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BY 4.0 license Open Access Published by De Gruyter Open Access April 28, 2022

Attractiveness index of national marine parks: A study on national marine parks in coastal areas of East China Sea

  • Li Wang , Guodong Wang EMAIL logo , Xiaohong Hou , Zhiwei Chen and Kai Lu
From the journal Open Geosciences


Balancing the development and protection of national marine parks in a suitable way is of great SIGNIFICANCE for environmental sustainability. Tourism attractiveness is an important indicator for measuring this development. In this study, by searching through online reviews of the national marine parks in the coastal areas of the East China Sea, and by analyzing tourists’ perceptions of them, an indicator system for tourism attraction was established. Natural attributes, supporting facilities, service experience, and tours were taken as secondary indicators. This study combines the analytic hierarchy process with questionnaires to calculate the attractiveness index of national marine parks. The study finds that national marine parks in the coastal areas of the East China Sea have a higher level of tourist satisfaction and attractiveness, but that more attention needs to be paid to supporting facilities, as tourists currently find them insufficient. Among these, natural attributes are an important factor affecting the attractiveness of the marine parks, while special cuisine, customer experience, public transportation, and attitudes are all indicators with higher weight within the attractiveness index. The tourism attractiveness of national marine parks was investigated quantitatively and the indicators affecting the tourism attractiveness index were illustrated clearly.

1 Introduction

Tourism involves all aspects of people’s lives. The tourism industry is an indispensable part of the national economy and plays an important role in the economy. Especially in the context of the current pandemic, the sustainable development of the national economy in general, and tourism in particular, has become a subject of research for academics both at home and abroad [13]. Moreover, the development of tourism is not only an activity that brings economic benefits but also has an impact on the natural environment. The serious environmental damage caused by tourism will not only inhibit sustainable development but will also bring other negative effects. Therefore, we have repeatedly promoted the concept of ecological civilization to respect and protect Nature. The creation of an ecological civilization is fundamental to the sustainable development of the Chinese nation, while the building of an ecological marine civilization is an important part of national ecological civilization. National parks are one of the most important forms of environmental protection [4]. It is inevitable to establish a nature protection system based on national parks, and national marine parks are an important type of national parks. As a part of this, the protection of these parks is very important for developing the tourism sector, protecting the marine ecosystem, and safeguarding national sovereignty.

In order to better plan, construct, and protect national marine parks, ensuring the balance of their social, economic, and ecological environment and its swift recovery after the pandemic is of great significance to the prediction and evaluation of the attractiveness index [5,6]. At present, there is no consistent conclusion on the concept of tourism attractiveness, which is mainly defined from the perspective of supply and demand. The supply refers to the number of tourists attracted by tourism destinations; the demand perspective refers to tourists’ perception and interest in destination attributes. The investigation of national marine parks was mainly focused on the associated ticket prices [7], management plans [8], and policy control [911]. However, only a few studies have dealt with the attractiveness of national marine parks. The research on the attraction of national marine parks mainly centers on qualitative analysis, and the quantity is small and lacks quantitative analysis.

There are quite a lot of studies on the attractiveness of tourist destinations that include the regression model and the space-time model for predicting the characteristics of different tourists [12,13], the modeling of factors that influence attractiveness [14], and the attractiveness model based on the amount of scenery to offer. All of these are important methods for the study of attractiveness. Factors affecting the attractiveness of tourist destinations include tourist products, tourist resources, tourist motivation, environment, disposable income, sightseeing experiences, and infrastructure [1522]. The evaluation of the attractiveness of tourist destinations refers to the construction of an indicator system and quantification of influencing factors such as service facilities, safety, and hygiene of tourist destinations, tour guides, and entertainment options. The analytic hierarchy process (AHP) combined with the Rosenberg-Fishbein digital models is used to study the tourism development value of intangible cultural heritage [23]. The factor analysis method combined with AHP, a combination of multivariate data, kernel density, and spatial autocorrelation was used to study the spatial distribution pattern of rural tourism attractions [24,25].

Based on online reviews of national marine parks in the coastal areas of the East China Sea, this study analyzes the tourists’ image perception of the marine parks in order to obtain their image attributes. The East China Sea is one of the earliest marine reserve construction areas in China in which natural resources are diverse such as biological resources, island resources, landscape resources, and ecological systems. Combining the Delphi method with AHP, an indicator system for tourism attractiveness is established with natural attributes, supporting facilities, service experience, and tours taken as secondary indicators. Combined with the questionnaires, the attractiveness index is then calculated and the attractiveness of national marine parks in the coastal areas of the East China Sea, along with the factors that influence that attractiveness, can be evaluated.

