Research on the Evaluation Model of Urban Tourism Management Efficiency with Uncertain Linguistic Information

Abstract

We investigate the multiple attribute decision making problems for evaluating the urban tourism management efficiency with uncertain linguistic information. We utilize the uncertain linguistic weighted averaging (ULWA) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the alternatives and, then rank the alternatives and select the most desirable one(s). Finally, a numerical example for evaluating the urban tourism management efficiency with uncertain linguistic information is used to illustrate the proposed model.

1. Introduction

China’s tourism industry has experienced the stages of formation, rapid growth, and steady development since 1978 and now has developed into one of the fastest growing industries and a new growth point of China’s national economy. As the core and foundation of the development of China’s tourism industry, urban tourism has made an important contribution to the rapid prosperity and growth of China’s tourism industry in the past 35 years [1, 2]. The industrial status of tourism industry in the urban economy has risen to become a key industry and one of the pillar industries of urban tertiary industry and has also become the core of urban vigorous development of tertiary industry so as to optimize the urban industrial structure [3, 4]. So in-depth study of the development of urban tourism industry is not only the objective requirement of promoting the development of china’s tourism industry but also the reality need of optimizing the allocation of the tourism system so as to optimize the urban industrial structure and promote the urban economic growth. Although the overall urban tourism industry has shown a scene of prosperity and development, we are concerned about the differences in the development of urban tourism industry, especially the regional differences in tourism industry of the eastern, central, and western cities showing the different characteristics of the development [5, 6]. The essence of these different characteristics is the macroperformance under the influence of microscopic mechanism of the development of the tourism industry. Therefore, we can analyse the microinfluencing factors under the macroscopic characteristics of the development of urban tourism industry in order to study the breakthrough point to grasp, refine, and identify the mode of development of urban tourism of the growth center of eastern, central, and western regions. To make out what factors are the key factors which contribute to the urban development of the tourism industry and what factors are the restrictive factors which hinder the development of the tourism industry in different development modes [7, 8]. Distinguishing the mode of development of urban tourism with a breakthrough point of its factors and refining and summarizing the characteristics of the development paths and effects of urban tourism industry in the growth centers of eastern, central, and western cities will play a demonstration effect for the other cities with similar industrial development conditions in the eastern, central, and western regions and provide reference of development mode and development path selection for other cities to improve the tourism industry system and enhance and optimize the structure of tourism industry [9, 10].

In this paper, we investigate the multiple attribute decision making problems [11, 12] for evaluating the urban tourism management efficiency with uncertain linguistic information. We utilize the uncertain linguistic weighted averaging (ULWA) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the alternatives and then rank the alternatives and select the most desirable one(s). Finally, a numerical example for evaluating the urban tourism management efficiency with uncertain linguistic information is used to illustrate the proposed model.

2. Preliminaries

Let 𝑆={𝑠_𝑖∣𝑖=1,2,…,𝑡} be a linguistic term set with odd cardinality. Any label, 𝑠_𝑖, represents a possible value for a linguistic variable, and it should satisfy the following characteristics [13, 14]: (1) the set is ordered 𝑠_𝑖>𝑠_𝑗, if 𝑖>𝑗; (2) there is the negation operator neg(𝑠_𝑖)=𝑠_𝑗 such that 𝑗=𝑡+1−𝑖. For example, 𝑆 can be defined as 𝑆=𝑠₁=extremelypoor,𝑠₂𝑠=verypoor,₃=poor,𝑠₄=medium,𝑠₅𝑠=good,₆=verygood,𝑠₇=extremelygood. (1)

Definition 1 (see [15]). Let ULWA∶𝑆^𝑛→𝑆; if ULWA_𝜔𝑠₁,𝑠₂,…,𝑠_𝑛=𝜔₁×𝑠₁⊕𝜔₂×𝑠₂⊕⋯𝜔_𝑛×𝑠_𝑛, (2) where 𝜔=(𝜔₁,𝜔₂,…,𝜔_𝑛) is the weighting vector of uncertain linguistic variables 𝑠_𝑖 (𝑠_𝑖∈𝑆, 𝑖=1,2,…,𝑛) with 𝜔_𝑖∈[0,1], ∑^𝑛_𝑖=1𝜔_𝑖=1, then the function ULWA is called the uncertain linguistic weighted averaging (ULWA) operator of dimension 𝑛.

