# Study on Evaluation of Leisure Diving Tourism Based on Fuzzy Comprehensive Method Optimized Bat Algorithm

Authors: Jin Sun
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

China’s leisure diving tourism has made gratifying achievements in the past years. It is necessary to evaluate the leisure diving tourism’s development level, and then the disadvantages of the leisure diving tourism can be found and the effective measures can be taken to develop the leisure diving tourism in China. A fuzzy comprehensive evaluation model based on the bat algorithm is proposed to solve the shortcomings of the fuzzy comprehensive evaluation method, which lacks a theoretical basis and completely depends on experience. Firstly, the basic conception of leisure diving tourism is discussed. Also, the main affecting factors of leisure diving tourism are analyzed. The evaluation model of leisure diving tourism developing level is constructed based on the fuzzy comprehensive method. The weight of the fuzzy comprehensive evaluation method is optimized by the bat algorithm to realize the optimal selection of weight. The fuzzy evaluation matrix is used to construct the judgment matrix to determine the weight of each evaluation index, and the bat algorithm is used to adaptively select the weight of the judgment matrix. Finally, three diving clubs are used as research objects to carry out evaluation analysis The results show that the fuzzy comprehensive evaluation method can effectively obtain the developing level of leisure diving tourism.


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## Body

## 1. Introduction

Diving is often accompanied by people’s tourism activities, which is more obvious in China. Since the establishment of the China International Diving Club in 1995, China’s leisure diving started. Diving has become a fashionable and healthy sport and is deeply loved by people. In recent years, China’s leisure diving tourism has developed rapidly. At present, diving clubs in China are widely distributed all over the country.In China, more than 1.5 million tourists participate in experiential diving every year. The main diving resorts in China are Sanya in Hainan, Qiandao Lake in Zhejiang Province, and Changdao in Shandong Province. Sanya has developed into one of the largest experiential diving bases in the world. The island attracts millions of tourists every year. In the peak season, it receives about 1500 diving tourists a day. In the off-season, it also keeps the daily number of 300 to 400. Diving has gradually become one of the most distinctive tourism products in Sanya. The existing diving companies and clubs are all concentrated in Sanya and Lingshui waters. There were about 1.4 million people diving in the sea and nearly 3000 people holding certificates and working as diving coaches in Sanya [1].But at the same time, it should be noted that there are many problems in China’s leisure diving tourism projects, such as unreasonable planning and layout and low professional quality of employees. However, in the face of the continuous development of leisure diving tourism, there is a lack of a relatively systematic grading evaluation system to score its development status. Therefore, it is urgent to formulate relevant grading evaluation standards to guide its steady and healthy development [2, 3].In order to promote the development of leisure diving tourism, an effective evaluation method should be selected. The fuzzy comprehensive evaluation method is an effective evaluation tool. It has been applied in many fields. This research constructs the framework of the leisure diving tourism development level evaluation system, determines the weight of the leisure diving tourism development level index by AHP, and evaluates different links in the development process of leisure tourism with the fuzzy comprehensive evaluation method, so as to find out the weak links in the development process of leisure diving tourism for improvement. At present, the weight of the evaluation index of the fuzzy comprehensive evaluation method is mainly determined by experience and lacks a scientific theoretical basis. The bat algorithm (BA) is introduced into fuzzy comprehensive evaluation, and a fuzzy comprehensive evaluation model based on the bat algorithm is proposed. The weight of the evaluation index is adaptively selected through the bat algorithm [4, 5]. This research first proposed an intelligent evaluation method for leisure diving tourism based on the fuzzy comprehensive method and the bat algorithm. The bat algorithm is an effective way to search for the global optimal solution and the accuracy of the bat algorithm is much better than that of other algorithms. Therefore, The evaluation accuracy and efficiency of leisure diving tourism; the evaluation results can provide favorable basis for improving the quality of leisure diving tourism.


## 2. Leisure Diving Tourism Based on the Fuzzy Comprehensive Method and the Bat Algorithm

### 2.1. Basic Conception of Leisure Diving Tourism

Leisure diving is a kind of underwater entertainment activity that has been rising in the past 50 years. It includes underwater tourism, underwater photography, underwater shooting, and exploratory cave diving and ice diving. It is a comprehensive sports event integrating appreciation, entertainment, and tourism under the water. It is a sports and entertainment activity that has risen all over the world. Experiential leisure diving refers to the cooperation between diving companies and travel agencies, which are responsible for attracting tourists, and diving companies are responsible for experiencing diving [6].Leisure diving is mainly for team diving tourists as the service object. Compared with other forms, this way is the cheapest. And the leisure diving of tourism is summarized, and it has been pointed out that leisure diving is only a part of the whole tourism.The main influencing factors of leisure diving tourism development in China are listed as follows.