2 Data sources and research methods

2.1 Data sources

2.1.1 Review data crawling

Review data for national marine parks in the coastal areas of the East China Sea was taken from the travel e-commerce platform – Ctrip. The data were gathered by a data acquisition unit before pre-processing was performed. For example, any introductions and repetitive descriptions of scenic spots would be deleted, along with prepositions, conjunctions, and meaningless words within the reviews, such as “because,” “then,” “so,” and “those”; words with the same meaning were merged. For example, “Small island” and “islands” were merged into “islands.” After data pre-processing, a total of 183 comments were provided. For detailed information on the data, please see Table 1.

Table 1

Information on the review data

Related attributes of comments Details
Collection method Data acquisition unit
Source Ctrip
Data content Review data of national marine parks in the coastal areas of the East China Sea
Numeric field Name, total score, user name, time, comments, and rating of the national marine park
Searching time range Jan 1st, 2016–April 20th, 2020
Number of comments after pre-processing 183

2.1.2 Survey data

Questionnaires were carried out through, and were based on such factors as tourists’ social attributes, travel activities, and the attractiveness of tourist destinations. The topics and options within the questionnaire were designed to be as reasonable and scientific as possible. Experts who study national marine parks helped design the questionnaire, and tourists who travel frequently were asked to provide suggestions and opinions. After repeated revisions and adjustments, the questionnaires were distributed to improve data quality. The questionnaires were distributed on March 21, 2020, and tourists could fill them out directly online. As of April 21, 2020, a total of 328 valid questionnaires were collected.

The formula for calculating the minimum sample size:

(1) n Z α 2 2 C 2 h 2 ,

n is the sample size, h is the relative sampling error, and C is the coefficient of variation. When the confidence level is 90% and the relative sampling error is 4%, the required minimum sample size is 271, and the sample size provided in this study is 328, which meets the requirements for the minimum sample size.

2.2 Research methods

2.2.1 Content analysis

Content analysis converts non-quantitative materials into quantitative data. This study analyzed the content of the review data. Through word frequency and semantic network analysis, the image perception of national marine parks in the coastal areas of the East China Sea was explored. First, word segmentation was performed on 183 reviews using software to extract high-frequency words; from this, we found the key characteristics of holiday destinations that tourists care about. Second, semantic network analysis of high-frequency words was performed to clarify the tourists’ image perception of the destination, forming a preliminary image perception.

2.2.2 AHP model

The AHP is primarily used to decompose complex problems into multiple simple units, with each unit including several factors with the same attributes, thereby forming a hierarchical structure. The AHP is widely applied in the selection of tourist destinations [25]; these can be divided into three levels: target level, criterion level, and planning level. In the selection of tourist destinations, the target level is the tourist destination to be selected, the criterion level is the tourism evaluation index, and the planning level is a series of plans that meet these criteria.

In the analysis of the attractiveness index of national marine parks in the research, the target level corresponded to the attractiveness of marine parks, the criterion level was the main indicator affecting that attractiveness, and the planning level was the secondary indicator included in the main indicator, thereby establishing the indicator system. Based on this, a Stanine was adopted to construct a hierarchical judgment matrix, as shown in Table 2. Finally, the index weight matrix was calculated through the total hierarchical order, and the inspection was passed at one time.

Table 2

Judgment matrix scale and meaning

Scale Meaning
1 U i is as important as Uj
3 U i is slightly more important than U j
5 U i is more important than U j
7 U i is much more important than U j
9 U i is extremely more important than U j
2, 4, 6, 8 The median between the above scales, respectively
Reciprocal The importance of U j over U i

2.2.3 Fuzzy comprehensive evaluation model

The fuzzy comprehensive evaluation model is an effective method to improve senior management’s decision-making and organizational abilities and can be used to evaluate people, things, and objects in a comprehensive, accurate, and quantitative manner. The fuzzy comprehensive evaluation model is as follows:

(2) L = B R = ( B 1 ,   B 2   ,   ,   B n ) ,

B refers to the fuzzy weight matrix of each factor obtained by the AHP, and R is the single-factor evaluation matrix obtained from the questionnaires. Within this matrix, the fuzzy evaluation results are quantified into different levels according to the five-level standard; these are {very satisfied (4.5–5], quite satisfied (3.5–4.5], acceptable (2.5–3.5], unsatisfied (1.5–2.5], and very unsatisfied (0–1.5]}, denoted as R 1, R 2, R 3, R 4, and R 5, respectively. The matrix R expression is:

(3) R = r 11 r 1 n r n 1 r n n ,

r nm refers to the probability that the nth indicator for evaluating the attractiveness of a national marine park may be at the Level R m (that is, the degree of affiliation). The formula for calculating the final index of each indicator is:

(4) I = 1 n n L n .

