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

Authors: Song-Mao Wang; Liang-Yan Fang; Feng Deng
Journal: Journal of Control Science and Engineering
 (2014)

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## 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.


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## Body

## 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

LetS={si∣i=1,2,…,t} be a linguistic term set with odd cardinality. Any label, si, represents a possible value for a linguistic variable, and it should satisfy the following characteristics [13, 14]: (1) the set is ordered si>sj, if i>j; (2) there is the negation operator neg(si)=sj such that j=t+1-i. For example, S can be defined as
(1)S={s1=extremelypoor,s2=verypoor,hhhs3=poor,s4=medium,s5=good,hhhs6=verygood,s7=extremelygood}.Definition 1 (see [15]).
LetULWA:S~n→S~; if
(2)ULWAω(s~1,s~2,…,s~n)=ω1×s~1⊕ω2×s~2⊕⋯ωn×s~n,
where ω=(ω1,ω2,…,ωn) is the weighting vector of uncertain linguistic variables s~i (s~i∈S~, i=1,2,…,n) with ωi∈[0,1], ∑i=1nωi=1, then the function ULWA is called the uncertain linguistic weighted averaging (ULWA) operator of dimension n.Definition 2 (see [15]).
Lets~1=[sα1,sβ1] and s~2=[sα2,sβ2] be two uncertain linguistic variables, and let len(s~1)=β1-α1 and len(s~2)=β2-α2, and then the degree of possibility of s~1≥s~2 is defined as [14]
(3)p(s~1≥s~2)=max⁡(0,len(s~1)+len(s~2)-max⁡(β2-α1,0))len(s~1)+len(s~2).


## 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. LetA={A1,A2,…,Am} be a discrete set of alternatives and G={G1,G2,…,Gn} the set of attributes; ω=(ω1,ω2,…,ωn) is the exponential weighting vector of the attributes Gj (j=1,2,…,n), where ωj∈[0,1], ∑j=1nωj=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
(4)r~i=ULWAω(r~i1,r~i2,…,r~in),gggggggggggi=1,2,…,m,
to derive the collective overall preference values r~i (i=1,2,…,m) of the alternative Ai, where ω=(ω1,ω2,…,ωn)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 pij=p(r~i≥r~j), and then we develop a complementary matrix as P=(pij)m×m, where
(5)pij≥0,pij+pji=1,hpii=0.5,i,j=1,2,…,m.Summing all the elements in each line of matrixP, we have
(6)pi=∑j=1mpij,i=1,2,…,m.Step
3. Rank all the alternatives Ai (i=1,2,…,m) and select the best one(s) in accordance with pi (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 citiesAi (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 Ai (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
(7)R~=G1[sg]G2[sdi]G3[sdi]G4A1A2A3A4A5([s4,s6][s5,s6][s3,s4][s2,s4][s2,s4][s2,s3][s4,s5][s4,s5][s4,s5][s3,s5][s1,s2][s5,s6][s5,s6][s4,s5][s4,s6][s2,s3][s3,s4][s5,s6][s3,s5][s5,s6])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 Ai (i=1,2,3,4,5):
(8)r~1=[s3.21,s5.18],r~2=[s3.74,s4.82],r~3=[s4.72,s5.46],r~4=[s3.36,s5.57],r~5=[s4.62,s6.03].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:
(9)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].Summing all the elements in each line of matrixP, we have
(10)p1=2.037,p2=1.108,p3=3.564,p4=2.246,p5=3.663.Step
3. Rank all the urban tourism cities Ai (i=1,2,3,4,5) in accordance with the values pi (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.



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*Source: 582454-2014-07-17.xml*