### 2.2. Management Standard of Leisure Tourism Industry

In China, diving is often combined with tourism, and the cost of diving is often tied with travel expenses. In the process of diving, there will be problems in tourism activities, such as forced consumption of tourists, bad service attitude, no protection of rights, and so on. Such as China’s diving resort and tourist Mecca, Hainan. With the rapid development of diving tourism, there are many problems with nonstandard management. In 2012, it was complained by the netizens that the diving spots on the island of Demarcation Island in Hainan were complained by netizens: they forced tourists to spend in disguised form; the diving spots on Wuzhizhou Island in Sanya were filmed by netizens to complain about the underwater photography of “digging people,” and the service attitude was bad. After these phenomena were exposed, netizens’ collective complaints against Hainan diving spots were triggered. Other diving spots in Hainan were also named and complained about by netizens due to high charges, forced tourists’ consumption, poor service, and kickbacks. These problems have seriously hindered the rapid development of diving tourism [7, 8].


### 2.3. Supervision

At present, domestic recreational diving operators generally pay attention to economic interests and ignore the safety of divers. Because of the unpredictable sea environment, diving equipment is not repaired or updated in time, which makes it very easy to cause safety accidents. Especially in the peak season, each diver brings too many tourists every day, which is also easy to cause diving accidents. In addition, the state has not yet issued the corresponding laws and regulations on the management of diving clubs, and there is no specific supervision and management method. Although some places have promulgated local regulations on the management of diving clubs, many problems are still unclear, and the enforcement of laws and regulations is not enough.


### 2.4. Awareness of Environmental Protection

Diving also has serious environmental protection problems, and people’s awareness of ecological protection is not enough in the whole development environment. Most Chinese diving tourists do not have a strong sense of protection, and most of them practice “savage diving.” In the process of diving, people often dig out small pieces of coral as a “memorial” for diving or touch the living coral with their hands, which will have a significant impact on the growth and development of corals. Now, the development of the underwater walk project has done greater damage to the seabed ecological environment. Because of the degradation of the ecological environment of coral reefs in some areas of Hainan, the seafloor scenery is not as good as before [9].


### 2.5. Leisure Diving Spot Project

At present, due to climate factors, the potential diving spots for leisure diving in China are very limited. They are mainly concentrated in the southern area. There are more famous cities such as Sanya, the Paracel Islands, Dry Island Lake, and Dong’ao Island. There are also some diving spots in the north, which are well developed, such as Beidaihe, Penglai, Weihai, and Qingdao. It is the diving point in the north, which is limited by season and climate, and the suitable time for diving is relatively short. In addition, many diving resorts in China have not been effectively developed for various reasons. Moreover, the types of recreational diving projects in China are relatively small, and the projects in different regions are similar, which seriously restricts the development of leisure diving in China.


## 2.1. Basic Conception of Leisure Diving Tourism

Leisure diving is a kind of underwater entertainment activity that has been rising in the past 50 years. It includes underwater tourism, underwater photography, underwater shooting, and exploratory cave diving and ice diving. It is a comprehensive sports event integrating appreciation, entertainment, and tourism under the water. It is a sports and entertainment activity that has risen all over the world. Experiential leisure diving refers to the cooperation between diving companies and travel agencies, which are responsible for attracting tourists, and diving companies are responsible for experiencing diving [6].Leisure diving is mainly for team diving tourists as the service object. Compared with other forms, this way is the cheapest. And the leisure diving of tourism is summarized, and it has been pointed out that leisure diving is only a part of the whole tourism.The main influencing factors of leisure diving tourism development in China are listed as follows.


## 2.2. Management Standard of Leisure Tourism Industry

In China, diving is often combined with tourism, and the cost of diving is often tied with travel expenses. In the process of diving, there will be problems in tourism activities, such as forced consumption of tourists, bad service attitude, no protection of rights, and so on. Such as China’s diving resort and tourist Mecca, Hainan. With the rapid development of diving tourism, there are many problems with nonstandard management. In 2012, it was complained by the netizens that the diving spots on the island of Demarcation Island in Hainan were complained by netizens: they forced tourists to spend in disguised form; the diving spots on Wuzhizhou Island in Sanya were filmed by netizens to complain about the underwater photography of “digging people,” and the service attitude was bad. After these phenomena were exposed, netizens’ collective complaints against Hainan diving spots were triggered. Other diving spots in Hainan were also named and complained about by netizens due to high charges, forced tourists’ consumption, poor service, and kickbacks. These problems have seriously hindered the rapid development of diving tourism [7, 8].