3 Calculation of the tourism attractiveness index

3.1 Establishment of the indicator system

Figure 1 shows a scheme summarizing the whole procedure of calculating the tourism attractiveness index. To evaluate the attractiveness index of national marine parks, it is first necessary to establish a suitable, scientific indicator system. By performing word segmentation and frequency analysis on the 183 comments after data cleaning, the first 24 high-frequency words can be obtained as shown in Table 3. The most frequent word was “Sea surface,” which had the deepest impression on tourists when they visited national marine parks. Next was “Seafood,” which showed that tourists also remembered the food clearly. After this, there were “Islands,” “Piers,” and “Scenery,” suggesting that tourists quite enjoyed the scenic spots at their destination. In order to intuitively show the tourists’ perception of the marine park, high-frequency words were used to generate a tag word cloud, as shown in Figure 2.

Figure 1 
                  A scheme summarizing the whole procedure of calculating the tourism attractiveness index.
Figure 1

A scheme summarizing the whole procedure of calculating the tourism attractiveness index.

Table 3

High-frequency words

High-frequency words Word frequency High-frequency words Word frequency High-frequency words Word frequency
Sea surface 53 Shipu 22 Island tour 16
Seafood 46 Ocean 20 Environment 16
Island 45 Suitable 19 Time 16
Place 36 Air 18 Ferry fare 16
Hour 27 Sunrise 18 Condition 15
Pier 24 Scenic area 17 Ticket price 15
Scenery 24 View 17 Lighthouse 15
Xiangshan 23 Clam 17 Sea fishing 15
Figure 2 
                  High-frequency tag word cloud image.
Figure 2

High-frequency tag word cloud image.

After calculating the word frequency, semantic network analysis was performed for the first 100 high-frequency words. As shown in Figure 3, the more lines connected each high-frequency word within the figure, the more frequently the word appeared in the comments. It can be seen from Figure 3 that words like “air,” “island,” “freshness,” and “sea fishing” all radiated from the core word “sea surface,” and are prominent features of national marine parks in the coastal areas of East China Sea. They can also all be recorded as natural attributes, which include tourist attractions, natural environment, and service facilities. The high-frequency words radiating from “Shipu” (the name of a port) include “Xiangshan,” “evening” and “hour,” which reflect the regional environment, transportation, distance, and travel time. “Seafood” radiated from the word “islands,” and reflected that local cuisine was especially favored by tourists.

Figure 3 
                  Semantic network diagram.
Figure 3

Semantic network diagram.

Combined with the current review standards of national marine parks, the literature on the calculation of tourism attractiveness, and the above-mentioned analysis of tourists’ perception of national marine parks in the coastal areas of the East China Sea, the indicator system for the evaluation of the attractiveness of national marine parks was initially established. After this, the opinions of experts, researchers, and certain tourists in relevant fields related to national marine parks were collected, in order to carry out some adjustments to the indicators as shown in Figure 4.

Figure 4 
                  Indicator system for the attractiveness of national marine parks.
Figure 4

Indicator system for the attractiveness of national marine parks.

There are three levels and 16 indexes in the indicator system shown in Figure 4. The first level is the target level, that is, the attractiveness index of national marine parks was named A. The second level was the criterion level, which included the four main indicators of natural attributes (B1), service experience (B2), supporting facilities (B3), and travel activities (B4). The third level was the planning level, with a total of 15 indicators, of which natural attributes include natural landscape (C1), and natural resources (C2). Service experience includes special cuisine (C3), service facilities (C4), experience (C5), hygiene (C6), and shopping (C7). The supporting facilities include public transportation (C8), commentary system (C9), ticket prices (C10), and security management (C11). Travel activities include advertising (C12), tourism attitude (C13), travel frequency (C14), and traveling time (C15).

