Microsoft Word - 8-门可佩.doc 48-54 Advances in Systems Science and Applications (2010), Vol.10, No.1 ISSN 1078-6236 International Institute for General Systems Studies, Inc. Research on Comprehensive Evaluation of Harmonious Society in East China* Kepei Men, Liangyu Jiang and Jing Liu Nanjing University of Information Science and Technology, Nanjing 210044, China Email: menkp@yahoo.com.cn Abstract The harmonious society is the general goal of social development. We select 5 subsystems and 35 evaluation index to establish an system for evaluating harmonious society, with the method of Principle Component-Cluster Analysis, according to 2007 Statistical Yearbook of China and some other statistical data. Meanwhile, we use TOPSIS method as an assistant certification to analyze the harmonious society development of east China. The result shows that the six provinces in east China and Shanghai city could be divided into 3 parts. The first part includes Shanghai. The second part includes Zhejiang, Jiangsu and Shandong. And the third part includes Fujian, Jiangxi and Anhui. The result is identical to practice developing of east China. Keywords East China Harmonious Society Comprehensive evaluation Principle Component-Cluster Analysis (PCCA) 1. Introduction Realizing social harmony and building a nice society is the social ideal that human being assiduously seeks. It is also the social ideal of all the Marxist Party including the Communist Party of China. To construct a socialist harmonious society is a great task that put forward in whole under the new situation of initiating the socialist road with the specific practice in China. Mr Hu Jintao proposed to realize harmony zone on the 5th anniversary forum of the foundation of Shanghai cooperation organization. East China is the most active economic growth zone. The six provinces and Shanghai city of it account for less than 1/4 of the whole country, the population is 28.74% of the whole nation and the land area only accounts for 8.13%. But it has made great contribution for China, because of its wonderful economy. According to the statistical bulletins of nation and east China in 2007, we knew that the resident income of the six provinces and Shanghai city was kept growing, and the living standard was improved further. The per capital dominating income of urban residents had exceeded 11 thousand yuan. Among them, Shanghai, Jiangsu, Zhejiang, Fujian and Shandong were over 14 thousand yuan, which were higher than the national average 13.786 thousand yuan. The GDP of this area in 2006 and 2007 were reached 8826.513 billion yuan and 10406.21 billion yuan respectively, which accounted for 41.86% and 42.20% of China’s GDP. Therefore, study on the problem about the construction of the harmonious society in east China is strongly representative and has a profound significance. In this paper, we focus on the construction idea of socialist harmonious society, to put forward a harmonious society index system with great operative, for the purpose of providing reference for the construction of harmonious society. 2. The introduction to research methods 2.1 The Method of Principal Component and Clustering Analysis[1-4] Suppose there are n samples, every sample has p indices, we get a original data matrix ∗ This work is supported by the Key Projects of National Statistics Research Program (2008LZ022). Advances in Systems Science and Applications (2010), Vol.10, No.1 49 ( )ij n pX x ×= , ( 1, 2, , ; 1, 2, )i n j p= = and we make linear combination (comprehensive index) with p vectors 1 2, , , pX X X , that is 1 1 2 2 , 1, 2, ,i i i pi pF a X a X a X i p= + + = Then we limit the combination coefficients 1 2( , , , )i i i pia a a a= with 2 2 2 1 2 1, 1, 2, ,i i pia a a i p+ + + = = in which, ia is a unit vector and 1i ia a = . The comprehensive index is determined by the following rules: (1) iF and jF ( , , 1, 2, ,i j i j p≠ = ) are uncorrelated, that is ( , ) 0i jCov F F = . (2) 1F is the biggest variance in all the linear combinations of 1 2, , , pX X X , namely, ' 1 1 ( ) max p i i c c i Var F Var c X = = ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ∑ , in which ' 1 2,( , , )pc c c c= . As to the rule (2), we will get the similar conclusions. 