## 2.3. Supervision

At present, domestic recreational diving operators generally pay attention to economic interests and ignore the safety of divers. Because of the unpredictable sea environment, diving equipment is not repaired or updated in time, which makes it very easy to cause safety accidents. Especially in the peak season, each diver brings too many tourists every day, which is also easy to cause diving accidents. In addition, the state has not yet issued the corresponding laws and regulations on the management of diving clubs, and there is no specific supervision and management method. Although some places have promulgated local regulations on the management of diving clubs, many problems are still unclear, and the enforcement of laws and regulations is not enough.


## 2.4. Awareness of Environmental Protection

Diving also has serious environmental protection problems, and people’s awareness of ecological protection is not enough in the whole development environment. Most Chinese diving tourists do not have a strong sense of protection, and most of them practice “savage diving.” In the process of diving, people often dig out small pieces of coral as a “memorial” for diving or touch the living coral with their hands, which will have a significant impact on the growth and development of corals. Now, the development of the underwater walk project has done greater damage to the seabed ecological environment. Because of the degradation of the ecological environment of coral reefs in some areas of Hainan, the seafloor scenery is not as good as before [9].


## 2.5. Leisure Diving Spot Project

At present, due to climate factors, the potential diving spots for leisure diving in China are very limited. They are mainly concentrated in the southern area. There are more famous cities such as Sanya, the Paracel Islands, Dry Island Lake, and Dong’ao Island. There are also some diving spots in the north, which are well developed, such as Beidaihe, Penglai, Weihai, and Qingdao. It is the diving point in the north, which is limited by season and climate, and the suitable time for diving is relatively short. In addition, many diving resorts in China have not been effectively developed for various reasons. Moreover, the types of recreational diving projects in China are relatively small, and the projects in different regions are similar, which seriously restricts the development of leisure diving in China.


## 3. Evaluation Model Based on the Fuzzy Comprehensive Evaluation Method and the Bat Algorithm

### 3.1. Fuzzy Comprehensive Evaluation Method

The main features of the fuzzy analytic hierarchy process are to solve the uncertainty affected by the evaluated object, decompose the problem level by level, and study the evaluation object through fuzzy mathematics. The analytic hierarchy process (AHP) is a qualitative thinking method. The use of AHP can help people make the correct decisions through analysis. And it can be used as a complex research object to form a system, analyze each element in the system and the correlation between elements, and finally want to get the results to help people make correct decisions [10].The fuzzy comprehensive evaluation method is used to analyze the multiple evaluation factors of the evaluation object, and the evaluation process and evaluation data are reused many times. In many complex cases, we decompose them step by step. Fuzzy comprehensive evaluation is a kind of fuzzy treatment of the influencing factors of complex research objects. It can carry out quantitative research on qualitative indicators and systematically and comprehensively evaluate the objects. The fuzzy comprehensive evaluation method can evaluate not only the subjective consciousness but also quantitative data analysis and evaluation and can be measured by different degrees of evaluation, so they have strong applicability. The subjective consciousness of the impact on the research object and the influence of many factors [11].The main idea of the fuzzy analytic hierarchy process is to find out various main factors through the characteristics of evaluation problems and construct the evaluation model according to their mutual relationship and subordinate relationship. In other words, first put forward an overall evaluation scheme, then decompose each evaluation index of the evaluation scheme level by level, determine the weight coefficient of each factor at the same evaluation level by comparison, establish an effective evaluation model, and finally determine the membership of each scheme index by the fuzzy comprehensive evaluation method to evaluate the final scheme effect.The fuzzy hierarchy evaluation realizes the synthesis of each evaluation index through quantitative graded fuzzy subset and fuzzy transformation. The specific steps are as follows:Step 1.
Determine the factor domain of the evaluation object. The evaluation index collections of leisure diving tourism are listed as follows [12].
The first level collection is(1)U=u1u2u3u4.
The second level collections are listed as follows:(2)u1=u11u12u13u14,u2=u21u22u23u24,u3=u31u32u33,u4=u41u42u43.Step 2.
Determine the comment level domain, that is, the level set. According to the development level of leisure diving tourism, it is divided into several grades, and the evaluation set formula is as follows [13]:(3)V=V1,V2,V3,V4,where V1 is I grade, the developing level of leisure diving tourism is excellent, V2 is II grade, the developing level of leisure diving tourism is good, V3 is III grade, the developing level of leisure diving tourism is medium, and V4 is IV grade, the developing level of leisure diving tourism is poor.
It is assumed that the distribution curves of membership functions obey the lower half trapezoid distribution. The parameters of the membership degree function are expressed by [13](4)μ1=1,x<S1,S2−xS2−S1,S1≤x≤S2,0,x≥S2,μ2=0,x<S1,x>S3,x−S1S2−S1,S1≤x≤S2,S3−xS3−S2,S2≤x≤S3,μ3=0,x≤S2,x>S4,x−S2S3−S2,S2≤x≤S3,S4−xS4−S3,S3≤x≤S4,μ4=0,x≤S3,x−S2S3−S2,S2<x≤S3,1,x>S4.Step 3.
Establish the fuzzy relation matrixR and determine the membership degree R|ui of the hierarchical fuzzy subset. The fuzzy relation matrix R can be expressed as [14](5)R=r11r12⋯r1nr21r22⋯r2n⋮⋮⋱⋮rp1rp2⋯rpn.
The fuzzy relation matrices of leisure diving tourism evaluation are listed as follows [15]:(6)R1=i1x11i2x11i3x11i1x12i2x12i3x12i1x13i2x13i3x13i1x14i2x14i3x14,R2=i1x21i2x21i3x21i1x22i2x22i3x22i1x23i2x23i3x23i1x24i2x24i3x24,R3=i1x31i2x31i3x31i1x32i2x32i3x32i1x33i2x33i3x33,R3=i1x41i2x41i3x41i1x42i2x42i3x42i1x43i2x43i3x43.Step 4.
Determine the weight vector of evaluation factorsA=a1,a2,…,ap.Step 5.
Fuzzy comprehensive evaluation result vector is generated.
The synthetic operator operation ofa and fuzzy relation matrix R is carried out to obtain the fuzzy comprehensive evaluation result vector B of the evaluated object. The comprehensive evaluation vector is calculated by [16](7)A⋅R=b1,b2,…,bm,where b1 represents the membership degree of the evaluated object of the vj grade fuzzy subset as a whole.Step 6.
Analyze the result vector of fuzzy comprehensive evaluation.


