An Improved RAHP/DEA Method and the Application of the Physical Education Teaching Quality Assessment

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1 , pp A Improved RAHP/DEA Method ad the Applicatio of the Physical Educatio eachig Quality Assessmet Hao Li ad ie Ru Health scieces of Xi a physical educatio Uiversity, Xi a, Shaa xi, Chia, Cetral laboratories, the Secod Affiliated Hospital of Xi a Medical Uiversity, Xi a, Shaa xi, Chia, xiaoguaizhag@6.com Abstract he teachig quality assessmet of physical educatio for the udergraduates has a very importat role for the developmet of the college physical educatio teachig. I the age of iformatio, we ca improve effectively the speed ad accuracy of the assessmet through usig ratioally the computer techology. he AHP method ad the DEA method are two kids of evaluatio methods which are used widely by the scholars. However, whether we use AHP or DEA, there are some defects o the usig ad scope. I order to overcome these shortcomigs, we propose the RAHP/DEA method. his method combies the advatages of the RAHP method ad the DEA methods. Ad we elarge the rage of use. Fially, i the computer simulatio experimet, we adopt the method to evaluate the teachig quality of college physical educatio. he experimetal results verify the ratioality of the proect evaluatio ad the decisio makig process. his shows that the evaluatio system ad the evaluatio method meet the decisio makig ideas ad the practical requiremets. Keywords: RAHP/DEA; College physical educatio teachig quality; Computer simulatio. Itroductio he evaluatio of college physical educatio teachig quality ca reflect the quality of the physical educatio for oe college. It ca also poit out the advatages ad the disadvatages of the college physical educatio teachig quality. hrough the evaluatio of college physical educatio teachig quality, we ca see easily the existed questios i the college physical teachig. At the same time, the evaluatio of college physical educatio teachig quality lays a solid foudatio for promptig more effectively the college studets to do the physical exercise. I the iformatio age, more ad more colleges itroduce the computer techology to improve the physical teachig, such as performace predictio, traiig ad teachig quality assessmet. I these applicatios, the teachig quality evaluatio is very importat for the developmet of the physical teachig for the colleges. With the college physical teachig becomig more ad more importat, the colleges ad the studets pay more ad more attetio to the physical teachig. May scholars study the evaluatio of college physical educatio teachig quality. Xiag Lili studied ad developed the ordiary college physical evaluatio maagemet iformatio system. She adopted the traditioal Cliet/Server(C/S) structure model ad used Visual Studio, the NE ad Crystal Report developmet eviromet ad SQL Server 000 database to develop a maagemet iformatio system []. he maagemet iformatio system has the fuctios of data statistics, assessmet ad auxiliary decisio. Zhu Chuaia studied the ifluece of the Meta evaluatio theory o improvig the physical evaluatio quality. ISSN: IJUNESS Copyright c 05 SERSC

