4) Compute the combination weight vector. If the sequencing weight vector of the (k − 1)th layer factor towards the total goal is

${W}^{\left(k-1\right)}={\left({W}_{1}^{\left(k-1\right)},{W}_{2}^{\left(k-1\right)},\cdots ,{W}_{n}^{\left(k-1\right)}\right)}^{\text{T}}$

The entire factors of the kth layer towards the synthetic sequence vector ${W}^{\left(k\right)}$ of the total goal are given by the following equation:

${W}^{\left(k\right)}=\left({P}_{1}^{\left(k\right)},{P}_{2}^{\left(k\right)},\cdots ,{P}_{n}^{\left(k\right)}\right){W}^{\left(k-1\right)}={P}^{\left(k\right)}{W}^{\left(k-1\right)}$

where ${P}^{\left(k\right)}$ is the sequencing weight vector of the kth layer factor towards the (k − 1) the layer factor.

4. Case Study

This next will take the Zhang Aiping’s former residence in Da Zhou as an example, using the fuzzy comprehensive evaluation model, which use the analytic hierarchy process to calculate weight, to evaluate the red tourism resources of Zhang Aiping’s former residence. Specific steps are as follows.

4.1. Data Source

According to the red tourism resources evaluation index system, the main content of the research questionnaire is the satisfaction degree of the visitors to the evaluation index, and the grade option is set to be very satisfied, satisfied, general, dissatisfied, very dissatisfied which is according to the Li Kete’s five scale. A total of 200 questionnaires are distributed, 187 copies are collected, and 175 valid questionnaires are collected, get data as shown in Table 2.

4.2. Determine the Index Weight

According to the expert investigation method, the pair-wise comparison matrixes are established as follows:

$A=\left[\begin{array}{ccc}1& 4& 2\\ 1/4& 1& 1/2\\ 1/2& 2& 1\end{array}\right]$ ; ${B}_{1}=\left[\begin{array}{cccc}1& 2& 5& 3\\ 1/2& 1& 3& 2\\ 1/5& 1/3& 1& 1/2\\ 1/3& 1/2& 2& 1\end{array}\right]$ ;

${B}_{2}=\left[\begin{array}{cc}1& 1/2\\ 2& 1\end{array}\right]$ ; ${B}_{3}=\left[\begin{array}{ccc}1& 2& 4\\ 1/2& 1& 2\\ 1/4& 1/2& 1\end{array}\right]$ .

The weight of each index as shown in Table 3.

4.3. Fuzzy Comprehensive Evaluation

The evaluation objects are ${B}_{1},{B}_{2},{B}_{3}$ , evaluation Indexes are ${U}_{1},{U}_{2},\cdots ,{U}_{9}$ , and comment set $V$ contents very satisfied, satisfied, general, dissatisfied, and very dissatisfied. Let the membership degree ${r}_{ij}$ be the ratio of the number of factor ${U}_{i}$ to comment ${V}_{j}$ to the total number of people participating in the survey, then the fuzzy evaluation matrixes can be structured as follows:

${R}_{1}=\left[\begin{array}{ccccc}0.26& 0.40& 0.20& 0.10& 0.04\\ 0.11& 0.36& 0.33& 0.12& 0.09\\ 0.15& 0.37& 0.31& 0.11& 0.06\\ 0.15& 0.39& 0.30& 0.10& 0.06\end{array}\right]$ ,

Table 2. The original survey data of comprehensive evaluation.

Table 3. Evaluation index weight of red tourism resources.

${R}_{2}=\left[\begin{array}{ccccc}0.10& 0.34& 0.35& 0.12& 0.09\\ 0.14& 0.38& 0.36& 0.09& 0.03\end{array}\right]$ ,

${R}_{3}=\left[\begin{array}{ccccc}0.09& 0.26& 0.42& 0.11& 0.12\\ 0.13& 0.34& 0.35& 0.13& 0.05\\ 0.05& 0.25& 0.36& 0.21& 0.14\end{array}\right]$ .