2F , uncorrelated with 1F , is the biggest variance in all the linear combinations of 1 2, , , pX X X . pF , uncorrelated with 1 2 1, , pF F F − , is the biggest variance in all the linear combinations of 1 2, , , pX X X , and so on. The comprehensive vectors 1 2, , , pF F F , satisfied above requirements, are the principal components. The information extracted from the information content of original indices decrease successively. We use variance to measure information extracted by every principal component, and the contribution of principal component variance is equal to corresponding eigenvalue iλ to correlation matrix of the original data. 1 2( , , , )i i i pia a a a= , the combination coefficient of every principal component, is the eigenvector it to corresponding eigenvalue iλ . The contribution rate of variance is 1 / p i i j j α λ λ = = ∑ . The more iα , the more information corresponding principal component explains. When the variance contribution rate of one principal component is very small, we think the information it provides is little, then we may delete it. In general case, if the cumulative variance contribution rate of first q principal components reaches 85%, we just consider the first q principal components, then explain properties of random vector X with them. Other principal components are the random errors caused by incorrect observation. Research on comprehensive evaluation has made process[5-7]. Papers [1-3] point the method popular in recent year is to structure a comprehensive evaluation function of principal components for ranking, which is based on the contribution rate of variance iα , but it is wrong. When the contribution rate of variance of the first principal component 1F is quite high (over 85%), we may think this principal component can almost reflect the information provided by the original variables. Then we may rank and evaluate according to the scores of the first principal component. To the ranking problems of multiple index system, when the contribution rate of variance of the first principal component is not over 85%, that is, the original data information expressed by the first principal component is not enough, it has one-sidedness, if we still rank and evaluate only by the scores of the first principal component. At this time, we combine principal Men: Research on Comprehensive Evaluation of Harmonious Society in East China 50 component analysis with cluster analysis, which is named “principal component-cluster analysis (PCCA)”. Table 1 The index system Subsystem Index Unit Directivity M at er ia l c iv ili za tio n 1 2 3 4 5 6 7 8 9 10 Yuan/person yuan yuan % % Square meter/person % Part/10 thousand agriculture=1 % positive positive positive negative negative positive positive positive medium positive Po lit ic al ci vi liz at io n 11 12 13 14 Person/10 thousand female=100 % Part/10 thousand positive medium negative negative Sp iri tu al ci vi liz at io n 15 16 17 18 19 % Person/100 thousand % % Kind/10 thousand positive positive positive positive positive So ci al ci vi liz at io n 20 21 22 23 24 25 26 27 Person/10 thousand person/100 thousand old % % Part/10 thousand % % positive negative positive positive positive positive negative positive H ar m on io us so ci et y Ec ol og ic al ci vi liz at io n 28 29 20 31 32 33 34 35 ton/10 thousand yuan % % % % % 10 thousand stere % negative positive positive positive positive positive positive positive Note: 1 means Per capital GDP; 2 means per capital disposable income of urban residents; 3 means per capital net income of rural residents; 4 means the Engle's coefficient of urban residents; 5 means the Engle's coefficient of rural residents; 6 means housing areas of rural residents; 7 means the proportion that the tertiary industry accounts for GDP; 8 means numbers of patents application; 9 means consumption level of urban and rural residents; 10 means the proportion that R&D accounts for GDP; 11 means lawyer’s numbers that per ten thousand people have; 12 means sex ratio of senior middle school graduates; 13 means registered unemployment rate of urban residents; 14 means numbers of criminal case; 15 means the proportion that education and culture entertainment account for total consumption expenditure; 16 means average students number of colleges and universities; 17 means excellent rate of product quality; 18 means the proportion that education operating expenses account for fiscal expenditure; 19 means book publishing kinds; 20 means doctor’s numbers that per ten thousand people have; 21 means death toll from traffic accidents; 22 means average life expectancy; 23 means mobile subscription; 24 means gross enrollment ratio of higher education; 25 means numbers of urban community service facilities; 26 means gross divorce rate; 27 means the proportion that numbers of participate in Advances in Systems Science and Applications (2010), Vol.10, No.1 51 medical insurance account for total amount; 28 means energy consumption in every unit; 29 means forest coverage; 30 means industrial wastewater treatment level; 31 means per capita park greenery area; 32 means water subscription; 33 means gas subscription; 34 means daily treatment ability of domestic sewage; 35 means harmless treatment rate of domestic waste. [11] “Principal component-cluster analysis” is such a method. First we do the principal component to get some principal components, with which we do cluster analysis to samples, then we rank and classify the samples by the scores of the first principal component. Specific ways are the following: (1) select first r principal components by cumulative contribution rate and calculate the scores of the principal components 1 1 2 2 , ( 1,2, , )l l l pl pF a X a X a X l r= + + = (2) do the systematic cluster analysis to the selected new matrix ( 1 2, , , rF F F ); (3) calculate the scores’ average value of the first principal component to determine ranking of every class; (4) determine ranking of every sample in the class to get comprehensive evaluation result, according to every sample’s score. 