### 3.2. Bat Algorithm

The bat algorithm (BA) is a bionic optimization algorithm proposed by Yang et al. according to the echolocation principle of bats in nature and their behaviors of preying on prey, avoiding danger and obstacles, and looking for hiding places. The bat algorithm is a new optimization algorithm rising in recent years. Its mechanism is easy to understand. After mathematical induction, there is only a small amount of parameter information such as frequency, speed, and position. The bat algorithm has a simpler structure than other intelligent algorithms, but its search ability is stronger, and the algorithm mechanism is easier to implement. Suppose that the frequency of sound waves emitted by bats has an upper and lower limit (fmin,fmax), bats can adjust the pulse emission frequency according to the distance and size of the prey/obstacle (λf=v, λ is adjusted according to the size of obstacles/prey). When close to prey or obstacles, the frequency of sound waves increases and the responsiveness decreases. The closer the pulse emissivity is to 1, the faster the pulse is sent, and the closer the response is to 0, indicating that the closer to the prey, the weaker the sound [17].The hunting behavior of bats can be simplified into the following criteria:(1)
All bats use the principle of echolocation to judge the distance from their prey and can accurately distinguish the prey from obstacles and dangerous objects(2)
Each bat flies at any speedv at position s, at a fixed wavelength λ, variable frequency f, loudness A, and pulse emissivity r to search prey and avoid obstacles(3)
Although there are many ways to transform the responsiveness, here we assume that its variation range has upper and lower limits, which are (Amin,Amax), and that the responsiveness is positiveInD-dimensional space, the location sit and velocity vit update formula of the position of the i th bat at time t are as follows [18]:(8)fi=fmin+αfmax−fmin,vit+1=vit+fisit−s∗,sit+1=sit+vit+1,where α is random variable ranging from 0 to 1, which serves as the mean distribution. s∗ is the global optimal position after comparing all local optimal values.For the local search part, when a solution is selected as the current optimal solution, the new solution is generated by the following random walk method:(9)sit+1=sit+β⋅Aavet,where β is random variable ranging from 0 to 1, which serves as the mean distribution. Aavet is the average responsiveness of bats at each iteration t.The updated formulas of the bat’s responsiveness and pulse emissivity are as follows [19]:(10)Ait+1=εAit,rit+1=ri01−e−γt,where ε and γ are constants.