3.2 Index weight acquisition

After the hierarchical indicator system for national marine parks was established, the affiliation between each indicator was determined. By comparing the importance of each indicator in the attractiveness index system by the experts of the national marine park, we formed the judgment matrix of the attractiveness index system. The judgment matrix included a comparison list of the attractiveness of national marine parks and the main influencing indicators at the criterion level (Table 4), along with a comparison list of the main influencing indicators and the corresponding secondary influencing indicators.

Table 4

Judgment matrix for the attractiveness and criterion level of national marine parks

Attractiveness of national marine parks Natural attributes Service experience Supporting facilities Tourism effects Wi
Natural attributes 1 3 5 7 0.5638
Service experience 0.3333 1 3 5 0.2634
Supporting facilities 0.2000 0.333 1 3 0.1178
Tourism effects 0.1429 0.2 0.3333 1 0.0550

In order to ensure the rationality of the judgment matrix, the importance of the quantitative indicators to the upper-level elements, and the overall goal, a consistency test was required. If the consistency ratio of the judgment matrix was less than 0.1, it proved that it had passed the consistency test and that the data were reasonable. Otherwise, the data needed to be modified. Table 5 shows the test results for the judgment matrix.

Table 5

Consistency test results

Matrix Attractiveness of national marine parks Natural attributes Service experience Supporting facilities Tourism effects
Consistency ratio 0.0438 0.000 0.0653 0.0975 0.0128

The consistency ratios in Table 5 are all less than 0.1, indicating that the matrix passed the consistency test. Using the square root method, the weight of each indicator in the indicator system for national marine parks was obtained, as shown in Table 6. It was found that natural attributes are the main factors affecting the attractiveness index. Second, the natural landscape was quite an important index in terms of natural attributes. Special cuisine and experience were also quite important for the overall service experience. The weight of public transportation was high in terms of supporting facilities and travel attitude was quite important when it came to travel activities.

Table 6

Index weighting for attractiveness

Target Level Criterion Level Weight Indicator Level Weight
attractiveness index of national marine parks A Natural attribute B1 0.5638 Natural landscape C1 0.7500
Natural resources C2 0.2500
Service experience B2 0.2634 Special cuisine C3 0.4574
Service facilities C4 0.1885
Experience C5 0.2088
Hygiene C6 0.1020
Shopping C7 0.0432
Supporting facilities B3 0.1178 Public transportation C8 0.4318
Commentary C9 0.1137
Ticketing system C10 0.0746
Security management C11 0.3800
Travel activities B4 0.0550 Advertising C12 0.0799
Travel attitude C13 0.4842
Travel frequency C14 0.2069
Traveling time C15 0.2290

3.3 Calculation of tourism attractiveness index

The fuzzy comprehensive evaluation model is used to calculate the evaluation index L of each indicator, where matrix B is the index weight obtained in Section 2. The single-factor evaluation matrix R is calculated from the probability of the five-level evaluation, which in turn is taken from the questionnaire data. The specific calculation of indicators in the criterion level and the target level of the indicator system for national marine parks in the coastal areas of the East China Sea is as follows. Appendix is the detailed process.

(5) L = B × R .

The evaluation matrices are defuzzied through I = I = 1 n n L n , where n is the level within the five-level scale, that is, within the evaluation matrix calculated above. The specific calculations for each indicator are as follows:

I natural attribute = 0.0256 × 1 + 0.1222 × 2 + 0.2125 × 3 + 0.2853 × 4 + 0.3543 × 5 = 3.8202 ,

I service experience = 0.0408 × 1 + 0.1703 × 2 + 0.2431 × 3 + 0.3345 × 4 + 0.2055 × 5 = 3.4762 ,

I supporting facilities = 0.0459 × 1 + 0.1016 × 2 + 0.2026 × 3 + 0.3645 × 4 + 0.2854 × 5 = 3.7419 ,

I travel activities = 0.0684 × 1 + 0.1663 × 2 + 0.2199 × 3 + 0.2243 × 4 + 0.3209 × 5 = 3.45624 ,

I attractiveness index = 0.0343 × 1 + 0.1349 × 2 + 0.2198 × 3 + 0.3042 × 4 + 0.3052 × 5 = 3.7063 .

This method not only calculates the attractiveness index, but also the index of each important indicator. In a subsequent study, we will compare the attractiveness index and the index of important indicators for different national marine parks from multiple aspects, both horizontal and vertical, to better develop and construct national marine parks.

