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.

晨间孩子们的入园时间陆陆续续并不是整齐划一的，于是结合实际情况我们灵活调整了幼儿的一日活动作息时间表中大班的晨间锻炼活动时间从接待来园后的半个小时以后固定开始，每天十五分钟的队列、操节活动后是大约二十五分钟的户外自主锻炼时间，小班则在中大班早操后在楼顶户外开始进行，时间上要短一些。

2 Comprehensive evaluation method

2.1 Dynamic entropy method If the information entropy ej of 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 entropy ej of 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 are m items to be evaluated, and n evaluation indicators, forming the original data matrix H = (hij)m×n

Calculate the proportion pij of the i-th indicator value in the j-th indicator:

where (U, V, R) forms a fuzzy comprehensive evaluation model, and U, V, and R are three essential factors of this model.

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

1.2 种植时间长技术成熟：彰武红干辣椒栽培，始于上世纪8O年代。是辽宁省大面积栽培红干辣椒的县份之一，至今已有20多年的种植历史。最高年份种植面积50000hm2。随着人民生活水平的不断提高，人们对辣椒的需求量越来越大，种植面积逐年扩大，种植区域由原来的2个乡（镇）扩展到15个乡（镇），种植区域由平地向沙地、风沙地、山地发展。种植方式由露地直播改进为地膜种植。

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

Obtain the entropy weight wj of the j-th indicator:

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Fig.1 Subordinate function

Then, we can get the single factor evaluation matrix R.

Calculate the entropy of the j-th indicator: gln pij, where

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

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.

3 Research object

B=AoR=(b1, b2, L, bm)∈F(V)

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:

深入推进不动产登记“最多跑一次”改革的几点思考（周张琪） ...................................................................6-38

（1）联调通信测试：FPGA与CPU进行双向的数据通信，通过FPGA显示CPU发送来的计数信号，CPU能接收FPGA的中断信号与指令等信号。

(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).

体检工作均由工作经验丰富的相关人员统一完成,进行手肘正中位置进行静脉采血,以碘酒进行注射器、体检人员手肘消毒,所有人员均在同一环境、同一针头规格、同一操作方式下完成整个体检采血工作。

Table 1 Livability index of eight cities

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

Fig.2 Livability index of eight cities

(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.

References

[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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