Tourism management efficiency maximization model AHP and Grey Theory Analysis

Keywords: AHP, gray theory, tourism management efficiency, maximization model, modeling, analysis.

Abstract. In this paper, we build housing performance evaluation model with AHP to determine the index system of residential properties. And further judgment matrix to determine the weight of each index. At the same time according to the weight of each index, combined with gray relational theory associate degree real residence with an ideal model among the analyzed system will simplify complex issues, the abstract problems concrete, the quantitative results and qualitative analysis of the perfect combination, and provide consumers with a practical assessment tool. Tourist Perception is tourism tourist objects, environmental conditions and other travel information psychological process obtained through the senses travelers. Tourist Perception involves many factors assessment, evaluation is not complete and inaccurate information, determine the comprehensive evaluation of gray for the characteristics of the analytic hierarchy process and gray combination of theoretical tourists were perceived perception evaluation. It analyzes the key factors that influence the perception of tourists, and on this basis, build a tourist perception evaluation system; then AHP to determine the weight of each index weight; final evaluation model based on five main Guilin Tourism Circle Tourism, for example, tourists perceive a comprehensive evaluation. Empirical studies show that the multi-level gray evaluation results obtained tourists perceived objective, reliable and able to provide a basis for decision-making tourism planning, management and marketing.


Extensive tourist behavior research relates to the field, Tourist Perception is one of the important areas. Tourist Perception refers to the tourists through the psychological process of tourism and the tourism objects obtained senses, environmental conditions and other travel information. From the perspective of behavioral geography to study the perception of tourists, contribute to enrich and improve the system of tourism geography research, provide guidance for tourism development and planning, making tourism resources development, tourism product design, development and other aspects of the tourist market work more effective.

With house prices rising, the housing problem is people’s lives is an important part. Therefore, evaluation of residential properties becomes increasingly important. However, the problem is very complex house performance evaluation, the system complex relationship between the factors and is constantly changing, yet can not accurately grasp its intrinsic relevant contact, with a certain grayness. In this context the AHP and gray correlation method combine residential properties were evaluated in order to make the evaluation results more scientific and practical.

Satie operations research by the famous American family in the early 1970s proposed AHP is a kind of decision-making qualitative analysis and quantitative analysis of the combination of decision makers thought process complex problems can be systematic, modeling , quantitative. This paper uses AHP to establish residential and functional evaluation system to determine the weight of each index.

Environmental quality assessment is a comprehensive contribution of various pollution factors of pollution on environmental quality, to be the extent of the merits of environmental quality assessment of environmental systems. Establish an objectively describe the environmental quality of mathematical models, has been an important topic in environmental science. In recent years, despite environmental quality assessment fuzzy comprehensive evaluation method made some progress. However, since this method has some deficiencies.

Tourist Perception tourists comprehensive tourism products and services reflect the degree of perception, is affected by several factors, and the link between factors with incomplete, difficult to accurately quantify the kind of multi-layered, complex evaluation problem, consider using AHP comprehensive evaluation, AHP identify systemic problems, high reliability is high, but when the use of expert consultation, easy to grasp the scale are not allowed to lose some information to the new media of Ideological and Political Education challenges.

In addition, tourists perceive the evaluation is based on the evaluator’s personal preferences, cultural background, experience and cognitive experience, it is difficult to exclude many deviations caused by human factors, resulting in the evaluation information provided in the evaluation less accurate, or with gray nature. Tourist Perception Evaluation solve the above information appears in incomplete, inaccurate information is an effective way to put the problem of gray system theory with analytic hierarchy Combination. Grey system theory for inaccurate information, with incomplete analysis system has obvious advantages, and the sample size is not critical requirements.

Figure.1 Analytic hierarchy process

The Proposed Methodology

Multilevel Grey Evaluation Method. Tourist Perception assessment should first analyze the key factors affecting the perception of tourists, build a multi-level hierarchical evaluation index system, using AHP to determine the weight of indicators, the development of standard rating scale evaluation of the last evaluation model based on a comprehensive assessment to determine the value.

Evaluation and the importance of the target is different, that have different weights. Using the principle of AHP, inter twenty-two indicators compare pairs of importance to construct judgment matrix, and then re-used method for solving matrix eigenvalues ​​obtained rights.

Evaluation is subjective indicators, namely qualitative indicators, qualitative indicators can be achieved through the development of quantitative indicators Grading standards.

Gray evaluation weight matrix as follows:


Evaluation results are:


Evaluation of each layer is determined by the weight of analytic hierarchy process. We chose from the Guilin Tourism Bureau, tourism experts Guilin College of 20 people, according to the scaling theory of AHP qualitative relative importance among the three indexes to compare. Given the relative importance of the different expert opinions vary between indicators, after two rounds of feedback, get the final calibration value comparison between the index and the right to seek re-evaluation of each of these indicators.

Figure.2 Multilevel evaluation method

The use of multi-level gray evaluation method Tourist Perception initial attempt evaluated. The analytic hierarchy process and gray system theory, to effectively address information Tourist Perception Evaluation appear incomplete and inaccurate information on the issue. Guilin Tourism Circle by empirical study five major tourist destination, results are objective and credible. Overall, the principle of the method is clear, simple calculation, and a small amount of sample required, it is possible for tourists perceive scientific and standardized evaluation provide a useful reference. Of course, this method also has some areas for improvement, such as the selection and improve the evaluation system, a reasonable sample size determination and the like.