4 Conclusion and discussion

  1. Comparing the evaluation results calculated above with the five-level quantitative standard, it can be seen that the overall tourism attractiveness index of national marine parks in the coastal areas of the East China Sea was relatively high, with a quantitative score for the tourism attractiveness index of 3.7063, belonging to quite satisfied (3.5–4.5]. This shows that tourists were quite satisfied with the overall construction of national marine parks in the coastal areas of the East China Sea. From the evaluation results, it can be seen that the development of some parks may ignore the true feelings of tourists, due to a focus on supporting facilities, meaning there were deficiencies in terms of service facilities, tourist experience, hygiene, and advertising. After the pandemic, the tourism industry has gradually returned to work. Improvements and optimization were required in the above-mentioned aspects, especially in terms of monitoring visitors’ close contacts. At the same time, an early warning mechanism for close contacts should be provided to prevent and control the pandemic so that tourists can rest assured.

  2. Tourists were quite satisfied with the natural landscape and resources of marine parks, and the quantitative score for natural attributes was 3.8202, belonging to quite satisfied (3.5–4.5]. Among these, the natural landscape index contributed a lot to the degree of satisfaction, which was very much related to the establishment of these parks. National marine parks cannot be created without field research, discussion, declaration, review, approval, and publication. In the process of field research, the most important part is to fully investigate the value of the ecosystem and the natural landscape. Therefore, during the construction of these parks, we should pay more attention to the protection of natural landscapes and natural resources.

  3. Tourists were not quite satisfied with the service experience, with an overall quantitative score of only 3.4762, belonging to acceptable (2.5–3.5]. Within this indicator, fishing, seafood, sanitary conditions, shopping, and infrastructure were the service needs tourists were most concerned about. In the actual surveys, it can be seen that some national marine parks have poor sanitation and infrastructure facilities. For example, the cuisine tends to be nothing special, the entertainment activities were unimpressive, food and accommodation costs were too high, the number of toilets and seats were insufficient, signage was unclear, and garbage was not cleaned up in time. These problems all contributed to a reduction in tourist satisfaction. As a result, the construction of national marine parks required the creation of special cuisine and entertainment activities, a reasonable selection of entertainment venues, a better arrangement of infrastructure, and more emphasis on the unique atmosphere of marine parks and the associated tourist experience. Against the background of the pandemic, there are more requirements for tourist attractions and infrastructure; for example, setting up large screens to monitor close contacts, or analyzing and predicting the flow of tourists in the marine parks to prevent gatherings of too many people. Having an active monitoring and prevention system in place, as well as a thorough analysis of situational awareness not only makes tourists feel more confident but also helps staff at the scenic spots to prevent and control the pandemic.

  4. Tourists were quite satisfied with the supporting facilities, with an overall quantitative score of 3.7419, belonging to quite satisfied (3.5–4.5]. Among these facilities, public transportation and security management contributed the most to the degree of satisfaction, while ticketing systems contribute the least. At present, there are 47 national marine parks in the country, and relevant regulations for the construction of supporting facilities in these parks are defined in the Measures for the Administration of Special Marine Reserves issued by the State Oceanic Administration in 2010. Therefore, the construction of supporting facilities should reach the prescribed standards, and regular maintenance and improvement works should be carried out. During the gradual recovery of the tourism industry after the pandemic, public transportation and safety management needs to be further improved to ensure a safe environment for tourists, and a predictive monitoring and tracking mechanism should be built to monitor people who came into close contact with the virus. After the pandemic, the number of tourists will be greatly reduced. Therefore, it is important to do a good job in epidemic prevention and control, as well as in the dissemination of this information, in order to further promote the recovery of tourism in the national marine parks.

  5. Tourists were generally satisfied with travel activities, with a quantitative score of 3.5624, belonging to quite satisfied (3.5–4.5]. Among the indicators, tourism attitude contributed the most, followed by travel frequency and times. Advertising contributed the least. Travel attitude is a part of tourist psychology and gives an idea of people’s psychological leaning towards the destination and the overall conditions. In the questionnaires, it was found that 60% of the tourists surveyed did not know about national marine parks, and 26% did not have much interest in going to one in the future. This shows that we should pay more attention to the change in tourists’ attitudes, and try to increase the popularity, reputation, and publicity of national marine parks in a variety of ways.

