CHEMICAL ENGINEERINGTRANSACTIONS VOL. 51, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors:Tichun Wang, Hongyang Zhang, Lei Tian Copyright © 2016, AIDIC Servizi S.r.l., ISBN978-88-95608-43-3; ISSN 2283-9216 The Comprehensive Evaluation Model of Fuzzy Mathematics Based on Third Class Cities’ Low Carbon Economy JianliSang Weifang University of Science and Technology,Shouguang, Shandong, CHINA. 403791013 @qq.com Large amounts of carbon dioxide emission are the main cause of climate warming, socarbon emission abatement is urgent for the cities. In this paper, the low carbon economy of third class cities is regarded as the research object, and evaluation is regarded as the breakthrough point. The evaluation index system of third class cities’ low carbon economy is established. Using AHP to determine the index weight, the fuzzy evaluation model of third class cities’ low carbon economy is constructed. This model is used to evaluate the low carbon economy of Weifang, and the result is general, which is consistent with the actual situation. The model is feasible. 1. Introduction Low carbon economy researches abroad started earlier. In 1987, the study of environmental indexes was carried out in the Netherlands. In 1994, a set of environmental indexes was released in Canada. In 2001, the environmental indexes were launched in the United States(Wang, 2000). While the domestic study of urban low carbon economy is still in the exploratory stage. And its evaluation research is even less. In this paper, on the basis of establishing the evaluation index system of the third class cities’ low carbon economy, using the fuzzy comprehensive evaluation method, the third class cities’ low carbon economy is evaluated. This method is novel and unique, scientific and reasonable which is feasible(Zhang, 2016). 2. The establishment of evaluation index system of third class cities’ low carbon economy Through the fieldwork to third class city, Weifang, the 5 first-level indexes and 19 second-level indexes of third class cities’ low carbon economy evaluation index system could be determined. The detailed indexes are shown in table 1. Table 1: The evaluation index system of third class cities’ low carbon economy The evaluation index system of third class cities’ low carbon economy P first-level evaluation indexes second-level evaluation indexes Economic factors A Resident income A1; Low carbon industry output value A 2. GDP per capita A 3; Financial input A 4; Environmental factors B Nature reserve area ratio B1; coverage of green land B2; green area per capita B3. Environmental protection investment ratio B4. Social factors C Low carbon popularity C 1; urbanization ratio C 2; car number per capita C 3; housing area per capita C4 Technical factors D Acquisition and preservation ratio of greenhouse gas D1; low carbon material ratio D2; utilization ratio of the three wastes D3; garbage disposal D4. energy emission factors E CO2 per GDP E1; SO2 per GDP E2; energy consumption per GDP E3; DOI: 10.3303/CET1651003 Please cite this article as: Sang J.L., 2016, The comprehensive evaluation model of fuzzy mathematics based on third class cities’ low carbon economy, Chemical Engineering Transactions, 51, 13-18 DOI:10.3303/CET1651003 13 http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(You-wei+Zhang)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://dict.cn/preservation%20life 3. The introduction of fuzzy mathematics comprehensive evaluation method Fuzzy mathematics comprehensive evaluation method is one of the most common methods used in fuzzy decision problems. (1)Determine the evaluation index factor set P={p1,p2,…pn}，and there arenindexes of the object. (2)Determine the grade evaluation setV={v1,v2,…vm}，andmis the grade number of the evaluation. (3)Determine the fuzzy evaluation matrixR=(rij)nm, the basic method is as follows: First of all, make a grade evaluation f(p)(i=1,2,…,n)to all index factorsp, we could get a fuzzy mappingf from P toV, namelyf: PF(P),pif(pi)=(ri1,ri2,…rim)F(V) Then, from the fuzzy mappingf, the fuzzy