Mathematical model of gray association.Factor between the two systems, which change with time or different objects and measure the size of the association, known as associate degrees. In the system development process, if the two factors are consistent trends, ie a higher degree of simultaneous changes that can be described as both a high degree of association; on the contrary, lower. Thus, the gray correlation analysis method, based on the degree of similarity or dissimilarity between the trends of factors, namely the “gray correlation degree” as a method to measure the degree of association between factors.

Comparative characteristic behavior of the system to determine the number of reference series and the system behaves column reflect the characteristics of system behavior data sequence, called the reference number of columns. Sequence data composed of factors affecting the behavior of the system, called the comparison sequence.

Due to the different systems of physical significance of various factors, resulting in dimensional data is not necessarily the same, is not easy to compare, or comparison is difficult to get the correct conclusion. Therefore, during the gray system analysis, it is generally required to be non-dimensional data processing.

Analytic Hierarchy Process above and gray association analysis of steel structure housing, residential and residential masonry structure framework of a comprehensive evaluation of the performance and the degree of correlation obtained with three different ideal residential residential structure between, so as to achieve three different evaluation of the structure of residential properties, advantages and disadvantages compare its performance level.

Using AHP and gray correlation method for comprehensive evaluation of residential properties, and residential steel frame and masonry structure residential housing construction comprehensive evaluation of performance, and obtain associate degrees in three different structures between residential housing over the same . It can be seen that the AHP and gray correlation combine residential properties were evaluated, taking into account not only of each index in the whole impact factor, but also to achieve the degree of association between actual residence with the ideal model of analysis, and quantitative results qualitative analysis of the perfect combination to make the evaluation results more reasonable, more scientific and practical. Thereby providing useful information for the real estate development, but also for consumers instructive.

Gray clustering method.Cluster analysis is to determine quantitatively using mathematical clustering Relationships between objects will be one kind of typing class of multivariate analysis method of gray cluster clustering is a common method of introduction of whitening function to generate gray theory is formed is a poly Whiting class object for different clusters indicators have, according to some kind of gray summarize, we put forward a number of whitening function green gray become the basis for a new clustering methods.

Grey clustering method generally includes the following aspects: (1) cluster sample, determine the number of indicators and whitening; (2) determine the gray class division; (3) the number and normalized Albino gray class; (4) Albino determine the function; (5) the right to strike clustering; (6) to calculate the clustering coefficient; (7) clusters.

Each sample has a corresponding coefficient for each cluster of Environmental Quality rating (gray type). In the clustering coefficient, usually gray clustering method is based on the maximum value of the coefficient is the level corresponding to the level of the sample belongs to .

Grey Decision.Grey situation decision refers to the decision contains a gray element as environmental quality assessment system environment, it can be evaluated or evaluation factors deemed gray element, the environmental system as an event, different environmental quality level response, through decision analysis to determine the optimal situation, it is the level corresponding environmental evaluation. Grey decision steps are summarized below.

The situation with the situation in the matrix structure;

Seeking objective measures of efficacy;

Multi-objective decision making;

The decision-making process, that is based on the performance of each project’s objectives, the selection of the maximum measure yuan, and according to the maximum measure to determine the optimal situation.

Evaluation of results using different methods to the same sample of gray very different; the evaluation results and the method of gray correlation method of gray situation given the low resolution; high-resolution gray clustering method.

Cause of these results, the study suggests that in the course of the first two evaluation methods used in processing right for each pollution factor; while the latter introduced the idea of ​​different weights (the right to strike clustering process).

In response to these phenomena, make the following improvements. Taking into account the different pollutants, different standard values, and sometimes the absolute value of the difference is large, the level of different effects of different concentration of pollutants on the quality of the environment. Therefore, this article on the method of gray correlation method and medium gray situation related to strike the right and a method of making the right to a reasonable improvement, according to the proposed pollutant exceedances (pollutants measured concentrations and the ratio of the standard limits) of each point (k = 1,2, … n) weighted correlation coefficient, then calculate correlation, based on the quality level of the size of the correlation degree determine samples (process weighted gray situation similar to this Act).

Taking into account (a) a level range of the right upper (lower) weight each has a contribution to make to judge quality level shall be determined in accordance with “a level greater than the sum of the” principles of classification.


Grey theory consistent evaluation methods Evaluation and comparison of evaluation results improved due to take into account the interrelated nature of different weights of thought and comprehensive weight values, the method can overcome the false otherwise arise. Improved Grey Theory Evaluation law on environmental quality to evaluate not only feasible, but the results more credible, more realistic. using multilevel gray evaluation method tourist perception initial attempt evaluated. The analytic hierarchy process and gray system theory, to effectively address information Tourist Perception Evaluation appear incomplete and inaccurate information on the issue. Guilin Tourism Circle by empirical study five major tourist destination, results are objective and credible. Overall, the principle of the method is clear, simple calculation, and a small amount of sample required, it is possible for tourists perceive scientific and standardized evaluation provide a useful reference. Of course, this method also has some areas for improvement, such as the selection and improve the evaluation system, a reasonable sample size determination and the like.

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