2 I this paper, he defied that the Meta evaluatio was ot oly the reflectio ad summary for the evaluatio itself, but also it was a higher level critique ad examie. his reflected the practical value of the Meta evaluatio i the optimizatio ad improvemet educatioal assessmet activities []. Che Yigie studied the selectio of weights i the college physical evaluatio system based o the iformatio etropy. He proposed a evaluatio idex weight selectio method based o the iformatio etropy. O the oe had, the method has the obectivity of the rigorous mathematical theory. O the other had, it had the subectivity of the expect experiece assessmet [3]. By Da studied the costructio of the physical workig evaluatio idex system of the ordiary college i Jiag Su provice [4]. Rua Qigti studied the evaluatio stadard of the ordiary college physical workig i Vietam [5]. AHP ad DEA are two importat methods for the evaluatio. AHP was proposed by Saatty. Ad AHP is a method which combies the qualitative research with the theory research [6]. he method has bee attracted the cocer of may scholars whe it was produced. I the subsequet decades, the scholars derived from a lot of the improved AHP methods [7-]. he DEA method was proposed by America famous strategist A.Chares ad W.W.Copper i 978. he mai idea is to compare the relative efficiecy of the evaluated istitutios through the mathematical programmig calculatio. Like the AHP method, the method has also bee the cocer of may scholars. hrough the cotiuous developmet ad iovatio, the method has become oe of the mai methods for the evaluatio [-5]. After readig the relevat literature, we foud that the AHP method relied o the past experiece. DEA method did ot cosider all of the target factors whe it made the decisio. Moreover, these two methods had limitatios i the rage of applicatio. Based o this, we proposed the RAHP/DEA method. he method combied the AHP method with the DEA method. It ca overcome the above shortcomigs effectively. he structure of this paper is as follows. he first past is itroductio. he secod part is the basic steps of AHP ad DEA. I this part, we recommed the basic steps of AHP ad DEA. he third part is RAHP/DEA method. I this part, we propose the ew assessmet method: AHP/DEA. he fourth part is the umerical aalysis ad the last part is the coclusio.. he Basic Steps of AHP ad DEA.. he Basic Steps of AHP Methods Whe we adopt AHP method to solve the decisio questios, the basic steps are as follows.. Costructig the Hierarchical Structure Model We divide the complex questios ito may elemets. hese elemets are divided ito several groups because of their properties. hese elemets compose the differet ladder level. I geeral, there are the target layer, the criterio layer ad the solutio layer etc. With the same level elemets as the stadard, we udge the importace of each sub-goal for the upper target. he first layer is the target layer. I geeral, there is oe factor. he middle layer is the criterio layer. It ca be divided ito oe or several. he followig is the scheme layer.. Establishig the Judgmet Matrix We costruct the hierarchical structure to determie the relatioship amog the differet levels. For example, we make the high level elemet C k as the criterio. C k Ca dispose the ext level elemets A, A,, A. he we udge the relative importace of A, A,, A for C i order to esure the correspodig weight for each other. AHP ca adopt the k 54 Copyright c 05 SERSC

3 digital scalig which is less tha 0 to weight the importace. Accordig to the scale, we establish the two ad two compariso matrix. Amog them, A = ( a ) ( i,,, ), a, a a a 0, a, a i i ii. a i i i i i 3. Solvig the relative weight of each elemet i a sigle criterio Accordig to C k criterio, the udgmet matrix A ca solve the relative importace amog each elemet A, A,, A ad obtai the characteristic roots. Accordig to A, we get the weight of A, A,, A m ax. he specific steps are as follows. he first step is to set vector 0 (,,, ). he secod step is to set k,,, ad calculate A k k he third step is to calculate m ax ad k. m ax k k ( k ) k k. Whe the precisio is ot high, we ca use the same approximatio to calculate m ax ad. 4. Cosistecy check We defie CI m a x. CI Is the idex of cosistecy. Whe the udgmet matrix has the character of cosistecy, CI 0 If m ax is large, CI is large. Ad the cosistecy is worse. For checkig whether the udgmet matrix has the character of cosistecy, we compare CI with the idex of cosistecy RI that is show i table.. able. he Idex of Cosistecy from -9 Orders order RI he Basic Steps of DEA DEA is short for the data evelopmet aalysis. It is a ew cross field of the mathematics, operatios research, mathematical ecoomics ad the maagemet sciece. It was propsed s by A.Chames ad W.W.Cooper i 978. Ad it is amed DEA. DEA model uses the mathematical programmig (icludig the liear programmig, multi-obective programmig, the geeralized optimizatio with coe structure, semi-ifiite programmig, stochastic programmig etc.) to evaluate the target. It has multiple iputs. Especially, it has may output sector ad uits. We call these uits as the decisio uits. It is short for the relative validity amog the DMU. O the basis of the cocept of the relative efficiecy, DEA method is a kid of evaluated method based o the covex aalysis ad the liear programmig. he method uses the mathematical programmig model to calculate the relative efficiecy amog the decisio uits. Ad the it evaluates the evaluatio obect. It ca cosider the optimal iput-output scheme for the decisio uit itself. herefore, it ca better reflect the Copyright c 05 SERSC 55