relationRfF(pV)could be induced, namelyRf(pi,vi)=f(PI)(vI)=Rijand i=1,2,…,n; j=1,2,…,m. The fuzzy evaluation matrix could be determined as R=(rij)nm. (4)AHP method is used to determine the weights of evaluation indexes at all levels (Han, 2005) AHP is one of the most common methods that determine the weight. It is an effective method that transforms non-quantitative problems into quantitative problems, by comparing the importance of two indexes to determine the comparison matrix so as to make a decision. The specific process is as follows: First of all, according to the evaluation index system, the hierarchical structure diagram of the system is established. Secondly, carry on the multiple comparisons to all the evaluation indexes at the same level, construct comparison matrix by using 1-9 scale value (The specific is shown in table 2.) Table 2: 1-9 scale value scale ij a 1 2 3 4 5 6 7 8 9 Comparison between index i and indexj The same A bit strong strong Obviously strong Absolute strong Thirdly,the determination of the weights of each evaluation index. The geometric average method is used to calculate the weight vector of each evaluation index. The specific process is divided into three steps: Carry on the product to the elements in each line of the comparison matrix, we could get vector; Carry on square root to vector n times, we could get vector；Carry on normalization processing to vector, we could get index weight vector. Fourth, carry on the consistency check. The process of consistency check is divided into three steps: Calculate consistency index: CI=(max-n)/(n-1)，and 1 max 1 1 n ij jn j i i a r n r       is the maximum eigenvalue. According to the numbern of evaluation indexes, the random consistency indexRIcould be determined. The specific values are shown in table 3; Table 3: the random consistency index n 1 2 3 4 5 6 7 8 9 10 11 12 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51 1.54 Calculate the consistency ratioCR=CI/RI, when CR0.10, the consistency check could pass. Finally, according to the weight of each evaluation index and the evaluation matrix, using the matrix multiplication, the comprehensive evaluation vectorw=TRcould then be obtained. 4. The fuzzy evaluation model of third class cities’ low carbon economy (1)According to table 1, the evaluation index factor setP={p1,p2,…p19}could be determined, and the evaluated object has 19 evaluation indexes (Liang and Cao.2007). (2)Determine grade evaluation setV={v1,v2,…v5}，the evaluation results of third class cities’ low carbon economy are divided into five levels: excellent, good, general, poor, very poor. The specific classification is shown in table 4. 14 Table 4: The second-level evaluation index classification of third class cities’ low carbon economy The second-level evaluation index evaluation grade Resident income A1； Very high high general low Very low Low carbon industry output value A2； Very high high general low Very low GDP per capita A3； Very high high general low Very low Financial input A4； Very high high general low Very low Nature reserve area ratio B1； very large large general small very small coverage of green land B2； very large large general small very small green area per capita B3； very large large general small very small Environmental protection investment ratio B4； very large large general small very small Low carbon popularity C1； very large large general small very small urbanization ratio C2； very large large general small very small car number per capita C3； Very few few general many A lot housing area per capita C4 very large large general small very small acquisition and preservation ratio of greenhouse gas D1; very large large general small very small low carbon material ratio D2； very large large general small very small utilization ratio of the three wastes D3； very large large general small very small garbage disposal D4； Very good good general poor very poor CO2 per GDP E1； little A little general much A lot SO2 per GDP E2； little A little general much A lot energy consumption per GDP E3； very