A Two-Tuple Linguistic Model for the Smart Scenic Spots Evaluation

The evaluation on the level of smart scenic spots is crucial in the planning and development of smart tourism destinations. However, existing evaluation approaches for smart scenic spots lack scientific rigor and practical applicability. To address this issue, this study proposes a comprehensive evaluation method that combines qualitative analysis and quantitative calculation to establish a weighted index system for assessing the level of smart scenic spots. The approach utilizes a fuzzy comprehensive evaluation model, integrating linear weighted comprehensive evaluation methods, fuzzy mathematics, and the concept of two-tuple. Moreover, the concept of level eigenvalue is introduced to facilitate the evaluation of smart scenic spots. The proposed two-tuple model and evaluation method demonstrate strong operability, applicability, and promotional potential, as evidenced through example calculations and analysis.


INTRodUCTIoN
Smart scenic spots play a crucial role in serving tourists and promoting sustainable development in scenic areas; evaluating these spots is essential for the successful planning and development of smart tourism.Although the term smart scenic spot is less common outside China, it has a significant historical background that has captured considerable academic attention regarding the technical advancements and applications of smart technology in scenic areas (Dimitrios Buhalis, 2008;Owaied et al., 2011;Borràs et al., 2014;Taehyee & Namho, 2019).Studies in China have primarily concentrated on the intrinsic concept of smart scenic spots, the development of smart tourism systems, the tourists' spatial behaviors, and investigations into the willingness of using the smart tourism systems (Dang et al., 2011;Ruan, 2017, Li et al., 2019;Xu & Huang, 2018).However, there is a noticeable lack of research on evaluating the smart level of these sites.Such evaluations aim to identify the factors contributing to the development of smart scenic spots, establish a weighted index system, and calculate corresponding grades.For instance, Tang (2014) developed an index system encompassing management, service, marketing, and support, and employed the analytic hierarchy process (AHP) to assign weights to the indices.Through a multi-factor comprehensive evaluation method, Tang conducted an empirical study on Nanjing Zhongshan Mausoleum (Tang, 2014).Similarly, Li and Shi (2017) constructed an index system for Lanzhou smart scenic spot, considering dimensions like environmental monitoring, intelligent security, energy management, traffic management, scenic spots public release platform, and intelligent management service.They used the analytic hierarchy process to weigh the indices, established an evaluation model, and proposed policy suggestions for the Lanzhou smart scenic spot (Li & Shi., 2017).Pan (2018) and Chen et al. (2019) developed a concise evaluation system that includes infrastructure, service smartness, marketing smartness, and management smartness, the CRITIC and AHP methods are employed to determine index weights and extended the application to evaluate the smart level of scenic spots above 4A in Jiangsu province.Moreover, Guo et al. (2022) utilized the entropy method to assess navigation, guide, and shopping in China's first and second batches of smart scenic cities above 3A, providing a crucial evaluation of their smart level.
Many researchers have treated the evaluation of smart level and level of smart scenic spots as interchangeable problems to solve.In this context, the comprehensive evaluation value of the smart scenic spots is obtained, and the associated smart level is determined by comparing the value against a predefined threshold.However, it is important to recognize that, conceptually and methodologically, the ranking evaluation of smart scenic spots differs from the ranking evaluation of the degree of smart.To address this issue and enhance the quality and credibility of evaluation on the smart level of scenic spots, this paper clearly defines the smart level evaluation on scenic spots.Additionally, a general model for conducting an evaluation on the smart level is developed with a rational, mathematical methodology.By differentiating the two types of evaluations, this approach aims to refine the assessment process and ensure accurate results for evaluating the smart level of scenic spots.
As a theoretical application piece, this paper incorporates the two-tuple linguistic mode with the evaluation of smart scenic spots.Therefore, our research differs in two ways from previous methods, which are both the contributions of this article and the core points that need to be demonstrated.First, in the existing literature, the old-fashioned approach to scenic spot evaluations mainly focused on the AHP, Delphi method, entropy method, and fuzzy comprehensive evaluation.Many of these methodologies rank scenic spot smartness as the grading of the smartness.Specifically, after obtaining a comprehensive evaluation score for a smart scenic spot, its smart level will be determined according to the grade thresholds, assessing whether the overall smartness score meets the criterion.A major flaw of these methods is that they can only judge the hierarchical level between objectives and cannot weigh the pros and cons of multiple objectives at the same level.With the help of the twotuple linguistic model, ranking within the level becomes possible for smart scenic spot evaluations.
Second, in contrast to the two-type fuzzy sets, which obtain the advantages in the hierarchical structure analysis, the two-tuple linguistic model not only captures preferences with quantitative representations during decision-making, but also extracts information behind the uncertainty of language using and terminology in evaluations.It mitigates information loss and hence builds a more accurate and robust result, and our conclusions support this point of view.

