Research on the Comprehensive Strength Evaluation for Universities based on the Fuzzy TOPSIS Method

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1 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy TOPSIS Method Fuqn Yue X'an Internatonal Unversty, X'an, Shaanx, Chna Abstract In recent years, the scale of enrollment n colleges and unverstes contnues to expand. The prvate colleges are also sprngng up. The comprehensve strength of each unversty s uneven. Evaluatng the comprehensve strength for the colleges s not only to provde the reference for the majorty students parents, but also to promote the contnue development for the comprehensve strength of the colleges. In ths paper, n order to make the better evaluaton of the comprehensve strength for the colleges, we combne the fuzzy theory wth the TOPSIS method and propose an mproved fuzzy TOPSIS method. Then, we use the method to evaluate the comprehensve strength for the college. The expermental results demonstrate the relablty and the valdty of the method. Keywords Fuzzy theory, Comprehensve strength, Evaluaton Introducton In 983 year, the Unted States famous news magazne of Amercan news and World Report released the world s frst unversty rankngs. And t opened the prologue of the world s college rankngs. In 987 year, Jang Guohua profess who s the founder of Chna s scentfc metrology publshed the frst college rankngs for Chnese colleges. It was the studed content for the world s scholars to rank and evaluate the colleges. It had the profound and broad sense. Evelyn Bergsmann and other scholars evaluated the competence-based teachng n hgher educaton nsttutons []. The author provded a more comprehensve evaluaton concept that contrbuted to sustanable mprovement of competence-based teachng n hgher educaton nsttutons. The evaluaton concept was composed of three stages. They were the evaluated ablty, the practcal obtaned ablty for the students and the specfc lnk of teachng. The man evaluaton objects for ths paper were the competence-based currculum n hgher educaton. Ren-Zhong Peng, We-Png Wu, We-We Fan assessed Chnese college students ntercultural competence based on the theores of ntercultural competence and the method of fuzzy comprehensve evaluaton [2]. In the process of constructng the model, the author adopted the vewpont of the experts to measure the mportance of each ndex of Chnese college students ntercultural competence. The comparson of the results suggested that the fuzzy 36

2 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy comprehensve evaluaton model can be used effectvely to assess Chnese college students ntercultural competence. Yn Zhmng studed the comprehensve evaluaton ndex system for Chnese unverstes [3]. The author began from the produce of evaluatng the tran at home and aboard. Frstly, the author revewed the evaluaton for the unverstes. Then, the author dscussed the prncple for settng the ndex from the sngle ndex and the ndex system and made the emprcal study for the colleges evaluaton. Fnally, the author compared the results wth the evaluaton report of the Chnese comprehensve evaluaton. Xu Mn studed and evaluated unversty knowledge management [4]. The author used the systematc analyss method to comb the college knowledge management content and the evaluated structure from up to down. Then, the author constructed the dmenson model of the college knowledge management wth the exstng theoretcal model. The paper used the mult-level grey correlaton evaluaton method to evaluate comprehensvely the knowledge management for 6 unverstes. Then we got the relatve evaluaton rankngs. Fnally, the paper combned wth the actual stuaton of one college and used the fuzzy comprehensve evaluaton method to get the absolute evaluaton score of the knowledge management for the college. L Bfang evaluated the college comprehensve strength accordng to the fuzzy evaluaton method of the set-valued teraton [5]. Huang Qngsun evaluated and analyzed the comprehensve strength status of the colleges n Guang X. And he studed the stratagem [6]. Accordng to the characterstcs of the evaluaton n colleges, Wang Xaoyan determned the fuzzy evaluaton matrx and the weght coeffcent. And he appled the fuzzy comprehensve evaluaton method to study the college teachng evaluaton method [7]. The fuzzy theory was developed on the bass of the fuzzy set theory, whch was founded n 965 by L.A.Zadeh, a professor at Calforna Unversty. The basc dea of the fuzzy theory was to accept the fact that the fuzzy phenomenon exsted. He took the uncertan objects as the research object. It manly contented the fuzzy mathematcs [8-9], fuzzy logc [0-], fuzzy system [2-3], fuzzy control [4-5] and fuzzy decson [6-7]. TOPSIS method s short for technque for order preference by smlarty to deal soluton. It was the common method for the system engneerng. TOPSIS method s one of the most evaluaton methods. It has appled to the felds, such as the economy [8-9], management [20-2], agrculture [22-23] and ndustral [24-25]. In ths paper, n order to make a better evaluaton for the college comprehensve strength, we combne the fuzzy theory wth TOPSIS method and propose the mproved fuzzy TOPSIS method. The structure of ths paper s as follows. The frst part s the ntroducton. In ths part, we manly ntroduce the status of the college evaluaton. The second part s the TOPSIS method. In ths part, we manly ntroduce the basc step of the TOPSIS method. The thrd step s the mproved fuzzy TOPSIS method. In the thrd part, we propose an mproved fuzzy TOPSIS method. The fourth part s the experment and the last part s the concluson. JET Vol. 2, No. 8,