Definition 2 (see [15]). Let 𝑠₁=[𝑠_𝛼1,𝑠_𝛽1] and 𝑠₂=[𝑠_𝛼2,𝑠_𝛽2] be two uncertain linguistic variables, and let len(𝑠₁)=𝛽₁−𝛼₁ and len(𝑠₂)=𝛽₂−𝛼₂, and then the degree of possibility of 𝑠₁≥𝑠₂ is defined as [14] 𝑝𝑠₁≥𝑠₂=max0,len𝑠₁+len𝑠₂−max𝛽₂−𝛼₁,0len𝑠₁+len𝑠₂. (3)

3. Research on the Evaluation Model of Urban Tourism Management Efficiency with Uncertain Linguistic Information

In this section, we investigate the multiple attribute decision making problems for evaluating the urban tourism management efficiency with uncertain linguistic information. Let 𝐴={𝐴₁,𝐴₂,…,𝐴_𝑚} be a discrete set of alternatives and 𝐺={𝐺₁,𝐺₂,…,𝐺_𝑛} the set of attributes; 𝜔=(𝜔₁,𝜔₂,…,𝜔_𝑛) is the exponential weighting vector of the attributes 𝐺_𝑗 (𝑗=1,2,…,𝑛), where 𝜔_𝑗∈[0,1], ∑^𝑛_𝑗=1𝜔_𝑗=1. Suppose that 𝑅=(𝑟_𝑖𝑗) is the decision matrix, where 𝑟_𝑖𝑗∈𝑆 are the uncertain linguistic variables.

In the following, we apply the ULWA operator to MADM forevaluating the urban tourism management efficiency with uncertain linguistic information.

Step 1. Utilize the decision information given in matrix 𝑅 and the ULWA operator 𝑟_𝑖=ULWA_𝜔𝑟_𝑖1,𝑟_𝑖2,…,𝑟_𝑖𝑛,𝑖=1,2,…,𝑚, (4) to derive the collective overall preference values 𝑟_𝑖 (𝑖=1,2,…,𝑚) of the alternative 𝐴_𝑖, where 𝜔=(𝜔₁,𝜔₂,…,𝜔_𝑛)^𝑇 is the weighting vector of the attributes.

Step 2. To rank these collective overall preference values 𝑟_𝑖 (𝑖=1,2,…,𝑚), we first compare each 𝑟_𝑖 with all the 𝑟_𝑗 (𝑗=1,2,…,𝑚) by using (2). For simplicity, we let 𝑝_𝑖𝑗=𝑝(𝑟_𝑖≥𝑟_𝑗), and then we develop a complementary matrix as 𝑃=(𝑝_𝑖𝑗)_𝑚×𝑚, where 𝑝_𝑖𝑗≥0,𝑝_𝑖𝑗+𝑝_𝑗𝑖=1,ℎ𝑝_𝑖𝑖=0.5,𝑖,𝑗=1,2,…,𝑚. (5)

Summing all the elements in each line of matrix 𝑃, we have 𝑝_𝑖=^𝑚_𝑗=1𝑝_𝑖𝑗,𝑖=1,2,…,𝑚. (6)

Step 3. Rank all the alternatives 𝐴_𝑖 (𝑖=1,2,…,𝑚) and select the best one(s) in accordance with 𝑝_𝑖 (𝑖=1,2,…,𝑚).

Step 4. End.

