Application of AHP Method and TOPSIS Method in Comprehensive Economic Strength Evaluation of Major Cities in Guizhou Province

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1 2017 Iteratioal Coferece o Computer Sciece ad Applicatio Egieerig (CSAE 2017) ISBN: Applicatio of AHP Method ad TOPSIS Method i Comprehesive Ecoomic Stregth Evaluatio of Major Cities i Guizhou Provice Liag Zhou *, Chagdi Shi ad Limig Luo Iformatio Egieerig College, Capital Normal Uiversity, Beijig, Chia ABSTRACT This paper establishes the comprehesive ecoomic stregth evaluatio system of major cities i Guizhou provice, ad puts forward the evaluatio model of comprehesive ecoomic stregth of major cities i Guizhou provice based o the AHP method ad the TOPSIS method. The AHP method was used to determie the weight of evaluatio idicator. The TOPSIS method is used to calculate the positive ad egative ideal solutios, aalyses the case, ad the the fial rakig of the comprehesive ecoomic stregth of the major cities i Guizhou provice. The result shows that the fial rakig, from high to low, of comprehesive ecoomic stregth of the major cities i Guizhou provice is: Guiyag, Zuyi, Liupashui, Togre ad Ashu. The evaluatio system of the comprehesive ecoomic stregth idicator of the major cities i Guizhou provice has a certai practicability, which provides a evaluatio basis i comprehesive ecoomic stregth for the major cities i Guizhou provice. INTRODUCTION I recet years, with the establishmet of large data ceters ad the promulgatio of precisio poverty alleviatio policies, the atioal ecoomy ad social developmet of the major cities i Guizhou have made breakthrough progress, but the cities developed uevely, so it is ecessary to explore how to establish a good ad scietific comprehesive ecoomic evaluatio system. This paper is focused o evaluatig the comprehesive ecoomic stregth of major cities i Guizhou provice effectively. Selectio amog alteratives depeds o a set of differet coflictig criteria that have differet optimizatio directios ad differet measuremet uits. The MCDM methods ca be used o the atioal, orgaizatioal ad project levels. However, most assessmet methods are iteded oly for ecoomic objectives (Sivilevičius et al., 2008). A appropriate mechaism for supportig maagemet practices at a early research o a fuzzy multi-criteria decisio makig algorithm, which itegrated the priciples of fusio of fuzzy iformatio, additive ratio assessmet method with fuzzy umbers (ARAS-F), fuzzy weighted-product model ad aalytic hierarchy process (AHP). Karabasevic et al. (2016) itroduced a approach for the selectio based o the SWARA ad ARAS methods uder ucertaities (Keršulieė & Turskis 2011). Turskis ad Juodagalvieė (2016) itroduced a hybrid MCDM model, which was based o te differet MCDM methods: Game Theory, AHP, ad SAW, Multiplicative Expoetial Weightig, TOPSIS, ad EDAS, ARAS, Full Multiplicative Form, Laplace Rule, ad Bayes Rule, is useful to solve complicated problems. Zavadskas et al. (2013) itegrated ELECTRE IV, MULTIMOORA, SWARA-TOPSIS, 687

2 SWARA-ELECTRE III, SWARA, ad VIKOR to assess, rak ad select the best alteratives. Štreimikieė et al. (2016) paper preseted the process of choice such multiple criteria decisio-makig methods as AHP ad ARAS. Staujkic et al. (2017) proposed usig the EDAS method with grey umbers. Zavadskas et al. (2016) overviewed developmets of TOPSIS method (Hwag & Yoo, 1981; Yoo, 1980) to solve differet complicated problems i recet two decades. There are some ew MCDM methods MABAC (Gigović, LJ., 2017) ad MAIRCA have bee used to assess, rak ad select the best alteratives (Pamučar, D., Ćirović,G, 2015; Pamučar, D. et al, 2017). O the basis of summig up the previous comprehesive ecoomic assessmet, this paper used the method of classical AHP ad TOPSIS to rak the comprehesive ecoomic stregth of major cities i Guizhou provice. Firstly, AHP method was used to costruct the evaluatio idicator system, ad calculate the weight of evaluatio idicator. Secodly, TOPSIS method was used to calculate the positive ad egative ideal solutios, ad the the case aalysis was carried out to solve the fial rakig of the evaluatio target, which provided the basis for the self-evaluatio of the comprehesive ecoomic stregth of the major cities i Guizhou provice. MODEL CONSTRUCTION Determiatio of Idicator Weight Based o AHP May factors affect the level of comprehesive ecoomic developmet of major cities i Guizhou provice, such as the geographical locatios of the cities, the characteristics of idustrial structure ad the characteristics of cultural exchage, it is difficult to quatitatively measure the level of ecoomic developmet of these cities, ad thus how to evaluate the ecoomic developmet level of major cities i Guizhou provice scietifically ad efficietly is the focus of this paper. Accordig to the basic priciples ad solvig steps of AHP, stratify the comprehesive ecoomic evaluatio idicator of major cities i Guizhou provice. The target layer is the comprehesive ecoomy of the major cities i Guizhou provice. The first level icludes five idicators, which iclude ecoomic aggregate idicator B1, idustrial structure idicator B2, wealth level idicator B3, foreig trade ad tourism idicator B4, ad stadard of livig idicator B5. The secod level icludes te idicators that cotai regioal GDP C11, total ivestmet i fixed assets C12, total value of agricultural output C21, idustrial-added value C22, GDP per capita C31, per capita reveue C32, total import ad export volume C41, total tourism reveue C42, disposable icome per capita of urba residets C51, ad disposable icome per capita of rural residets C52. The evaluated objects are Guiyag city D1, Zuyi city D2, Togre city D3, Liupashui city D4, Ashu city D5. W i represets the combied weight. The idicator system is show i Figure