3 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy 2 TOPSIS method TOPSIS method was frstly proposed by Hwang and Yoon n 98. Due to the complexty of the real decson problems, TOPSIS method was used to deal wth the decson problems n dfferent stuatons, such as fuzzy decson problem and group decson problem. The basc dea of TOPSIS method s to make the deal pont and the negatve deal pont as the reference and adopt the Eucldean dstance to measure the dstance between any feasble scheme and the deal pont. The bass for evaluatng the merts of each scheme s to approach the deal pont and to be far away from the negatve deal pont. The steps of TOPSIS method are as follows. The frst step s to standard the decson matrx X=(x j ) mn. And we get the standardzed decson matrx Y=(y j ) mn. xj yj =, ( =, 2,, m; j =, 2,, n) m 2 x j = () The second step s to construct the weghted standardzaton matrx Z=(z j ) mn. zj = wy j j, ( =, 2,, m; j=, 2,, n) (2) The thrd step s to determne the postve deal soluton A + and the negatve deal soluton A - for the mult attrbute decson A = ( z, z2,, zn ) = {(max zj j I),(mn zj j J)} (3) A = ( z, z2,, zn ) = {(mn zj j" I),(max zj j" J)} (4) Where, I s the set of the ncome property ndex. And J s the set of the cost property ndex. The fourth step s to calculate the dstance d + between each scheme A, =, 2,, m and the postve deal soluton. The d - s the dstance between each scheme A, =, 2,, m and the negatve deal soluton. + n 2 = z + = "( j + j ),( =,2,, ) j= d A z z m n 2 = z = "( j j ),( =,2,, ) j= d A z z m (6) + d C = + The ffth step s to calculate the relatve degree d + d of each scheme. Obvously, 0"C + I ", =, 2,, m. The relatve degree of the postve deal pont s. And the relatve degree of the negatve deal pont s 0. The sxth step s to use the value of the relatve degree to rank the schemes. (5) 38

4 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy 3 The mproved fuzzy TOPSIS method In ths paper, we dvde the ftness value range nto fve grades. They are S={poor(s ), general(s 2 ), good(s 3 ), excellent(s 4 )}. We assume that A s the evaluated scheme, =, 2,, m. D k s the evaluated expert. And the attrbute weght s # k. # k [0, ] and, k=, 2,.., t. C j s the evaluated ndex. The weght s w j. w j [0, ] and, j=, 2,, n. The attrbute value of the evaluated ndex C j s x k j that the expert D k evaluates for the scheme A. Then, t consttutes the language fuzzy decson matrx R (k) =(r (k) j ) mn. Defne : We assume that S={s 0, s,, s g } s a language evaluaton set. $ [0, ] s the real number whch s accepted by one assembly method for the language evaluaton set. The bnary semantc whch s correspondng to $ can be expressed by the followng functon. :[0,] " S#$ [ / 2 g,/ 2 g] (7) "() = ( s, a) (8) # s, = round( " g) $ Where, & a = % / g, a = [ % /2 g,/2 g] (9) Defne 2: We assume that S={s 0, s,, s g } s a language evaluaton set. (s k, a) s a dual language. Then, t exsts the nverse functon. The nverse functon can transfer the Bnary semantc to the correspondng numercal. " : S# [ / 2 g,/ 2 g] $ [0,] (0) " # :( sk, a) = / g+ a = () Defne 3: If X={(r, a ), (r 2, a 2 ),, (r n, a n )} s a set of bnary semantc set. W=(w, w 2,, w n ) T s the correspondng weght vector. Then, the weghted average operator of the bnary semantc s as follows. n n " ( ) = #( $ # (, ) ) = #( $ ) = = TWA X r a w w (2) Defne 4: We assume that (s k, % k ) and (s, % ) are two bnary semantc. () If k>l ( sk, k) > ( s, ) (3) (2) If k=l k =,( sk, k) = ( s, ) (4) k >,( sk, k) > ( s, ) (5) k <,( sk, k) < ( s, ) (6) For the beneft ndex and the cost ndex, n order to elmnate the nfluence of dfferent dmensonal attrbute value on the decson results, we need to deal wth them for the unfcaton. The beneft ndex for the language type s to use the nverse operator of the natural language evaluaton set S={s 0, s,, s g }. It transfers the correspondjet Vol. 2, No. 8,