By analyzing the overall attractiveness and various indicators, we can clearly see the advantages and disadvantages of the national marine parks in the coastal areas of the East China Sea. After the pandemic, the tourism industry is slowly getting back to normal, meaning there will be even more requirements for these indicators. First of all, we should place epidemic prevention and control as a priority, and carry out detection and monitoring of close contacts. At the same time, an early warning mechanism for close contacts should be provided, so that tourists can travel in a safe environment. Meanwhile, in subsequent research, we can consider applying this methodology for tourism attractiveness to more marine parks in other areas of the country, and compare the attractiveness index both horizontally and vertically. Through comparative analysis, we can provide more constructive suggestions for the future construction and development of national marine parks.

AHP method quantifies some factors that are not easy to quantify and then conducts a comprehensive evaluation, which is widely used and effective. The model used in this study was mainly constructed on the basis of referring to the tourist destination attractiveness evaluation system and combined with the opinions of relevant experts. It was highly subjective, which may lead to certain deviations in the evaluation results. In addition, the factors affecting tourism attractiveness were complex and changeable, and the model cannot explain the relationship between various variables. And, the attractiveness evaluation model applicable to certain types of parks may not necessarily satisfy other types of parks. At present, the above-mentioned models are used to study tourism attractions, but various models have different application scenarios. In this study, the attractiveness of marine parks was mainly studied through the models about attractiveness.


The authors gratefully acknowledge the financial support from the Shanghai Chenguang project (No: 19CGB09) and Cultivating Academic Key Teacher project by the Shanghai Institute of Tourism (No: E3-0250-20-001-031).

  1. Funding information: Shanghai Chenguang project (No: 19CGB09) and Optional project of the Shanghai Institute of Tourism (No: KY2021-D1L10).

  2. Conflict of interest: Authors state no conflict of interest.


  1. Natural attribute evaluation (L B1)

    (1) L B 2 = B × R = ( 0.7500 , 0.2500 ) × 0.0174 0.0500    0.1130 0.1500    0.2000 0.2500    0.3304 0.1500    0.3391 0.4000 = ( 0.0256 , 0.1222 , 0.2125 , 0.2853 , 0.3543 ) .

  2. Service experience evaluation (L B2)

    (2) L B 2 = B × R = ( 0.4754 , 0.1885 , 0.2088 , 0.1020 , 0.0432 ) × 0.0700 0.2261 0.2807 0.3043 0.1130 0 0.1652 0.2435 0.3740 0.2174 0.0087 0.0867 0.1391 0.3913 0.3739 0.0348 0.0696 0.2609 0.3304 0.3043 0.0783 0.2435 0.3043 0.2174 0.0870 = ( 0.0408 , 0.1703 , 0.2431 , 0.3345 , 0.2055 ) .

  3. Supporting facilities evaluation (L B3)

    (3) L B 3 = B × R = ( 0.4318 , 0.1137 , 0.0746 , 0.3800 ) ×   0.0522 0.0870 0.1304 0.1304 0.0696 0.2174 0.0087 0.0867    0.1826 0.3739 0.2087 0.2957 0.2783 0.2783 0.2087 0.3913   0.3043 0.2348 0.1565 0.3043 = ( 0.0459 , 0.1016 , 0.2026 , 0.3645 , 0.2854 ) .

  4. Tourism effect evaluation (L B4)

    (4) L B 4 = B × R = ( 0.0668 , 06432 , 0.2140 , 0.0759 ) × 0.0522 0.1304 0.0500 0.2000 0.1000 0.1000 0.1500 0.1000    0.2348 0.3478 0.2000 0.2000 0.3000 0.2500 0.1500 0.2500    0.2348 0.3500 0.2500 0.3500 = ( 0.0684 , 0.1663 , 0.2199 , 0.2243 , 0.3209 ) .

  5. Tourism attractiveness index evaluation (L A )

(5) L A = B × R = ( 0.5638 , 0.2634 , 0.1178 , 00550 ) × 0.0256 0.1222 0.0408 0.1703 0.0459 0.1016 0.0684 0.1663     0.2125 0.2853 0.2431 0.3345 0.2026 0.3645 0.2199 0.2243    0.3543 0.2055 0.2854 0.3209 = ( 0.0343 , 0.1349 , 0.2198 , 0.3042 , 0.3052 ) .


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Received: 2021-09-15
Revised: 2022-02-15
Accepted: 2022-03-13
Published Online: 2022-04-28

© 2022 Li Wang et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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