### 3.3. Computing Model of Weight

In order to realize the high-precision quality grade determination of the fuzzy comprehensive evaluation method, a mathematical model of the bat algorithm optimizing the weight factor of fuzzy comprehensive evaluation has been established [20]:(11)fωi=min∑i=1m∑j=1myij−ωijxij,s.t.∑i=1mωi=1,ωi≥0,i=1,2,…,m,where xij represents the scores of different evaluation indexes, ωij represents the weights of different indexes, and yij represents the scores of comprehensive evaluation grades. Under the condition of ensuring the minimum error of fuzzy comprehensive evaluation, the optimal selection of weight ωij is realized through the optimization of bat algorithm.The process of fuzzy comprehensive evaluation based on the bat optimization is as follows:Step 1: Normalize the evaluation index data and construct the fuzzy evaluation matrix of leisure diving tourism [21].Step 2: Set parameters of the bat algorithm: the population sizeN, the searching pulse range fmin,fmax, pulse velocity r0, the maximum sound response A0, the initial location of the bat Xii=1,2,…,N, the pulse velocity enhancement coefficient γ, and the response attenuation coefficient α.Step 3: Calculate the fitness of the objective function: calculate the fitness of each individual in the bat population according to the objective function [22].Step 4: Determine whether the termination conditions of the algorithm are met. If so, output the optimal weightωij j for the fuzzy comprehensive evaluation of leisure diving tourism levels; if the termination conditions are not met, proceed to step 5.Step 5: A new solution is generated by adjusting the frequency, and the bat speed and position are updated [23];Step 6: Determine whether to accept the new solution: If yes, proceed to step 7. On the contrary, turn back to process Step 5.Step 7: Update the response and transmission frequency and go back to process step 3.


### 3.4. Case Study

In order to verify the effectiveness of the proposed evaluation model, three diving clubs were selected to carry out simulation results.When constructing the index system, we should objectively reflect the connotation of leisure diving tourism and also better and truly study the development level of leisure diving tourism. When selecting and studying the comprehensive evaluation index of leisure diving tourism, we must take the leisure tourism theory as the basis, take the international and domestic leisure tourism practice as the guidance, and draw lessons from the research of domestic authoritative scholars in relevant fields to build a comprehensive and objective evaluation system of leisure diving tourism. The setting of indicators should be as easy to quantify as possible, and the indicators themselves should be more representative, that is, use as few indicators as possible to include as much leisure diving tourism information as possible, as well as the difficulty of index data collection, so as to make the evaluation index system scientific, comprehensive, and easy to operate. The evaluation index system of leisure diving tourism's developing level is designed according to the main influence factors of it, which are listed in Table1.Table 1
Evaluation index system of leisure diving tourism developing level.
First level indexSecond level indexManagement standard of leisure tourism industry I1Diving fee rule I11Travel rule I12Service attitude management I13Protection of tourists' rights I14Supervision I2Safety of divers I21Maintenance or renewal of diving equipment I22Diving accident management I23Diving club management regulations I24Awareness of environmental protection I3Scuba diving I31Dig small pieces of coral I32Touch the living coral I33Leisure diving spot project I4Number of diving spots for leisure diving I41Development of diving resorts I42Types of leisure diving events I43Based on the principle of fuzzy mathematics, the fuzzy comprehensive evaluation method is a multiple factor decision-making method that comprehensively evaluates the system affected by many factors. It can effectively quantify the fuzziness of the system description by means of a fuzzy set.This research uses a 1–7 scale analytic hierarchy process to determine the weight of the leisure diving tourism development level. According to the importance comparison and scoring of the indicators at the same level in the evaluation index system of the development level of leisure tourism diving tourism, 30 experts were invited to score.The judgment matrixA of the first level index is expressed by(12)A=141/531/411/3353161/31/31/61.The judgment matrices of second level index are listed as follows:(13)A1=161/341/611/5435171/41/41/71,A2=131/231/311/7627151/31/61/51,A3=1541/51641/61,A4=1751/71351/31.Using MATLAB software to process the data, if the consistency test index CR of the expert scoring judgment matrix is less than 0.1, that is, the consistency is effective, then the expert's scoring is acceptable, and the index weight calculated by the expert's judgment matrix is considered in the weight average calculation. Otherwise, if the CR of the expert's score is greater than or equal to 0.1, the expert’s score is invalid, and the score is not considered in the calculation of the average weight of the index.The weights of the first and second level indicators are as follows:(14)W=0.2100.1120.6130.065,W1=0.180.3120.4320.076,W2=0.260.2970.3310.112,W3=0.220.430.35,W4=0.190.540.27.The evaluation results are listed in Table2.Table 2
Evaluation results of 4 diving clubs.
Number of diving clubsMaximum membership degree of evaluation vectorEvaluation level10.853Excellent20.699Good30.531MediumAs seen from Table2, the leisure diving tourism of the first diving club is best, and the leisure diving tourism of the third diving club is worst. Therefore, the third diving club should learn the effective experience from the first diving club. Therefore, the effective methods of diving club 1 can provide a basis for other clubs.In order to verify the effectiveness of the proposed method, the particle swarm algorithm and genetic algorithm are also used to analyze the same problem, and the analysis results are listed in Table3.Table 3
Comparison results of different algorithms.
AlgorithmEvaluation precision (%)Evaluation time (s)Bat algorithm95.446Particle swarm algorithm86.798Genetic algorithm79.4104As seen from Table3, the bat algorithm has higher evaluation precision and efficiency than the particle swarm algorithm and genetic algorithm, therefore it can be applied to leisure diving tourism with better effect.