4 characteristics ad the iformatio of the obect itself. I additio, it has the uique characteristics to aalyze the multiple iputs ad output system for the evaluatio. he characteristics of DEA method It is suitable for the effective comprehesive evaluatio problems of the multiple output-iput. It has the absolute advatage i the effectiveess of the treatmet for the multiple output-iput. he DEA method is ot directly to sythesize the data. herefore, the optimal efficiecy idicators of the decisio uit are idepedet of the choice of the iput idex ad the output idex. Usig the DEA method to establish model does ot the odimesioal processig for the data. 3 It is ot ay weight hypothesis. It uses the actual data of the iput ad output of the decisio uit to obtai the optimal weights. his excludes may subective factors ad has the very strog obectivity. 4 he DEA method assumes that each iput is related to oe or more output ad iput. Ad it exist a certai relatioship amog the outputs. However, it eeds ot to determie the expressio of this relatioship. Figure. he Applicatio Steps of DEA Method he basic priciple of DEA method is as follows. DEA is a mathematical programmig model aimig to establish the most favorable model for each decisio uit. It ca get the weight of the idicator accordig to solve the optimal solutio. Differet decisio uits have differet idex weights ad they are relatively optimal. herefore, the DEA evaluatio is a kid of variable weight evaluatio method. It belogs to the o-uiform evaluatio. he most commoly DEA model is C R model. he basic priciple is to assume that there is decisio uits D M U,,,. heir iput ad output are as follows. X,,, x x x 0,,,, ( ) m Y,,, y y y 0,,,, ( ) k 56 Copyright c 05 SERSC

5 We use the matrix to express. It is show as table. able. he Iput ad Output able of the Decisio Uit Decisio uit 0... Iput x x x 0... x Output y y y 0... y k I the productio process, the status ad the role of various iput ad output are differet. herefore, if we evaluate the DMU, we eed to sythesize the iput ad the output. hat is, we treat them as the whole productio process of a geeral iput ad a geeral output. So we eed to give each iput ad output a appropriate weight. For example, the weight of x is v. he weight of y is u. We assume that the weight vectors of the iput ad output are v v, v,, v m ad u u, u,, u s. Firstly, we see them as variables. he we determie them i the process of the aalysis accordig to a certai priciples. Firstly, we evaluate i 0 decisio uit. s u y k k u y k h,,,, m v x v x i i i (3) h is the efficiecy evaluatio idex of the decisio uit D M U. We ca always select appropriate weight coefficiet v ad u. Ad it makes h,,,,.he we evaluate the 0 decisio uit. I geeral, the bigger the h 0 is, D M U ca use relatively litter iput 0 to obtai the relatively more output. he the C R model is as follows. m a x S.. s k m i u k y v x k 0 i i 0 s k m i k i k i,,,, u 0, k,,, s k v 0, i,,, m u y v x (4) his is a fractioal programmig problem. By the chares-coopre trasform, t v x tv tu Ad we get the followig liear programmig model. 0 (5) Copyright c 05 SERSC 57

6 m a x y V 0 p S.. P x y C R 0,,,, x 0 0, 0 (6) Whe we use the above model to evaluate the lie, it ofte appears the efficiecy idexes is the same or similar. It leads that we caot rak these schemes effectively. I order to overcome this shortcomig, the model eeds to be improved. herefore, we itroduce a virtual decisio uit i order to distiguish the differece amog the effective decisio uits. For the schemes which the efficiecy evaluatio idexes are the same or similar, we make x m i x i,,, i, y m i y i,,, s r r, X x, x,, x Ad Y y, y,, y s. We make X ad Y as the virtual decisio uits. Ad we merge the virtual decisio uit ito the decisio uits. he we ca get the evaluatio model which is based o the virtual decisio uit. m a x y V 0 p S.. P x y C R 0,,,,, x 0 0, 0 m (7) 3. RAHP/DEA Method 3.. he Steps of RAPH/DEA I the traditioal AHP method, because the importace degree of each elemet is give by experts, the subectivity of experts ca affect the fial evaluatio results. he AHP method relies o the past experiece as the udgmet, the subective factor is too large. herefore, it caot persuade others. Compared with AHP method, DEA method has the absolute advatage o hadlig the multi-iput ad output problems. However, it relies o DEA method simply to evaluate. It gives little iformatio for the effective decisio makig uits. he respective characteristics of AHP method ad DEA method determie the complemetarity betwee them. Aimig to the above problem, we propose a ew method RAHP/DEA. Firstly, this method uses regressio aalysis AHP method to get the weight of each factor. he it uses DEA method to obtai the efficiecy evaluatio idex. Fially, accordig to the weight ad efficiecy evaluatio idex, we get the evaluatio results. I this paper, we propose RAHP/DEA method Firstly, it uses the regressio aalysis AHP method to calculate the weight vector of each factor which relates to the overall goal. Secodly, it classifies the idexes ad establishes respectively the decisio uit set. It makes the egative idex as the iput idicators ad uses the positive idex ad the output idicators. he it uses the data evelope aalysis method to get the optimal value h i expresses the efficiecy evaluatio idex of the i factor for scheme.. h i 58 Copyright c 05 SERSC