EVALUATING THE SMART LEVEL oF SCENIC SPoTS
This study implemented a comprehensive methodology to ensure the applicability of smart level evaluation.First, a weighted index system was constructed, considering various factors contributing to scenic spots' smartness.Next, the grade of smartness was calculated using fuzzy comprehensive evaluation, which allows for a more nuanced and precise assessment.To optimize the evaluation results further, the study introduced the concepts of level characteristic value and two-tuple linguistic.These additions not only aid in determining the smart level of a scenic spot but also enable the ranking of smart degrees within each level.This approach significantly enhances the applicability of evaluating and comparing different smart scenic spots.By combining these elements, the methodology presented in this paper ensures a more accurate, reliable, and practical evaluation of the smart level of scenic spots.This comprehensive approach is well-suited for guiding the development and improvement of smart scenic spots, promoting sustainability, and offering a valuable tool for decision-makers in the tourism industry.

Indices on Evaluating the Smart Level of Scenic Spots
Following the "Beijing Smart Scenic Spot Construction Guidelines (for Trial Implementation)" (2012), "Fujian Province Classification and Accreditation for Smart Tourism Destinations" (2022), and other relevant literature (Tang, 2014;Wang et al., 2015;Li & Shi, 2017;Chen et al., 2019), we built the index system of smart scenic spots evaluation by expert interview and field research.The system is organized into three levels.1.

Standards for Smart Scenic Spots Level
The smart level of kth scenic spot is represented by e k (k = 1, 2, . .., h) with the partial order e e e h 1 2 > > ... , it follows that the smart level of kth scenic spot is superior to the (k + 1)th one, this specific partial order gives the level set of smart scenic spots evaluation such that V e e e n = { } 1 2 , ,... .Moreover, the ground bases for us to construct smart level are "Beijing Smart Scenic Spot Construction Guidelines (for Trial Implementation)" (2012), "Fujian Province Classification and Accreditation for Smart Tourism Destinations" (2022), and Tang (2014), and according to the evaluation standards and grade thresholds in each smart scenic spot, the smart level is set to h = 5, and e 1 -e 5 indicate levels I-V, respectively.Specifically, e 1 denotes a very high smart level, e 2 denotes the high one, e 3 denotes the ordinary one, e 4 denotes the poor one, while e 5 is the worst-case scenario.The details can be seen in Table 2.

Weights of the Index System
On the data and level indices of smart scenic spots, we gauge the impact on the benefits of these spots and the challenges of their implementation.We sought insights from industry experts and employed the AHP method.Using a 1-9 scale, we pairwise assessed the relative significance of the smart level indices.Based on these comparisons, we formulated judgment matrices for each tier, utilized Excel to determine the maximum eigenvalue and its associated eigenvector, and performed a consistency check.In the end, we established the weights for the index system of the smart scenic spots, details are shown in Table 1.

The Grade Membership Function of the Evaluation Indices
The evaluation indices can be divided into two categories: the quantitative one and the qualitative one.

