6 shows the total influence (*s*˜*<sup>i</sup>* + *o*˜*i*) and net influence (*s*˜*<sup>i</sup>* − *o*˜*i*) for all criteria. The larger *s*˜*<sup>i</sup>* − *o*˜*i*, the greater the degree to which this criterion affects other criteria. In addition, *s*˜*<sup>i</sup>* + *o*˜*<sup>i</sup>* can indicate the total influence in the overall evaluation system to show the proportion of importance. We use *s*˜*<sup>i</sup>* + *o*˜*<sup>i</sup>* as the horizontal axis and *s*˜*<sup>i</sup>* − *o*˜*<sup>i</sup>* as the vertical axis to draw the cause-and-effect diagram of the criteria, as shown in Figure 2.

This approach allows policy-makers to quickly understand which criteria are the main causes and which are the effects to support the formulation of an appropriate management strategy. In Figure 2, the upper-right criteria indicate a high total influence and net influence, which are the main causes. In contrast, the lower-left criteria indicate lower total and net influences, which are the effects. Obviously, I4 is the most important affecting factor for cities to promote sustainable sports tourism and the rest are E7, I7, E5 and I2. In addition, G4, G8, S7 are the factors most affected by other criteria. The management implications derived from rough DEMATEL's analysis are discussed in Section 5.

**Figure 2.** Cause-and-effect diagram of criteria.

#### **5. Discussion**

Sports will positively change a person's physical fitness and mental state [30,31]. The awakening of the consciousness of "sports for all" has forced major cities to invest resources to host sports events and thus shape the image of the sports cities. In order to achieve sustainable urban development, economic, social and environmental aspects are the main evaluation dimensions [8,9,24,32]. Many publications from the literature advocate the importance of institutional substantiality, so this study includes the institutional aspect as one of the evaluation dimensions to make the evaluation structure more comprehensive. By reviewing the literature and integrating the opinions of multiple experts, an evaluation system for sustainable urban tourism development was established. However, it is important to understand those criteria and to explore their mutual influential relationships. To our knowledge, these issues have not been studied and discussed.

This study proposes a two-stage MCDM decision model. Bayesian BWM is used to determine the importance weights of the criteria and rough DEMTAEL is used to identify the mutual influential relationships of the important criteria. The studies of Mohammadi and Rezaei [17] and Yang et al. [24] point out that Bayesian BWM solves the problem of integrating expert opinions for the conventional BWM and obtains a set of optimal group criteria weights. This study reduced 30 evaluation criteria to 16, which are relatively important criteria for measuring the performance of sustainable sports tourism. In terms of the Social (S) dimension, maintaining the quality of urban public order (S8) is the most important criterion in the evaluation system, with a weight of 0.223. This result echoes the findings of Gkoumas [22] and Musavengane et al. [23], where they mentioned that public order in the region affects the safety of the tourists. Some famous tourist attractions have had negative incidents, including theft, robbery, scams, traffic accidents, viral infections and racial discrimination. Before large-scale sports events are held, public security management must be strengthened and rigorous planning and control of personnel entry and exit to ensure passenger confidence in safety. In terms of the institutional (I) dimension, the development efficiency of sports tourism depends on the marketing and promotion by local governments (I7). In order to prevent urban tourism from falling into the off-season, periodic events should be organized to maintain the stability of the number of tourists. Sponsorship and support from local businesses (E5) is the most important criterion in the Economic (E) dimension. It is not difficult to understand that business sponsorship often brings more and more resources to sports activities. The sponsors and the organizers can achieve a win-win result by mutual benefit; for the participants, they can further understand the sponsor brands and

experience their products. When it comes to environmental protection (G), planning for the city's mass transit system (G6) helps reduce the city's transportation carbon emissions and noise. At present, many environmental sports events have promoted zero-pollution itineraries. The measures include using electric vehicles, not using plastic materials and using recyclable containers.

Rough DEMATEL maps out the main causes and effects. The promotion of sustainable sports tourism in the cities must particularly focus on the following criteria: In conjunction with festivals in the city (I4), increasing the number of visits to the attractions in the city (E7), marketing and promotion by local governments (I7), sponsorship and support by local businesses (E5) and maintenance of the urban tourism website (I2). These criteria will affect the performance of other criteria. This result echoes the management implications of many studies, including Pouder et al. [3], Huang et al. [18], Lee and Xue [9] and Yang et al. [24]. The government must pay special attention to the performance of these five criteria. In order to allow the public to understand that the city is promoting sports tourism plans, print and online media promotion should be strengthened; sports events should be organized in conjunction with festivals. Business sponsorship also helps to increase the spread of sports ethos and makes the implementation of sports tourism plans more effective. In addition, for restrictions on plastic materials (G4), monitoring the quality of drinking water (G8) and formulating procedures for handling emergencies (S7), they require the development of other criteria to achieve high performance. The development of sports tourism in the city is a complex and difficult project: continuous simulation and review are required to make subsequent sports events more successful.

#### **6. Conclusions**

In summary, the two-stage evaluation model proposed in this study provides a complete and systematic method, providing the management implications of the development of sports tourism in the cities. This effective soft calculation method can reduce the subjectivity of management decisions. The academia has not yet studied and explored the mutual influential relationships among the criteria for sustainable sports tourism. Our model integrates several state-of-the-art methods and takes into account a variety of realistic factors, including the consideration of message uncertainty and the introduction of the concept of rough set theory.

It is well known that sports bring many benefits to people's physiology and psychology. The spirit of sustainability has brought into the sports tourism industry the purpose of accelerating the expansion of the "sports for all". This study proves the effectiveness and reliability of the proposed model. It should bring several benefits to practitioners and sports-related sectors: (i) identifying the most important and influential criteria; (ii) providing an improved basis for urban development sports tourism; (iii) helping decision-makers in the decision-making process to be more systematic.

In the future, researchers can further investigate the quantitative data of the actual assessment, making the evaluation results more accurate. Beyond that, using Bayesian BWM for cross-dimensional criteria comparison can entail more discussion.

**Author Contributions:** J.-J.Y. collected the data and wrote the paper. Y.-C.C. and H.-W.L. designed the research, administrated the project and verified the model. T.-I.L. co-wrote and revised the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** All authors declare that they have no conflict of interests.

#### **References**


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International Journal of *Environmental Research and Public Health*