7 hirdly, it uses the weight which is calculated i step to calculate the overall priority vector 4 h c. Compared i i i, we ca get the order of each scheme. 3.. he Compariso of AHP, DEA ad RAHP/DEA Methods 3... AHP Method: he advatage of AHP evaluatio Firstly, whe usig AHP method to solve the complex decisio questios, accordig to the combiatio of the qualitative ad quatitative aalysis, we eed to itroduce the preferece iformatio of the decisio makers at the same time. herefore, the results make the decisio more scietific ad reasoable. Secodly, usig the AHP method to decide ad makig the thig process mathematic, it ca improve the effectiveess of the decisio makig. he disadvatage of AHP evaluatio Firstly, this method is based o the previous experiece as the udgmet basis. Although the method ca avoid the serious o-coformace i the thikig process, it still caot avoid the oe-sided udgmet problems of the subective factors. Secodly, whe usig the method to make a decisio, due to the imperfect process, it could ot use the method i the high required questio. he scope of AHP he applicatio coditio of AHP is the combiatio of the qualitative ad quatitative scheme. Whe aalyzig the complex questio, the questio which is eeded to solve exists idepedetly. here are some qualitative ad quatitative relatioships amog each item. For such problem, i order to hadle these questios, AHP method provides a ew thikig way. At the same time, the method has the characteristics of mathematically rigorous, simple, ad easy to uderstad. It is more coductive for the decisio makers. 3.. he Advatage of DEA Method:he advatage of DEA is that it is ot iflueced by the subective factors. he results are based o the correspodig data to cout. I this process, it does ot eed to set the weights of iput ad output. his makes the method ca reduce some error which is caused by the subective factors. At the same time, i the usig process, DEA method does ot exist the restricted relatioship of the sub-item. It ca evaluate ad decide at the same time. I additio, it adopts the complex productio relatios. he disadvatage of DEA method Whe decidig the target, we do ot cosider all of the factors. I fact, we use the extreme value evaluatio factors. herefore, the characteristics of some uits do ot display. he disadvatage of this method is the rage. It has the certai restrictive coditios. Ad these restrictive coditios affect the efficiecy. he applicatio rage of DEA rage he DEA method is applied to the field of ecoomic aalysis, the efficiecy ad beefit aalysis ad the evaluatio techological level HE Advatage of RAHP/DEA:RAHP/DEA has ot oly the merits of DEA method, but also it ca avoid the disadvatages that DEA method ca oly udgmet the decisio uits. I additio, it ca reduce effectively the subectivity of the decisio makers whe they use the AHP method to order the scheme layer. RAHP/DEA is more reasoable ad effective for the rakig of the decisio uits. It ot oly iherits the advatages of AHP ad DEA which is used aloe, but also it solves the sidedess ad limitatios. he disadvatages of RAHP/DEA Compared with DEA method, RAHP/DEA method caot completely elimiate the ureasoable parts. Copyright c 05 SERSC 59