## 3.1. Fuzzy Comprehensive Evaluation Method

The main features of the fuzzy analytic hierarchy process are to solve the uncertainty affected by the evaluated object, decompose the problem level by level, and study the evaluation object through fuzzy mathematics. The analytic hierarchy process (AHP) is a qualitative thinking method. The use of AHP can help people make the correct decisions through analysis. And it can be used as a complex research object to form a system, analyze each element in the system and the correlation between elements, and finally want to get the results to help people make correct decisions [10].The fuzzy comprehensive evaluation method is used to analyze the multiple evaluation factors of the evaluation object, and the evaluation process and evaluation data are reused many times. In many complex cases, we decompose them step by step. Fuzzy comprehensive evaluation is a kind of fuzzy treatment of the influencing factors of complex research objects. It can carry out quantitative research on qualitative indicators and systematically and comprehensively evaluate the objects. The fuzzy comprehensive evaluation method can evaluate not only the subjective consciousness but also quantitative data analysis and evaluation and can be measured by different degrees of evaluation, so they have strong applicability. The subjective consciousness of the impact on the research object and the influence of many factors [11].The main idea of the fuzzy analytic hierarchy process is to find out various main factors through the characteristics of evaluation problems and construct the evaluation model according to their mutual relationship and subordinate relationship. In other words, first put forward an overall evaluation scheme, then decompose each evaluation index of the evaluation scheme level by level, determine the weight coefficient of each factor at the same evaluation level by comparison, establish an effective evaluation model, and finally determine the membership of each scheme index by the fuzzy comprehensive evaluation method to evaluate the final scheme effect.The fuzzy hierarchy evaluation realizes the synthesis of each evaluation index through quantitative graded fuzzy subset and fuzzy transformation. The specific steps are as follows:Step 1.
Determine the factor domain of the evaluation object. The evaluation index collections of leisure diving tourism are listed as follows [12].
The first level collection is(1)U=u1u2u3u4.
The second level collections are listed as follows:(2)u1=u11u12u13u14,u2=u21u22u23u24,u3=u31u32u33,u4=u41u42u43.Step 2.
Determine the comment level domain, that is, the level set. According to the development level of leisure diving tourism, it is divided into several grades, and the evaluation set formula is as follows [13]:(3)V=V1,V2,V3,V4,where V1 is I grade, the developing level of leisure diving tourism is excellent, V2 is II grade, the developing level of leisure diving tourism is good, V3 is III grade, the developing level of leisure diving tourism is medium, and V4 is IV grade, the developing level of leisure diving tourism is poor.
It is assumed that the distribution curves of membership functions obey the lower half trapezoid distribution. The parameters of the membership degree function are expressed by [13](4)μ1=1,x<S1,S2−xS2−S1,S1≤x≤S2,0,x≥S2,μ2=0,x<S1,x>S3,x−S1S2−S1,S1≤x≤S2,S3−xS3−S2,S2≤x≤S3,μ3=0,x≤S2,x>S4,x−S2S3−S2,S2≤x≤S3,S4−xS4−S3,S3≤x≤S4,μ4=0,x≤S3,x−S2S3−S2,S2<x≤S3,1,x>S4.Step 3.
Establish the fuzzy relation matrixR and determine the membership degree R|ui of the hierarchical fuzzy subset. The fuzzy relation matrix R can be expressed as [14](5)R=r11r12⋯r1nr21r22⋯r2n⋮⋮⋱⋮rp1rp2⋯rpn.
The fuzzy relation matrices of leisure diving tourism evaluation are listed as follows [15]:(6)R1=i1x11i2x11i3x11i1x12i2x12i3x12i1x13i2x13i3x13i1x14i2x14i3x14,R2=i1x21i2x21i3x21i1x22i2x22i3x22i1x23i2x23i3x23i1x24i2x24i3x24,R3=i1x31i2x31i3x31i1x32i2x32i3x32i1x33i2x33i3x33,R3=i1x41i2x41i3x41i1x42i2x42i3x42i1x43i2x43i3x43.Step 4.
Determine the weight vector of evaluation factorsA=a1,a2,…,ap.Step 5.
Fuzzy comprehensive evaluation result vector is generated.
The synthetic operator operation ofa and fuzzy relation matrix R is carried out to obtain the fuzzy comprehensive evaluation result vector B of the evaluated object. The comprehensive evaluation vector is calculated by [16](7)A⋅R=b1,b2,…,bm,where b1 represents the membership degree of the evaluated object of the vj grade fuzzy subset as a whole.Step 6.
Analyze the result vector of fuzzy comprehensive evaluation.