The weight of ${U}_{1},{U}_{2},{U}_{3},{U}_{4}$ relative to ${B}_{1}$ :

${W}_{1}=\left({w}_{11},{w}_{12},{w}_{13},{w}_{14}\right)=\left(0.4824,0.2718,0.0883,0.1575\right)$ ;

The weight of ${U}_{5},{U}_{6}$ relative to ${B}_{2}$ :

${W}_{2}=\left({w}_{21},{w}_{22}\right)=\left(0.3333,0.6667\right)$ ;

The weight of ${U}_{7},{U}_{8},{U}_{9}$ relative to ${B}_{3}$ :

${W}_{3}=\left({w}_{31},{w}_{32},{w}_{33}\right)=\left(0.5717,0.2857,0.1429\right)$ ;

The weight of ${U}_{1},\cdots ,{U}_{9}$ relative to $A$ :

$W=\left(0.2757,0.1553,0.0504,0.0900,0.476,0.0952,\mathrm{0.1633.0.0816},0.0408\right).$

The fuzzy evaluation result contains two parts: the target hierarchy and the rule hierarchy. The fuzzy sets of three rule hierarchy are calculated as follows:

${C}_{i}={W}_{i}{R}_{i}\text{,}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,3$

And it can be calculated:

${C}_{1}={W}_{1}{R}_{1}=\left(0.1910,0.3843,0.2605,0.1071,0.0571\right)$ ;

${C}_{2}={W}_{2}{R}_{2}=\left(0.1295,0.3676,0.3562,0.09851,0.0495\right)$ ;

${C}_{3}={W}_{3}{R}_{3}=\left(0.0955,0.2816,0.3910,0.1290,0.1029\right)$ ,

Let ${R}^{*}=\left(\begin{array}{c}{R}_{1}\\ {R}_{2}\\ {R}_{3}\end{array}\right)$ , the fuzzy sets of target hierarchy can be calculated as:

$C=W{R}^{*}=\left(0.1549,0.3526,0.3114,0.1119,0.0691\right)$ .

Finally, according to the Li Kete’s five scales, the five comments are evaluated as Table 4:

Then the evaluation results are calculated:

${E}_{1}=5\times 0.1910+4\times 0.3843+3\times 0.2605+2\times 0.1071+0.0571=3.5449$ ${E}_{2}=5\times 0.1295+4\times 0.3676+3\times 0.3562+2\times 0.0971+0.0495=3.4305$ ${E}_{3}=5\times 0.0955+4\times 0.2816+3\times 0.3910+2\times 0.1290+0.1029=3.1380$ $E=5\times 0.1549+4\times 0.3526+3\times 0.3114+2\times 0.1119+0.0691=3.4123$

It is shown in Table 5.

5. Result Analysis and Suggestion

Based on the evaluation result, the comprehensive evaluation value E for Zhang Aiping’s, Former Residence, red tourism resource is 3.4123. According to evaluation standard, this red tourism resource is above average, which means that the development of it is reasonable and positive although some spaces for development and improvement exist.

The evaluation value for resource value, scale of scenic spot and auxiliary business are
${E}_{1}=3.5449,{E}_{2}=3.4305,{E}_{3}=3.1380$ respectively. Resource value (E_{1}) is the best, which shows that it is the most obvious worth and contribution to comprehensive evaluation of this red scenic spot. According to the portion of four evaluation indexes, revolutionary historical culture value takes significant part. As the glorious history of General Zhang Aiping, it indicates that this red scenic spot contains rich revolutionary historical culture connotation, which has affected later generations positively too much. Evaluation value of scale of scenic spot is better than comprehensive evaluation value, which means that this spot

Table 4. Fuzzy score table of evaluation grades.

Table 5. Comprehensive evaluation results of red tourism resources.

possesses preferable capacity for visitors. Actually, it covers an area of around 500 Mu to be able to bear more than 10 thousand tourists’ visiting at the same time. Tourism auxiliary business is the worse, which is lower than comprehensive evaluation value to bring negative effect for comprehensive evaluation. So auxiliary business needs to be developed and improved dedicatedly by related parties. Among traffic, catering and tourism goods, catering takes the highest portion and traffic takes the lowest portion. It indicates that traffic of this spot is relatively good, but catering and tourism good is poor, which should be improved as soon as possible.

Fund

This research was supported by scientific research fund of Sichuan Provincial Education Department of China (18ZA0416; 16ZA0357).

Cite this paper

Hu, R. and Zhang, C. (2018) An Empirical Study on Fuzzy Comprehensive Evaluation of Red Tourism Resources Based on AHP.*Applied Mathematics*, **9**, 171-177. doi: 10.4236/am.2018.92012.

Hu, R. and Zhang, C. (2018) An Empirical Study on Fuzzy Comprehensive Evaluation of Red Tourism Resources Based on AHP.

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