3 Figure 1. Comprehesive ecoomic idicator system of major cities i Guizhou provice. The origial data collected by the Guizhou Provicial Bureau of Statistics i 2013 are show i Figure 2. Figure 2. Raw data table. Determiig the Weight of Evaluatio Idicators The ratioality of the settig ecoomic idicator weight is directly related to the scietific rigor of the evaluatio structure. This paper ivited the experts i the ecoomic field to discuss the importace of the idicators with the real data collected by the Provicial Bureau of Statistics i The judgmet matrix rule i AHP, which is show i TABLE I, was used to determie the weight of each idicators. The author calculated the weight accordig to the AHP solvig steps. The AHP solvig steps are show i Figure 3. W = [ω 1, ω 2,..., ω ], W i ad λ max were calculated as what is show i (1). 689

4 TABLE I. RELATIVELY IMPORTANT DEGREE JUDGMENT MATRIX. Relatively importat degree Defiitio 1 Equally importat 3 Slightly importat 5 Very importat 7 Obviously importat 9 Absolutely importat 2,4,6,8 Determiig a itermediate value of adjacet Costruct decisio-makig matrixs Solvig λmax ad Wi by eigevector method Cosistecy check of matrix A scheme sort Figure 3. AHP solutio steps. i i1 a i1 i1 ij a ij, max 1 i ( AW) i [ ] i (1) Topsis This algorithm s core idea is to detect how well the positive ad egative ideal solutios match the evaluated objects. That is, it is the best if the evaluated object is closest to the Positive Ideal Solutio ad, meawhile, the farthest away from the Negative Ideal Solutio. The solvig steps of TOPSIS are represeted i Figure 4, where B = (b ij ) m *, b ij = W i * y ij, ad W i is obtaied by the AHP method. Usig Vector Specificatio to Solve Normative Decisio Matrices Costruct a weighted ormative matrix Caculatig the positive ad egative ideal solutio(s +, S - ) The proximity of the scheme to the positive ad egative ideal solutios(d +, D - ) Figure 4. TOPSIS solvig steps. Calculate the degree of proximity of the scheme to the ideal solutio scheme sort The formula to calculate the positive ad egative ideal solutios of the evaluatio object are as follows: (2). S {max bij j J 1,{mi bij j J 2}}, S - { mibij j J 1,{max bij j J 2}} (2) The formula to calculate the distace betwee the positive ad egative ideal solutios are descripted i (3). D i m j1 ( bij S ) 2 (i=1,2,...,m), D i m j1 ( bij S ) 2 (i=1,2,...,m) (3) 690

5 CASE STUDY Solvig Idicator Weight Based o the actual data from the Provicial Bureau of Statistics ad the expert team, this paper puts forward a scietific ad effective evaluatio model for the evaluatio of the ecoomic stregth of the major cities i Guizhou provice, costructs the two compariso matrices, ad uses the AHP software to carry out the cosistecy test. Some of the results are as follows: The cosistecy ratio of the comprehesive ecoomic idicator system of the major cities i Guizhou provice: ; the weight of A: ; λmax: , as Figure 5 shows. Figure 5. The relative weight of B1, B2, B3, B4 ad B5 to target layer A. TABLE II. THE RELATIVE WEIGHT OF C11 AND C12 TO THE FIRST INDICATOR B1. Ecoomic aggregate idictor Regioal Total ivestmet i fixed Wi GDP assets Regioal GDP Total ivestmet i fixed assets TABLE III. THE RELATIVE WEIGHT OF C21 AND C22 TO THE FIRST INDICATOR B2. Idustrial structure Total value of agricultural Idustrial-added Wi idicator output value Total value of agricultural output Idustrial-added value TABLE IV. THE RELATIVE WEIGHT OF C31 AND C32 TO THE FIRST INDICATOR B3. Wealth level idicator GDP per capita Per capita Wi reveue GDP per capita Per capita reveue TABLE V. THE RELATIVE WEIGHT OF C41 AND C42 TO THE FIRST INDICATOR B4. Foreig trade ad tourism Total import ad export Total tourism Wi idicator volume reveue Total import ad export volume Total tourism reveue