The Membership Degree of the Qualitative Evaluation Indices
On the actual characteristics and requirements of the smart scenic spots, the grade membership 1 2 , ,... can be defined as follows:

Multimedia display
Need to use multimedia display tools, including arc curtain system, circular screen system, ball screen system, threedimensional projection system, digital audio system, VR system, spherical projection system, desktop projection system, digital sand table system, virtual pages system, interactive game system, electronic signature, and electronic survey system ≥ 8, using 8 or more tools above ≥ 6, using 6 to 7 tools above ≥ 4, using 4 to 5 tools above ≥ 2, using 2 to 3 tools above   two-level and first-level qualitative evaluation indicators.This methodology allows us to assess the smartness of scenic spots across multiple levels and indicators, providing a comprehensive and effective evaluation approach.

The Membership Function of the Quantitative Evaluation Indices
To obtain an efficient evaluation index system, the membership function of the quantitative evaluation index O ijl of smart scenic spot A t can be selected as follows: 1 2 , ,..., is assigned to kth smart level e k .When the grade reference value (Or division value) of the quantitative evaluation indices is the same or falls within the same interval, the level membership function of the quantitative evaluation index O ijl of smart scenic spot A t can be selected as follows: The above approach is also capable of determining the membership functions of second-level and first-level qualitative evaluation indicators.By using these membership functions, the smartness level of scenic spot A t can be accurately assessed based on the quantitative evaluation indices and their relationship to the established benchmark values for each level.

Comprehensive Model and Two-Tuple Linguistic Method for Evaluating the Smart Level
Based on the characteristics of the smart scenic spots, the membership function µ tijlk for the evaluation index O ijl can be calculated using Equations 1-5 with both qualitative and quantitative evaluation indices.This calculation results in the membership matrix μ µ , which provides the basic data for the smart level evaluation.

Fuzzy Comprehensive Model of Smart Scenic Spots Evaluation
Our fuzzy comprehensive evaluation model based on the fuzzy linear weighted comprehensive evaluation method.This model is designed to meet the inherent requirements of evaluation on the smart level and its three-layer evaluation index structure characteristics.To calculate the comprehensive membership degree of smart scenic spot A t with respect to the three-level evaluation index O ijl for level e k , the fuzzy linear weighted comprehensive evaluation method is employed.The calculation is as follows: In the preceding equation, ˆ, ,..., represents the kth column vector of µ tij in the membership matrix.By arranging these column vectors, the comprehensive membership vector u ij of smart scenic spot A t for all levels e k can be obtained as û . By using the comprehensive membership vector, the membership matrix μ µ The same model can determine the comprehensive membership vector and membership matrix for the second-level and first-level evaluation indices.In the general evaluation on the smart level, the principle of maximum membership is commonly applied.This means that the smart scenic spot is rated according to the level of membership it belongs to.However, relying solely on the principle of maximum membership can be unreasonable at times.To address this, we introduce the concept of level eigenvalue (Li, 2023).

Decision Value of the Smart Level
The subscript k of the intelligence level e k is called the level variable; therefore, the level characteristic value of the smart scenic spot A t can be defined as: Note that , and , then there is: Indeed, as mentioned in Equation 7, the level eigenvalues υ t ( ) of smart scenic spot A t provides a dimensionless quantity indicator that lies between the 1st level e 1 ( ) and the hth level e h ( ) .The level eigenvalues convey two critical pieces of information: the comprehensive membership degree and the scenic spot smart level (level location).The value υ t       , represented as the maximum integer not greater than υ t , is used to determine the smart level of A t .If υ t       equals q, it indicates that A t is at the qth degree of smart level.Obtaining the maximum integer value from the level eigenvalues υ t is generally considered more comprehensive and objective than relying solely on the principle of maximum membership.However, there are some limitations in this approach.Different levels of eigenvalues may yield the same maximum integer value, leading to some unreasonable evaluations of the smart level of scenic spots.Additionally, this method may fail to clearly distinguish the difference in the degree of smart construction among the scenic spots (Liu & Li, 2016).
To address these challenges and ensure a more accurate and nuanced evaluation of the smart level of each scenic spot, our paper introduces the concept of two-tuple linguistic (Yu et al., 2018;Yu et al., 2016;Herrera & Martinez, 2000;Martinez & Herrera, 2012;Yu & Li, 2022), aiming to refine the assessment process and enhance the distinction between the smart levels of different smart scenic spots.By incorporating the two-tuple linguistic method, we aim to provide a more robust and valuable evaluation on the smart level, considering both the comprehensive membership degree and the variations among smart scenic spots.