## 3.2. Bat Algorithm

The bat algorithm (BA) is a bionic optimization algorithm proposed by Yang et al. according to the echolocation principle of bats in nature and their behaviors of preying on prey, avoiding danger and obstacles, and looking for hiding places. The bat algorithm is a new optimization algorithm rising in recent years. Its mechanism is easy to understand. After mathematical induction, there is only a small amount of parameter information such as frequency, speed, and position. The bat algorithm has a simpler structure than other intelligent algorithms, but its search ability is stronger, and the algorithm mechanism is easier to implement. Suppose that the frequency of sound waves emitted by bats has an upper and lower limit (fmin,fmax), bats can adjust the pulse emission frequency according to the distance and size of the prey/obstacle (λf=v, λ is adjusted according to the size of obstacles/prey). When close to prey or obstacles, the frequency of sound waves increases and the responsiveness decreases. The closer the pulse emissivity is to 1, the faster the pulse is sent, and the closer the response is to 0, indicating that the closer to the prey, the weaker the sound [17].The hunting behavior of bats can be simplified into the following criteria:(1)
All bats use the principle of echolocation to judge the distance from their prey and can accurately distinguish the prey from obstacles and dangerous objects(2)
Each bat flies at any speedv at position s, at a fixed wavelength λ, variable frequency f, loudness A, and pulse emissivity r to search prey and avoid obstacles(3)
Although there are many ways to transform the responsiveness, here we assume that its variation range has upper and lower limits, which are (Amin,Amax), and that the responsiveness is positiveInD-dimensional space, the location sit and velocity vit update formula of the position of the i th bat at time t are as follows [18]:(8)fi=fmin+αfmax−fmin,vit+1=vit+fisit−s∗,sit+1=sit+vit+1,where α is random variable ranging from 0 to 1, which serves as the mean distribution. s∗ is the global optimal position after comparing all local optimal values.For the local search part, when a solution is selected as the current optimal solution, the new solution is generated by the following random walk method:(9)sit+1=sit+β⋅Aavet,where β is random variable ranging from 0 to 1, which serves as the mean distribution. Aavet is the average responsiveness of bats at each iteration t.The updated formulas of the bat’s responsiveness and pulse emissivity are as follows [19]:(10)Ait+1=εAit,rit+1=ri01−e−γt,where ε and γ are constants.


## 3.3. Computing Model of Weight

In order to realize the high-precision quality grade determination of the fuzzy comprehensive evaluation method, a mathematical model of the bat algorithm optimizing the weight factor of fuzzy comprehensive evaluation has been established [20]:(11)fωi=min∑i=1m∑j=1myij−ωijxij,s.t.∑i=1mωi=1,ωi≥0,i=1,2,…,m,where xij represents the scores of different evaluation indexes, ωij represents the weights of different indexes, and yij represents the scores of comprehensive evaluation grades. Under the condition of ensuring the minimum error of fuzzy comprehensive evaluation, the optimal selection of weight ωij is realized through the optimization of bat algorithm.The process of fuzzy comprehensive evaluation based on the bat optimization is as follows:Step 1: Normalize the evaluation index data and construct the fuzzy evaluation matrix of leisure diving tourism [21].Step 2: Set parameters of the bat algorithm: the population sizeN, the searching pulse range fmin,fmax, pulse velocity r0, the maximum sound response A0, the initial location of the bat Xii=1,2,…,N, the pulse velocity enhancement coefficient γ, and the response attenuation coefficient α.Step 3: Calculate the fitness of the objective function: calculate the fitness of each individual in the bat population according to the objective function [22].Step 4: Determine whether the termination conditions of the algorithm are met. If so, output the optimal weightωij j for the fuzzy comprehensive evaluation of leisure diving tourism levels; if the termination conditions are not met, proceed to step 5.Step 5: A new solution is generated by adjusting the frequency, and the bat speed and position are updated [23];Step 6: Determine whether to accept the new solution: If yes, proceed to step 7. On the contrary, turn back to process Step 5.Step 7: Update the response and transmission frequency and go back to process step 3.