8 4. Numerical Aalysis We use RAHP/DEA method to evaluate college physical educatio teachig quality of three colleges. Firstly, we establish the evaluatio idex. he evaluatio idex is show i the followig able. he first layer evaluatio idex Cotet of courses eachig attitude eachig method eachig efficiecy able. he Evaluatio Idex he secod layer evaluatio idex Explicit the teachig goal Reasoable time arragemet Suitable to the studets Formig the lifelog sports cocept Dressig eachig preparatio Studets attedace he commuicatio betwee teachers ad studets Clear actio ad specificatio Studets iterest ad learig ethusiasm Exercisig the method diversificatio Iformatio feedback Class vividly Masterig the skills Guidig the studets to lear autoomously Cultivatig sports ethics, team spirit ad sese of competitio Firstly, we use RAHP method to calculate the weights of the idex. I this paper, we use SPSS8.0 software to calculate the weights of the first layer by the regressio aalysis. We use AI to express the evaluatio idicators ad cotet of courses. he teachig cotet is expressed by CC. eachig attitude is expressed by A. eachig method is expressed by M. eachig efficiecy is expressed by E. After the regressio aalysis, we ca see that the regressio coefficiet of the cotet of courses is 0.3. he regressio coefficiet of the eachig attitude is he regressio coefficiet of the eachig method is 0.9. he regressio coefficiet of the eachig efficiecy is herefore, the regressio equatio for college physical educatio teachig quality assessmet is as follows. able 3. he Aalysis Result of the Dimesio Regressio Model No-stadard coefficiet Stadard coefficiet t sig B Stadard error rial versio Costat term Cotet of courses eachig attitude eachig method eachig efficiecy Copyright c 05 SERSC

9 he regressio equatio is as follows. A I C C A M E he we calculate the weights. he calculatio process is as follows. he weight of the covet dimesio is as follows. 0.3 X he weight of the covet dimesio is as follows X he weight of the covet dimesio is as follows X he weight of the covet dimesio is as follows X herefore, the regressio coefficiets ad the weights for all idictors are as follows. able 4. he Regressio Coefficiets ad the Weights Dimesio Regressio coefficiets Weights Cotet of courses eachig attitude eachig method eachig efficiecy Because the evaluatio idexes of college physical educatio teachig quality are qualitative idexes, we adopt the assessmet scorig method. he obects are composed of 00 experts. he scorig stadards are divided ito excellet, good, geeral, poor grades. Firstly, we evaluate the cotet of courses for college oe. he evaluatio results are show as follows. Grade able 5. he Idex Calculatio of College Physical Educatio eachig Quality Idex Explicit the teachig goal Reasoable time arragemet Suitable to the studets Formig the lifelog sports cocept poor qualified geeral good excellet 0 4 Virtual decisio makig uits Copyright c 05 SERSC 6

10 Accordig to the fuctio m a x 5 y 0 y S.. 5 x 3 5 x 4 0 x 5 y 0 y x 3 0 x 4 7 x y y x 8 x 3 6 x 7 y 4 y x 8 x 5 x 6 y y x 7 x 4 x 7 y y x 3 5 x 4 0 x 3 x, x, x, y, y 0 3 k h h k i i, we ca get the evaluatio idex of cotet of courses for the first college is Similarly, we ca get the evaluatio idexes of cotet of courses for the secod college ad the third college three ad he results are show i the followig able 6. he Results of hree Colleges Evaluatio idex College College College 3 Cotet of courses I the same way, we ca get the evaluatio idexes for cotet of courses, teachig attitude, teachig method ad teachig efficiecy. he results are show i the followig table. able 7. he Evaluatio Idex of hrees Colleges Evaluatio idex College College College 3 Cotet of courses eachig attitude eachig method eachig efficiecy Accordig to the fuctio h c i i physical educatio teachig quality of the three colleges. Amog them, 4 i, we ca get the evaluatio idicators for college herefore, the three colleges rakig is 3 5. Coclusio. he rapid developmet of the iformatio techology promotes the efficiecy of the college physical educatio teachig quality assessmet improvig cotiually. It also makes the evaluatio result more reasoable. It has the wide applicatio combied the iformatio techology with the physical teachig. I this paper, we have doe the followig works. ()Firstly, we itroduce the basic priciple of AHP method ad DEA method. ()Secodly, aimig to determiig of AHP method ad DEA method, we propose the RAHP/DEA method. (3)hirdly, we establish the evaluatio system of college physical educatio teachig quality. (4)Lastly, we adopt the RAHP/DEA method to the 6 Copyright c 05 SERSC