Two-Tuple Linguistic Method for the Evaluation of Smart Level
If the level eigenvalue υ t of smart scenic spot A t is met: then the smartness rating of A t is the sth level e s ( ) .
To depict the difference degree of smart level of different smart scenic spots within the same level, deviation value between level eigenvalue and its corresponding smart level s (subscript s of level e s ) is denoted as α υ ts t s = − (see Figure 1).Obviously, − ≤ < 0 5 0 5 . .α ts .The basic idea of two-tuple linguistic method for the evaluation on the smart level of smart scenic spots as follows.First, level eigenvalue υ t of smart scenic spot A t is denoted as a two-element ordered group e s ts , α ( ) , and e s is the evaluated smart level of A t , while α ts expresses the deviation value of υ t and its smart level s ts , ., .α ∈ −    ) 0 5 0 5 .Second, by assessing the smart level of scenic spot A t -given the size of e s in e s ts , α ( ) , it adjusts and determines the relative difference of the smart scenic spots (that is, determines the priority of the smart scenic spots within a smart level).Obviously, α ts serves as a regulatory signal in the smartness grade rating, implying whether the smart level s is larger or smaller than υ t .Therefore, we call e s ts , α ( ) the two-tuple linguistic pair, and α ts is semantic symbol.To facilitate the computation of the two-tuple linguistic evaluation on the smart level, the size of the two-tuple is specified as follows: 1.If e e s d e e α , the smart level of scenic spot A t is higher than that of A r , that is e s ts , α

(
) and e d rd , α ( ) are the two-tuple linguistic of level eigenvalue υ t and υ r of smart scenic spots A t and A r .

If e e s d
) , the smart level of scenic spots A t and A r is the same, they can be adjusted according to the linguistic symbol to determine the degree of difference., , , , A t has more smart grade than A r , A t is hence ranked before A r .Obviously, the preceding two-tuple linguistic ranking method not only assesses the smart level of each scenic spot but distinguishes the difference degree of the smartness within same smart level.

EMPIRICAL ANALySIS oF SMART SCENIC SPoT EVALUATIoN
Three national 5A scenic spots in Fujian Province, denoted by A 1 , A 2 and A 3 , were selected as the evaluation objects or samples for smartness evaluation.The three scenic spots began their smart tourism construction in year 2012, 2013, and 2003, respectively.They have achieved varying degrees of success in intelligent ticketing, transportation, intelligent resource management, intelligent service, precise marketing, and office automation.We obtained the smart level evaluation in the three smart scenic spots (see Table 3).
given Equation 7.Besides scenic spot A 1 , the eigenvalue of A 2 and A 3 is υ υ Following the previous specifications, the smart level of A 1 and A 2 should be assessed by e 3 , and A 3 is assessed by e 2 .However, A 1 and A 2 are not at the same smart level and the order for them is given by A A A 3 1 2 > > .From the comparison of each single index of the three smart scenic spots above, all indices of A 3 are higher than those of A 1 and A 2 in general, while the individual index of A 2 states the worstcase scenario.These results are not only consistent with the comparison of single index, but more rigorous, reliable and intuitive.
As Table 4 shows, the maximum membership principle claims that both A 1 and A 3 scenic spots are ranked at level 2 in terms of smartness, while A 2 is at level 3.While the level eigenvalue evaluation justifies that all three scenic areas ranked at level 2, showing no clear distinction.By utilizing twotuple linguistic model, however, the rankings for A 1 , A 2 , and A 3 were 2, 3, and 1, respectively, adhering to a strict ranking criterion.During the smart scenic spot evaluation, both of maximum membership principle and grade eigenvalue evaluation have certain limitations.Although there are slight differences between the results of the smart scenic spots rating, the latter, which is mixed with the two-tuple linguistic method and the two methods above, exhibits a more reasonable, closer fact to the reality.Above all, two-tuple linguistic method, it on the one hand reasonably determines the smart scenic spots level, on the other hand the difference of the smart degree of different scenic spots within the same smart level gets accurately distinguished on the effort of this method.