small small general large very large (3)Determine the fuzzy evaluation matrixR=(rij)nm. Using the expert judgment method, the second-level indexes of third class cities’ low carbon economy are evaluated. Here we choose 10 experts to evaluate. And we could get that: ( ) ( ) ( ) 11 12 15 ( ) ( ) ( ) 41 42 45 A A A A A A A r r r r r r R            and rij=The expert number of level J/10. Similarly to the following conclusions: RB, RC, RD, RE (4)Determine the weights of evaluation indexes at all levels. First, select 10 experts to score, and get the average value. Confirm the influence of each index so as to determine the comparison matrixes: A, B, C, D, E, P. Second, calculate the weight vector of each index, the five weight vectors could be obtained as follows:A,B， C，D，E，R. Finally, carry on the consistency check. (5)According to the corresponding weight of each second-level evaluation index, the fuzzy evaluation matrixes of 5 first-level evaluation indexes could be calculated as follows: Rp=(T A RA T B RB T C RC T D RD T E RE) T. According to the weights of the first-level evaluation indexes, the level evaluation vector of third class cities’ low carbon economy could be obtained as follows:w=T p-Rp. Based on the maximum principle, the biggest component among wis the level of third class cities’ low carbon economy. 15 http://dict.cn/preservation%20life 5. The empirical analysis of third class cities’ low carbon economy evaluation Table 5: The comparison matrix and the test results of first-level evaluation indexes aiming to the target layer Target layer the evaluation index system of third class cities’ low carbon economy P The largest eigenvalue The consistency ratio First-level evaluation indexes Economic factors A Environmental factors B Social factors C Technical factors D energy emission factors E weight Economic factors A 1 1/5 1/3 1/2 1/7 0.0506 5.1457 0.0325 Environmental factors B 5 1 3 2 1/3 0.2339 Social factors C 3 1/3 1 2 1/4 0.1285 Technical factors D 2 1/2 1/2 1 1/5 0.0931 energy emission factors E 7 3 4 5 1 0.4939 Table 6: The comparison matrix and the test results of second-level evaluation indexes aiming at first-level evaluation indexes’ economic factors A first-level evaluation indexes economic factors A The largest eigenvalue The consistency ratio second-level evaluation indexes Resident income A1 Low carbon industry output value A 2 GDP per capita A 3 Financial input A 4 weight Resident income A1 1 1/5 1/2 1 0.1154 4.2507 0.0939 Low carbon industry output value A 2 5 1 5 2 0.5455 GDP per capita A 3 2 1/5 1 2 0.1940 Financial input A 4 1 1/2 1/2 1 0.1451 Table 7: The comparison matrix and the test results of second-level evaluation indexes aiming at first-level evaluation indexes’ environmental factors B first-level evaluation indexes Environmental factorsB The largest eigenvalue The consistency ratio second-level evaluation indexes Nature reserve area ratio B1 coverage of green land B2 green area per capita B3 Environmental protection investment ratio B4 weight Nature reserve area ratio B1 1 1/3 1/4 1/2 0.0931 4.0873 0.0327 coverage of green land B2 3 1 1/3 2 0.2452 green area per capita B3 4 3 1 3 0.5050 Environmental protection investment ratio B4 2 1/2 1/3 1 0.1567 Table 8: The comparison matrix and the test results of second-level evaluation indexes aiming at first-level evaluation indexes’ social factors C first-level evaluation indexes social factors C The largest eigenvalu e The consistenc y ratio second-level evaluation indexes Low carbon popularity C1 urbanization ratio C2 car number per capita C3 housing area per capita C4 weight Low carbon popularity C 1 1 7 5 9 0.648 9 4.2313 0.0866 urbanization ratio C 2 1/7 1 1/4 3 0.088 1 car number per capita C 3 1/5 4 1 5 0.217 8 housing area per capita C4 1/9 1/3 1/5 1 0.045 2 16 Table 9: The comparison matrix and the test results of second-level evaluation indexes aiming at first-level evaluation indexes’ technical factors first-level evaluation indexes technical factors D The largest eigenvalue The consistency ratio second-level