## 3.4. Case Study

In order to verify the effectiveness of the proposed evaluation model, three diving clubs were selected to carry out simulation results.When constructing the index system, we should objectively reflect the connotation of leisure diving tourism and also better and truly study the development level of leisure diving tourism. When selecting and studying the comprehensive evaluation index of leisure diving tourism, we must take the leisure tourism theory as the basis, take the international and domestic leisure tourism practice as the guidance, and draw lessons from the research of domestic authoritative scholars in relevant fields to build a comprehensive and objective evaluation system of leisure diving tourism. The setting of indicators should be as easy to quantify as possible, and the indicators themselves should be more representative, that is, use as few indicators as possible to include as much leisure diving tourism information as possible, as well as the difficulty of index data collection, so as to make the evaluation index system scientific, comprehensive, and easy to operate. The evaluation index system of leisure diving tourism's developing level is designed according to the main influence factors of it, which are listed in Table1.Table 1
Evaluation index system of leisure diving tourism developing level.
First level indexSecond level indexManagement standard of leisure tourism industry I1Diving fee rule I11Travel rule I12Service attitude management I13Protection of tourists' rights I14Supervision I2Safety of divers I21Maintenance or renewal of diving equipment I22Diving accident management I23Diving club management regulations I24Awareness of environmental protection I3Scuba diving I31Dig small pieces of coral I32Touch the living coral I33Leisure diving spot project I4Number of diving spots for leisure diving I41Development of diving resorts I42Types of leisure diving events I43Based on the principle of fuzzy mathematics, the fuzzy comprehensive evaluation method is a multiple factor decision-making method that comprehensively evaluates the system affected by many factors. It can effectively quantify the fuzziness of the system description by means of a fuzzy set.This research uses a 1–7 scale analytic hierarchy process to determine the weight of the leisure diving tourism development level. According to the importance comparison and scoring of the indicators at the same level in the evaluation index system of the development level of leisure tourism diving tourism, 30 experts were invited to score.The judgment matrixA of the first level index is expressed by(12)A=141/531/411/3353161/31/31/61.The judgment matrices of second level index are listed as follows:(13)A1=161/341/611/5435171/41/41/71,A2=131/231/311/7627151/31/61/51,A3=1541/51641/61,A4=1751/71351/31.Using MATLAB software to process the data, if the consistency test index CR of the expert scoring judgment matrix is less than 0.1, that is, the consistency is effective, then the expert's scoring is acceptable, and the index weight calculated by the expert's judgment matrix is considered in the weight average calculation. Otherwise, if the CR of the expert's score is greater than or equal to 0.1, the expert’s score is invalid, and the score is not considered in the calculation of the average weight of the index.The weights of the first and second level indicators are as follows:(14)W=0.2100.1120.6130.065,W1=0.180.3120.4320.076,W2=0.260.2970.3310.112,W3=0.220.430.35,W4=0.190.540.27.The evaluation results are listed in Table2.Table 2
Evaluation results of 4 diving clubs.
Number of diving clubsMaximum membership degree of evaluation vectorEvaluation level10.853Excellent20.699Good30.531MediumAs seen from Table2, the leisure diving tourism of the first diving club is best, and the leisure diving tourism of the third diving club is worst. Therefore, the third diving club should learn the effective experience from the first diving club. Therefore, the effective methods of diving club 1 can provide a basis for other clubs.In order to verify the effectiveness of the proposed method, the particle swarm algorithm and genetic algorithm are also used to analyze the same problem, and the analysis results are listed in Table3.Table 3
Comparison results of different algorithms.
AlgorithmEvaluation precision (%)Evaluation time (s)Bat algorithm95.446Particle swarm algorithm86.798Genetic algorithm79.4104As seen from Table3, the bat algorithm has higher evaluation precision and efficiency than the particle swarm algorithm and genetic algorithm, therefore it can be applied to leisure diving tourism with better effect.


## 4. Conclusions

Although there are more leisure diving tourists in China than anywhere else, and the annual growth rate is relatively high, there are also many problems. Leisure diving is almost experiential, and there are few clubs focusing on leisure diving talent training. The leisure diving tourism development level evaluation model is constructed based on the fuzzy comprehensive method and the bat algorithm. The weight factor of the fuzzy comprehensive evaluation method is optimized by Ba to realize the optimal selection of weight. The evaluation analysis was carried out for three diving clubs. The results show that the proposed evaluation model can effectively get the developing level of leisure diving tourism. The result of the bat optimized fuzzy comprehensive evaluation method is more in line with the actual situation and the effect is better. The bat algorithm should be improved in the future for improving the analysis accuracy and precision, and a more effective evaluation system of leisure diving tourism should be constructed.



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*Source: 9047644-2022-06-07.xml*