11 college physical educatio teachig quality. Accordig to the evaluatio results, we make the decisio. he experimetal results prove that the method is ratioal. Refereces [] L. Xiag, Research ad developmet of college physical educatio valuatio maagemet iformatio system, Naig Normal Uiversity,Physical Educatio raiig, (004). [] C. J. Zhu, Research o Applicatio of meta evaluatio theory i improvig the quality of physical educatio evaluatio, Nigbo Uiversity, Physical Educatio raiig, (03). [3] Y. J. Che, Study o the selectio of weights of College Physical Educatio Evaluatio System Based o iformatio etropy, Joural of Fuyag eachers College (Natural Sciece). [4] B. Da, Research o the costructio of the sports work of Jiagsu provice college evaluatio idex system, Jiaga Uiversity,Educatioal Priciple, (03). [5] Q.. Rua, Research o Vietamese ordiary uiversity sports evaluatio stadard, Beiig Sport Uiversity,Physical Educatio raiig, (0). [6]. L. Saaty, A scalig method for priorities i hierarchical structures, Joural of Mathematical Psychology, vol. 5, o. 3, (997), pp [7] N. Somsuk ad. Laosirihogthog, A fuzzy AHP to prioritize eablig factors for strategic maagemet of uiversity busiess icubators: Resource-based view, echological Forecastig ad Social Chage, vol. 85, (04), pp [8] M. C. Kim, Y. C. Jag ad S. G. Lee, Applicatio of Delphi-AHP methods to select the priorities of WEEE for recyclig i a waste maagemet decisio-makig tool, Joural of Evirometal Maagemet, vol. 8, (03), pp [9] A. Göreer, K. oker ad K. Uluçay, Applicatio of Combied SWO ad AHP: A Case Study for a Maufacturig Firm, Procedia - Social ad Behavioral Scieces, vol. 58, o., (0), pp [0] G. Bruo, E. Esposito, A. Geovese ad R. Passaro, AHP-based approaches for supplier evaluatio: Problems ad perspectives, Joural of Purchasig ad Supply Maagemet, vol. 8, o. 3, (0), pp [] W. W. Zuo, Q. K. Wag ad P. Yag, Research o the Curret Situatio of Peasat-Workers i Costructio Idustry Based o AHP, Systems Egieerig Procedia, vol. 5, (0), pp [] Y. Yu ad Q. F. Shi, wo-stage DEA model with additioal iput i the secod stage ad part of itermediate products as fial output, Expert Systems with Applicatios, vol. 4, o. 5, (04), pp [3] M. M. Núñez ad W. S. P. Aguiar, Iput output substitutability ad strogly mootoic p-orm least distace DEA measures, Iformatio & Maagemet, vol. 5, o. 6, (04), pp [4] J. Wu, Q. X. A, S. Ali ad L. Liag, DEA based resource allocatio cosiderig evirometal factors, Mathematical ad Computer Modelig, vol. 58, o. 5-6, (03), pp [5] Y. Che, S. Damasbi, J. Du ad S. M. Lim, Iteger-valued DEA super-efficiecy based o directioal distace fuctio with a applicatio of evaluatig mood ad its impact o performace, Iteratioal Joural of Productio Ecoomics, vol. 46, o., (03), pp Authors Hao Li, , Xi a, Shaa xi, P.R. Chia. She is a lecturer i health scieces of Xi a physical educatio Uiversity, Xi a, Shaa xi, Chia. Her scietific iterests are sports sciece ad pedagogy. ie Ru, , Xi a, Shaa xi, P.R. Chia. She is a lecturer i cetral laboratory, the Secod Affiliated Hospital of Xi a Medical Uiversity, Shaa xi, Chia. Her scietific iterest is cardiovascular Physiology. (Maor i Cardiovascular Physiology). Copyright c 05 SERSC 63

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