evaluation indexes acquisition and preservation ratio of greenhouse gas D1 low carbon material ratio D2 utilization ratio of the three wastes D3 garbage disposal D4 weight acquisition and preservation ratio of greenhouse gas D1 1 1/4 1/3 5 0.1445 4.2323 0.0870 low carbon material ratio D2 4 1 1/2 9 0.3705 utilization ratio of the three wastes D3 3 2 1 6 0.4406 garbage disposal D4 1/5 1/9 1/6 1 0.0444 Table 10: The comparison matrix and the test results of second-level evaluation indexes aiming at first-level evaluation indexes’ energy emission factors E first-level evaluation indexes energy emission factors E The largest eigenvalue The consistency ratio second-level evaluation indexes CO2 per GDP E1 SO2 per GDP E2 E2 energy consumption per GDP E3 weight CO2 per GDP E1 1 4 3 0.6250 3.0183 0.0176 SO2 per GDP E2E2 1/4 1 1/2 0.1365 energy consumption per GDP E3 1/3 2 1 0.2385 Table 11: The level evaluation results of Weifang low-carbon economy’s second-level evaluation indexes second-level evaluation indexes evaluation level Resident income A1； 0 2 6 2 0 Low carbon industry output value A 2； 1 2 4 2 1 GDP per capita A 3； 1 3 3 2 1 Financial input A 4； 0 2 4 3 1 Nature reserve area ratio B1； 0 2 5 2 1 coverage of green land B2； 0 1 7 1 1 green area per capita B3； 2 4 4 0 0 Environmental protection investment ratio B4； 5 3 2 0 0 Low carbon popularity C 1； 3 5 1 1 0 urbanization ratio C 2； 1 3 5 1 0 car number per capita C 3； 4 3 3 0 0 housing area per capita C4 1 2 4 3 0 acquisition and preservation ratio of greenhouse gas D1； 0 2 6 1 1 low carbon material ratio D2； 4 5 1 0 0 utilization ratio of the three wastes D3； 2 4 3 1 0 garbage disposal D4； 1 3 5 1 0 CO2 per GDP E1E1； 2 3 4 1 0 SO2 per GDP E2； 1 3 6 0 0 energy consumption per GDP E3； 3 2 4 1 0 17 http://dict.cn/preservation%20life http://dict.cn/preservation%20life http://dict.cn/preservation%20life (1)The weight solution interviewing the experts of Weifang low carbon economy research, according to its results, the comparison matrixes could be determined. The calculation results are shown in table 5 to table 10. (2)The evaluation research of Weifang low-carbon economy First of all, ten experts carry on the fuzzy evaluation to the 19 second-level evaluation indexes of Weifang low- carbon economy. The results are shown in table 11: Secondusing procedure MATLB(attachment), the evaluation vector of Weifang low carbon economy is calculated as follows: w=(0.2098,0.3081,0.3877,0.0807,0.0137), Based on the maximum principle we could get that the evaluation level of Weifang low carbon economy is general. 6. Conclusion It is feasible to use the fuzzy mathematics to evaluate the third class cities’ low carbon economy. From the application we could get that the 5 first-level indexes of third class cities’ low carbon economy don’t coordinate well, especially the environmental aspect. 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Procedia Engineering, Vol.135.DOI: 10.1016/j.proeng.2016.01.096 18 http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(Matthew+R.+Hallowell)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(Daniel+Hansen)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://d.scholar.cnki.net/link/doi/SJESTEMP_U/SJES26FEE096873EB13FA4D8CEAF2A569A0A?UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(Mazen+Hassanain)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(Shirin+Anil)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(Ayman+Abdo)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://d.scholar.cnki.net/link/doi/SJESTEMP_U/SJES718673F369FF634F7155BCB1C7EDC821?UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://scholar.cnki.net/result.aspx?q=%e4%bd%9c%e8%80%85%3a(You-wei+Zhang)&uid=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!&UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!! http://d.scholar.cnki.net/link/doi/SJESTEMP_U/SJES4CD9A5374765D13B1A00892D59EB0E7B?UID=WEEvREcwSlJHSldRa1FiNXRYWlFGVTlBcnp4M2dYYkdyZGNkTEN4Y3dFQ29WcStKQnppc1J4NGcxcGMyU2wvbk13PT0=$9A4hF_YAuvQ5obgVAqNKPCYcEjKensW4IQMovwHtwkF4VYPoHbKxJw!!