6 Combied with TABLE II-VI, the secodary idicator relative weight W *, W * = (0.1269, , , , , , , , , ). TABLE VI. THE RELATIVE WEIGHT OF C51 AND C52 TO THE FIRST INDICATOR B5. Stadard of livig Disposable icome per Disposable icome Wi idicator capita of urba residets per capita of rural residets Disposable icome per capita of urba residets Disposable icome per capita of rural residets The fial idicators weight of the major cities i Guizhou are show i TABLE VII. TABLE VII. FINAL RESULTS Program Weight Guiyag City Zuyi City Togre City Liupashui City Ashu City The Result of Evaluatio Objectives This paper used the C laguage to implemet the TOPSIS method ad combied with the weight obtaied by AHP method ad fially obtaied the matrix after the weighted specificatio, as Figure 6 shows. Figure 6. Normative decisio matrix. Accordig to the third step of TOPSIS method, the positive ad egative ideal solutios of 10 secodary idicators i the evaluatio ecoomic stregth of major cities of Guizhou are obtaied, which are show i TABLE VIII. Guiyag city is the capital of Guizhou provice. Its political, ecoomic, cultural, sciece ad educatio developmet top the other cities. Recetly, multiple big data busiesses were built i Guiyag city, at the same time, the three major idustries have bee developig rapidly. Zuyi city, kow as the "Qiabei graary," was raked secod because of its first idustry ad political ifluece; Liupashui was raked third, thaks to its rich agricultural products raks third. Accordig to table 7 ad table 9, the AHP method ad the TOPSIS method ca be used to obtai the comprehesive 692

7 ecoomic stregth rakig of the cities i Guizhou provice. The rakig, ordered from most developed to least developed, is raked as follows: Guiyag City, Zuyi City, Liupashui City, Togre City ad Ashu City. This rakig is geerally cosistet with the actual level of developmet of the aforemetioed cities. TABLE VIII. THE POSITIVE AND NEGATIVE IDEAL SOLUTIONS OF SECONDARY INDICATORS. Idicator Attribute positive ideal value Attribute egative ideal value Regioal GDP Total ivestmet i fixed assets GDP per capita Per capita icome Total value of agricultural output Idustrial-added value Total import ad export volume Total tourism reveue Disposable icome per capita of urba residets Disposable icome per capita of rural residets The TOPSIS method was used to obtai the rakig of the comprehesive ecoomic stregth of major cities i Guizhou provice, which is show i TABLE IX. TABLE IX. THE FINAL RANKING OF MAJOR CITIES IN GUIZHOU. Guiyag city Zuyi city Liupashui city Togre city Ashu city CONCLUSIONS This paper combied the AHP method ad the TOPSIS method. The AHP method was used to determie the weight of the idicator, ad the TOPSIS method was used to calculate the positive ad egative ideal solutios ad proximities. The comprehesive ecoomic stregth rakig of major cities i Guizhou provice was obtaied. The stregth, ordered from high to low, is Guiyag, Zuyi, Liupashui, Togre, ad followed by Ashu. This rakig is basically i lie with the actual level of developmet of the major cities i Guizhou provice. It provides a scietific ad practical evaluatio model for self-evaluatio of the major cities i Guizhou provice. The model proposed i this paper ca be used i solvig the similar ecoomic sortig problems. This article completely solved the research problem, ad the research results were cosistet with the actual level of developmet of these cities. Future research: buildig a more iovative model, ad comparig the use of differet MCDM method to obtai the results. REFERENCES 1. Hwag, C. L., ad Yoo, K Methods for multiple attribute decisio makig, I Multiple attribute decisio makig, pp Spriger Berli Heidelberg. 2. Keršulieė, V., ad Turskis, Z Itegrated fuzzy multiple criteria decisio makig model for architect selectio, Techological ad Ecoomic Developmet of Ecoomy, 17(4):

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