2.2 The Method of TOPSIS Main steps of TOPSIS: (1) select p evaluation index to n evaluation units for comprehensive evaluation, then get a evaluation matrix ( )ij n pX x ×= , in which ijx is observation data in unit i . (2) make original data being dimensionless, then get a normalized evaluation matrix ( )ij n pZ z ×= , in which 2 1 / ( 1,2, , ; 1,2, , ) n ij ij kj k z x x i n j p = = = =∑ . (3) determine the positive ideal solution Z + and negative ideal solution Z − of matrix Z , then get 1 2( , , , )qZ z z z+ + + += , 1 2( , , , )qZ z z z− − − −= , in which 1 2max{ , , , } ,j j j njz z z z+ = 1 2min{ , , , }, ( 1, 2, , )j j j njz z z z j q− = = . (4) calculate the distances between every unit and positive ideal solution, and the distances between every unit and negative ideal solution: 2 1 ( ) q i ij j j D z z+ + = = −∑ , 2 1 ( ) q i ij j j D z z− − = = −∑ ( 1, 2, , )i n= (5) calculate relative approach degrees between every evaluation unit and the optimal solution: 100%, ( 1, 2, , )i i i i DC i n D D − + −= × = + (6) rank according to the relative approach degree. The more it closes to 100, the more iC . It indicates that unit i is more close to the optimal level. Otherwise, unit i is less close to the optimal level. 3. Establishment of Index System and Empirical Analysis To build a harmonious society is a great social system engineering. From the horizontal point of view, it is closely associated with society, politics, economy and culture. From the vertical point of view, it involves in macro-view, medium-view and micro-view. The concept of harmonious society is extensive, comprehensive and systematic. It includes every aspect of Men: Research on Comprehensive Evaluation of Harmonious Society in East China 52 economy, politics, society, culture, environment and people’s life. Therefore, the index system of harmonious society should embody the comprehensive and systematic connections among index, and reflect progress condition of construction in many aspects. In this paper, we will divide it into 5 subsystems to make it have good operability, that is, material civilization system, political civilization system, spiritual civilization system, social civilization system and ecological civilization system, (Details in Table 1) [8-11] . 3.1 Calculation with the Method of Principal Component and Cluster Analysis First we do pretreatment to the original data. Then we make principal component analysis to the harmonious index of six provinces and Shanghai city with SAS program. Finally, we get the following eigenvalues of the correlation matrix. Eigenvalues of the Correlation Matrix Eigenvalue Difference Proportion Cumulative 1 18.6926827 12.4745482 0.5341 0.5341 2 6.2181345 2.0407184 0.1777 0.7117 3 4.1774161 1.4626788 0.1194 0.8311 4 2.7147372 0.8307516 0.0776 0.9087 5 1.8839856 0.5709418 0.0538 0.9625 6 1.3130439 1.3130439 0.0375 1.0000 ………… In which, PRIN1, PRIN2, PRIN3, PRIN4 denote the first four principal components. The second list is eigenvalues of sample correlation matrix, the fourth list is contribution proportions of variance, and the fifth list is cumulative contribution proportions. As cumulative contribution proportion of the first four eigenvalues reaches 90.87%, which is higher than 85%, we only need to select the first four principal components to summarize the all data, then get the scores of the principle components (see Table 2). Table 2 The scores of the principle components analysis Cities Scores The first Principal component The second principal component The third principal component The fourth principal component Shanghai 8.52652 -2.49745 -0.61749 0.58853 Jiangsu 0.68228 1.08935 1.92012 -1.20837 Zhejiang 1.99413 4.24675 -0.908082 -0.56337 Anhui -3.85481 -2.3237 -2.88072 -1.98804 Fujian -1.67628 1.85291 -0.83024 1.03237 Jiangxi -3.62903 -0.86869 -0.02778 2.92133 Shandong -2.04282 -1.49017 3.34413 -0.78246 The contribution proportion of first principal component’s variance is 53.41%, which is the largest of all linear combinations, and the information of the first principal component is the biggest. We get samples’ ranking the first time by calculating the scores of the first principal component. If we rank only according to the scores of the first principal component, as contribution proportion is not over 85%, the information will not be big enough and the result will have one-sidedness. Thus, we do the cluster analysis to the first four principal components’ score matrix with SAS program, then we get the cluster graph (see Figure 1). From Figure 1, we know that the six provinces and Shanghai city can be divided into three classes, that is, {Shanghai}; {Jiangsu, Shandong, Zhejiang}; {Fujian, Jiangxi, Anhui}. Then we rank according to the scores of first principal component. That is, {Shanghai}; {Jiangsu, Shandong, Zhejiang}; {Fujian, Jiangxi, Anhui}. Finally, we get the ranking by the scores of the first principal component in every class. That is, {Shanghai, Zhejiang, Jiangsu, Shandong, Fujian, Jiangxi, Anhui}. From Table 3, we get the rankings by principal component-cluster analysis and the scores of the first principal component. We find that they are almost the same, the only different is ranking between Shandong and Fujian. However, 20 index in Shandong are better than Fujian, Shandong should be in front of Fujian. Therefore, it is more reliable to get the ranking by principal Advances in Systems Science and Applications (2010), Vol.10, No.1 53 component-cluster analysis. Figure 1 Cluster graph Table 3 The compositors of the principal component cluster and the first principal component Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Ranking by principal component-cluster analysis 1 3 2 7 5 6 4 Ranking by the scores of the first principal component 1 3 2 7 4 6 5 3.2 Calculation with the Method of TOPSIS We calculate relative approach degree iC of every subsystem by MATLAB program. The more it closes to 100, the more iC . It indicates that unit i is more close to the optimal level. Otherwise, unit i is less close to the optimal level. Details in Table 4. The construction of material civilization, political civilization, spiritual civilization, social civilization and ecological civilization are closely linked with each other in the process of building a socialist harmonious society and a well-off society. They are very important, so we should treat them equally. We get the final scores of the six provinces and Shanghai city after doing the equal weight. Then we rank by the final scores, which is listed in Table 4. The result is the same as the ranking by principal component-cluster analysis, which verifies rationality of the method of principal component-cluster analysis. Table 4 The development level of six provinces in east China and Shanghai city Material civilization Political civilization Spiritual civilization Social civilization Ecological civilization Score Ranking Shanghai 86.6131 46.87 80.45 71.89 32.28 63.62062 1 Jiangsu 38.4696 32.37 19.50 32.84 57.44 36.12392 3 Zhejiang 53.6959 23.66 20.32 47.55 52.83 39.61118 2 Anhui 12.3374 31.65 9.48 17.73 24.29 19.09748 7 Fujian 21.9262 28.24 23.78 22.12 49.08 29.02924 5 Jiangxi 8.7141 35.27 27.04 27.24 41.41 27.93482 6 Shandong 24.8297 60.62 14.78 26.26 44.15 34.12794 4 4. Conclusions and Discussions 2006 was the beginning of eleventh five-year plan. Under the leadership of provincial and municipal governments in east China, we had acquired remarkable achievement in the field of social economic development, by insisting in carrying out macro-control policy and guiding with scientific development view. According to the methods of principal component-cluster analysis Men: Research on Comprehensive Evaluation of Harmonious Society in East China 54 and TOPSIS, we divide six provinces and Shanghai city into 3 classes on the level of social harmonious development. (1) Shanghai city is the first class. The score of Shanghai is far higher than any other province. It shows that Shanghai city is superior to other places in the construction of harmonious society. Since reform and opening up to the outside world, Shanghai city has got great achievement as the first metropolitan. The index of per capital GDP, per capital disposable income of urban residents and per capital net income of rural residents are in the first place. (2) Zhejiang, Jiangsu and Shandong are in the second class, which are high in harmony. The scores of Zhejiang province and Jiangsu province are high in material civilization system, ecological civilization system and social civilization system, but low in spiritual civilization system. These places have strong economic strength, good security systems and harmonious living condition. The scores of Shandong province are low in material civilization system, spiritual civilization system and social civilization system, but high in political civilization system. Shandong province is one of the best provinces in public security. (3) Fujian, Jiangxi and Anhui are in the third class. It has significant gap to others. The relatively backward social economy restricts social development, leading to the development of society unbalanced. From above conclusions, we know that Shanghai, Zhejiang, Jiangsu and Shandong are in the leading positions of the whole nation. In the future, we should not only focus on the quantity of economic operation, but also focus on the quality. 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