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College of Science, Hebei Agricultural University, Baoding 071000, China

1 Introduction

A livable city is characterized by beautiful environment, social stability, advanced civilization, comfortable life, economic harmony, and high reputation, which are comprehensive evaluation of the degree of livability. The China Institute of City Competitiveness (CICC) has released the "Top Ten Livable Cities in China" for many consecutive years. In the mathematical models, commonly used evaluation models include composite index method, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method, AHP (analytic hierarchy process), RSR (Reshaped Sequential Replacement) method, fuzzy comprehensive evaluation method, grey system method and so on. In this study, we mainly applied the fuzzy comprehensive evaluation method. In the evaluation of livable cities, the livability of the city is evaluated according to the livability index, and the comprehensive evaluation method converts the qualitative evaluation into quantitative evaluation based on the subordination theory in fuzzy mathematics.

2 Comprehensive evaluation method

2.1DynamicentropymethodIf the information entropyejof a certain index is smaller, it means that the degree of variation of the index is greater, and the information it provides is more, the function it plays in the comprehensive evaluation is greater, and its weight is greater. Conversely, if the information entropyejof a certain index is greater, it means that the degree of variation of the index is smaller, and the information it provides is less, the function it plays in the comprehensive evaluation is smaller, and its weight is smaller. The entropy method can measure the amount of information provided by the data and avoid the influence of invalid information. Effectively measuring the impact of information on the research object is the importance of comprehensive indicators and the amount of information provided by the indicators. It determines the final weight through these two aspects.

Assume there aremitems to be evaluated, andnevaluation indicators, forming the original data matrixH= (hij)m×n

Calculate the proportionpijof thei-th indicator value in thej-th indicator:

Obtain the entropy weightwjof thej-th indicator:

Determine the comprehensive weightβjof the indicator: assume that the evaluator determines the weight of indicator importance according to his purpose and requirement asαj,j=1, 2…n, combined with the entropy weightwjof the indicator, it is able to calculate the comprehensive weight of the indicatorj:

2.2FuzzycomprehensiveevaluationmethodThe fuzzy comprehensive evaluation method needs determining the factor setU={u1,u2,…un}, determining the judgment set (evaluation set or decision set)V={v1,v2,…vm}, and establishing the single factor judgmentf∶U→F(V)·ui→f(ui)=(ril,ri2,…rim)∈F(V), and also determining the subordinate function (Fig.1):

Fig.1Subordinatefunction

Then, we can get the single factor evaluation matrixR.

For the weightA=(a1,a2,L,an), the comprehensive evaluation takes the fuzzy matrix synthesis operation, we can get the comprehensive evaluationB:

B=AoR=(b1,b2,L,bm)∈F(V)

3 Research object

We selected eight cities (Suqian, Lianyungang, Suzhou, Shangqiu, Jining, Zaozhuang, Xuzhou and Huaibei) for comprehensive evaluation of livable cities. According to the survey data, the degree of livability of a city is generally evaluated from five factors: social civilization, economic affluence, environmental beauty, resource carrying capacity, and life convenience. However, considering that there are many uncertainties in the search of data in these five fields, we surveyed some related data by the conversion method, namely, we calculated the degree of livability of these eight cities through the survey and reasoning. According to survey data, a city’s environmental beauty can be measured by the degree of beautification of a city’s construction, while an important indicator of social civilization degree is morality and education level; economic affluence is measured mainly through GDP and per capita GDP; the resource carrying capacity is mainly measured through the urban infrastructure carrying capacity, and in the life convenience, the per capita commercial facilities takes up the largest portion. Then, we took the per capita GDP, school coverage density, air quality index (AQI), per capita commercial floor space, and beauty spot density as the sub-indicators of the social civilization, economic affluence, environmental beauty, resource carrying capacity, and life convenience.

4 Fuzzy comprehensive evaluation

(i) Based on the dynamic entropy weight method, we calculated the weight of the five factors in the evaluation of livable cities:

A=(0.146 7 0.264 4 0.015 6 0.007 6 0.565 7)

(ii) The single factor evaluation matrix for eight cities is as follows:

(iii) Through multiplying the weight of each evaluation indicator with the single factor evaluation matrix, we obtained the livability index of these eight cities (Table 1 and Fig.2).

Table1Livabilityindexofeightcities

CityLivabilityindexSuqian0．1403Lianyungang0．5963Suzhou0．1152Shangqiu0．3461Jining0．5386Zaozhuang0．7115Xuzhou0．6858Huaibei0．3161

Fig.2Livabilityindexofeightcities

(iv) According to the livability ranking of cities, the livability degree of Zaozhuang was relatively high, while the livability degree of Suzhou was relatively low.

5 Conclusions

In this study, taking the fuzzy comprehensive evaluation method, we evaluated the livability degree of eight cities, and established an evaluation model integrating many factors. This model is objective in evaluation of livability degree of cities. On the basis of the established model, we selected eight cities to make evaluation and obtained the different livability of eight cities in different evaluation criteria. Finally, we concluded that the livability degree of Zaozhuang was relatively high, while the livability degree of Suzhou was relatively low. We are intended to provide a quantitative analysis method on the basis of qualitative analysis for evaluation of livable cities.

[1] XIA JJ, LIU CP. Fuzzy mathematics method and its application[M]. Wuhan：Huazhong University of Science & Technology Press，2000. (in Chinese).

[2] WANG XH, LIU YY. Discussion on the air quality index and air pollution index[J]. China Terminology, 2011,13(6):49-51. (in Chinese).

[3] YAO YG, ZHU YL, ZOU Q. Research on air quality index with Excel software[J]. Environmental Science and Management，2013, 38(6)：140-142. (in Chinese).

[4] LI GJ. Environmental quality assessment of fuzzy comprehensive evaluation[J]. Journal of Dalian Nationalities University，2009,11(1):1-3. (in Chinese).

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