CoNCLUSIoN
In this study, we developed a weighted index system to evaluate the smart level of scenic spots.By applying this system, we established a fuzzy comprehensive model and introduced a twotuple linguistic method for evaluation.For the empirical results on the application of evaluation method (see Table 4), we surveyed three 5A-level scenic spots, which are Xiamen's Gulangyu Scenic spot A 1 ( ) , Fuzhou's Sanfang Qixiang A 2 ( ) , and Wuyishan A 3 ( ) , with the exploiting of the maximum membership principle, level eigenvalue evaluation, and two-tuple linguistic model respectively.Our findings revealed that, according to the first method, both A 1 and A 3 scenic spots are ranked at level 2 in terms of smartness, while A 2 is at level 3.The second method claims that all three scenic areas ranked at level 2, showing no clear distinction.By utilizing two-tuple linguistic model, however, the rankings for A 1 , A 2 , and A 3 were 2, 3, and 1, respectively, adhering to a strict ranking criterion.This comparison echoes the efficiency of two-tuple linguistic model on capturing missing information, which should be deemed as a proven method to enhance the accuracy of smart scenic spots evaluations.
For the derivative theoretical implications, we find that the two-tuple linguistic model not only captures preferences with quantitative representations during decision-making, but also extracts information behind the uncertainty of language using and terminology in evaluations.It mitigates information loss and builds a more accurate and robust result for the sake of smart scenic spots evaluations.Meanwhile, the results demonstrate that the two-tuple linguistic method aligns with the conceptual requirements for evaluating the smart level of scenic spots and its properties is proven to be a practical, efficient, and applicable approach.Our study offers a novel solution to address the evaluation on the smart level of scenic spots and can be adapted for use in other similar cases.
For the management implications, on one hand we offer a viable assessment method for tourism regulatory authorities to determine and evaluate the smart level of scenic spots for a more accurate result.On the other hand, we also provide a foundation of decision-making for scenic spots building, allowing them to discern differences in smart levels to the competitors and further help them to implement several precise business strategies.
1 represents the hierarchical membership function for the three-level evaluation indices, and it can also be applied to determine the grade membership functions of functions, y tijl represents the value of the lth three-level (quantitative) evaluation index O ijl of smart scenic spot A t , a ijlk denotes that O ijl belongs to level .. where h = 5 in such case (similarly for other cases).Moreover, O tijlk indicates that at smart scenic spot A t , the lth three-level evaluation index (quantitative) O ijl of the jth two-level evaluation index O of the ith first-level evaluation index -level evaluation indices of A t .

Figure 1 .
Figure 1.Relation between two-tuple linguistic and grade eigenvalue comprehensive membership degree of smart scenic spot A 1 on the first-level evaluation index O 1 for smart level e e e e 1 2 3 4 , , , and e 5 is given by: The associated grade membership matrix of A 1 with respect to the first-level evaluation indices is: The primary level has four evaluation indicators: smart management (O 1 ), smart services (O 2 ), smart marketing (O 3 ), and smart support (O 4 ).The secondary level encompasses nine indicators, including intelligent security (O 11 ) and environmental monitoring (O 12 ).The tertiary level consists of 30 indicators, such as the scope of video surveillance coverage (O 111 ) and the development level of emergency response systems (O 112 ).Details are shown in Table

Table 1 . Evaluation indices and weight of smart scenic spots for the goal: Comprehensive development level of smart scenic spots
2 , ,... of A t satisfies the benchmark value of e k , then the grade membership function µ tijlk is equal to 1. On the contrary, if the index O ijl does not meet the benchmark

Table 2 .
Continued continued on following page

Table 2 .
Continued continued on following page , then the grade membership function µ tijlk is 0. In the above equation, µ tijlk indicates the membership of the lth three-level evaluation index (qualitative) O ijl of the jth two-level evaluation

Table 3 . Continued
Table 1, the comprehensive membership degree of smart scenic spot A 1 on the second level evaluation index O 11 for smart grade the comprehensive membership degree of A 1 over smart level e e e e