4. Illustrative Example

With the rapid development of world tourism, the phenomena of cities “tourlized” and urbanization of tour destination are becoming more and more prominent. All these promote the function and facilities of cities to cater for a urban tourist in the course of urban plan and construction, which meet the requirement of tourism and meanwhile form the convergence and development of tourist economic elements. As the carrier of tourist development, tourist urban management is the key problem to be solved in the urban development of our country, and it would bring significant influence to the development of economy and society of our country. In this section, we present an empirical case study of evaluating the urban tourism management efficiency with uncertain linguistic information. There is a panel with five possible urban tourism cities 𝐴_𝑖 (𝑖=1,2,3,4,5) to select. The team of experts must take a decision according to the following four attributes: (1) 𝐺₁ is the informatization level; (2) 𝐺₂ is the financial level; (3) 𝐺₃ is the service level; (4) 𝐺₄ is the business level. The five possible urban tourism cities 𝐴_𝑖 (𝑖=1,2,3,4,5) are to be evaluated using the linguistic term set 𝑆 by the decision makers under the above four attributes (whose weighting vector 𝜔=(0.20,0.30,0.40,0.10)^𝑇) and construct, respectively, the decision matrix as follows: 𝑅=(𝑟_𝑖𝑗)_5×4 and 𝐺𝑅=¹𝐺₂𝐺₃𝐺₄𝐴₁𝐴₂𝐴₃𝐴₄𝐴₅𝑠₄,𝑠₆𝑠₅,𝑠₆𝑠₃,𝑠₄𝑠₂,𝑠₄𝑠₂,𝑠₄𝑠₂,𝑠₃𝑠₄,𝑠₅𝑠₄,𝑠₅𝑠₄,𝑠₅𝑠₃,𝑠₅𝑠₁,𝑠₂𝑠₅,𝑠₆𝑠₅,𝑠₆𝑠₄,𝑠₅𝑠₄,𝑠₆𝑠₂,𝑠₃𝑠₃,𝑠₄𝑠₅,𝑠₆𝑠₃,𝑠₅𝑠₅,𝑠₆ (7)

In the following, we apply the ULWA operator to MADM forevaluating the urban tourism management efficiency with uncertain linguistic information. To get the most desirable urban tourism cities, the following steps are involved.

Step 1. Utilizing the ULWA operator, we obtain the collective overall preference values 𝑟_𝑖 of the urban tourism cities 𝐴_𝑖 (𝑖=1,2,3,4,5): 𝑟₁=𝑠_3.21,𝑠_5.18,𝑟₂=𝑠_3.74,𝑠_4.82,𝑟₃=𝑠_4.72,𝑠_5.46,𝑟₄=𝑠_3.36,𝑠_5.57,𝑟₅=𝑠_4.62,𝑠_6.03. (8)

Step 2. Rank these overall preference values 𝑟_𝑖 (𝑖=1,2,3,4,5); we first compare each 𝑟_𝑖 with all the 𝑟_𝑗 (𝑗=1,2,3,4,5) by using (3) and then develop a complementary matrix: 𝑃=.0.5000.7200.1800.4590.1320.2800.5000.0100.3500.3900.8200.9900.5000.7580.4500.5410.6500.2420.5000.2220.8680.6100.5500.7780.500 (9)

Summing all the elements in each line of matrix 𝑃, we have 𝑝₁=2.037,𝑝₂=1.108,𝑝₃𝑝=3.564,₄=2.246,𝑝₅=3.663. (10)

Step 3. Rank all the urban tourism cities 𝐴_𝑖 (𝑖=1,2,3,4,5) in accordance with the values 𝑝_𝑖 (𝑖=1,2,3,4,5): 𝐴₅≻𝐴₃≻𝐴₄≻𝐴₁≻𝐴₂. Thus, the most desirable urban tourism city is 𝐴₅.

5. Conclusions

With the rapid development of tourism and city, the development of tourism in promoting the city has also brought a series of problems: the integration of tourism resources among the cities is more difficult, lacking of urban tourism regional planning, the chaos of urban tourism functions and other features, tourism functional area is difficult to develop and so on, and the internal region has also suffered more severe competitive pressures. How to cultivate and improve the tourist city of travel services functional areas, in order to improve tourism services, and better development of urban tourism are becoming the most urgent problems to be solved in each tourist city currently. In this paper, we investigate the multiple attribute decision making problems for evaluating the urban tourism management efficiency with uncertain linguistic information. We utilize the uncertain linguistic weighted averaging (ULWA) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the alternatives and then rank the alternatives and select the most desirable one(s). Finally, a numerical example for evaluating the urban tourism management efficiency with uncertain linguistic information is used to illustrate the proposed model.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

The work was supported by the Xinjiang Social Science Fund (13BGL035).