5 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy ng beneft ndex to the cost ndex. On the contrary, t use the nverse operator to transfer the cost ndex to the beneft ndex. For the calculaton convenence, we gve the followng defne. It unfes the ndexes for the transton between the cost ndex and the beneft ndex. Defne 5: We assume that S={s 0, s,, s g } s a language evaluaton set. The formula that the cost ndex transfers to the beneft ndex whch s based on the two tuple lngustc nverse operator Neg s as follows. Neg( sk, k) = "( #(" ( sk, k))) (7) Then, we use the new weght dstrbuton method. That s, we use the dynamc weght dstrbuton method to calculate the weght of each ndex. The steps are as follows. The frst step s as follows. We make each factor as the measure standard. And we put the prorty factor nto the rght of the factor. And we put the unmportant factor nto the left of the factor. It s easy for the desgn staff to acheve the process. Table. The mportance of the factors Left measure standard Rght S 3, S 4 S S 2 S, S 3, S 4 S 2 S 3 S, S 2, S 4 S 3 S 4 S, S 2 The second step s to statstc the compared results. NL s =, N L s = 0, N 3, 2 L s = N 3 L s4 = 2; NR s = 2, N 3, 0, R s = N 2 R s = N 3 R s = 4 (8) Where, N L-s s the number that the factor S n the left. N R-s s the number that the factor S n the rght. That s the mportance. Ns = N R s N L s = 2 = Ns = N 2 R s N 2 L s2 = 3 0= 3 Ns = N 3 R s N 3 L s3 = 0 3= 3 Ns = N 4 R s N 4 L s4 = 2= (9) The thrd step s to calculate the most mportant factor S 2 and the least mportant factor S 3. Accordng to the -9 rato scalng method, the desgn staff gves the mportant degree b 23 (<b"9) of U3. Therefore, we can dvde the numercal scale [Ns 3, Ns 2 ]=[-3, 3] nto b Each node represents a scale. We assume that b 32 =5. Then we can get the followng table. Table 2. scale comparson table Numercal soluton pont Scalng

6 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy For other b 3, we determne s accordng to the nearest prncple. N 3 s near to whch numercal node, b 3 wll take that correspondng scalng. The ntermedate value takes the rght node. Then we can get b 3 =4, b 32 =5, b 33 =4, b 34 =3. Then, the relatve mportance of other factors can be calculated by the scalng of the least mportant factor for each factor. The calculaton method s b j =+(b 3 -b 3j ), b 3 &b 3j. Where, b 3 &b 3j. The calculaton results are as follows. Table 3. Factor scalng value table Attrbute S S 2 S 3 S 4 S 2 /4 /2 S 2 /2 /5 3 S S 4 2 /3 /3 The fourth step s to calculate the feature vector of the matrx. Then we make the normalzed processng and get the weght values. We apply the mproved fuzzy TOPSIS method to evaluate. The specfc step s as follows. The frst step s to use the bnary semantc nverse operator to transfer the cost ndex to the beneft ndex. The second step s to transfer the language evaluaton matrx R k =(r (k) j ) mn to the bnary semantc evaluaton matrx R k=(r (k) j, 0) mn for the scheme. The thrd step s to use TWA operator to buld up R k nto the bnary semantc evaluaton matrx R=(rj, a j ) mn. () (2) ( k ) ( r, a ) = TWA(( r,0),( r,0),,( r,0)) j j j j j t " ( k ) = #( $ (# ( r j,0) k )) k = (20) The fourth step s to determne the bnary semantc postve deal soluton O + and the bnary semantc postve deal soluton O O = ( r, a ) = (( r, a ),( r2, a2),( r3, a3),,( rn, an)) (2) O = ( r, a ) = (( r, a ),( r2, a2),( r3, a3),,( rn, an)) (22) Where + + ( rj, aj ) = max{( rj, aj )}, j =,2,, n (23) ( rj, aj ) = mn{( rj, aj )}, j =,2,, n (24) The ffth step s to calculate the weght w=(w, w 2,, w n ) T of each attrbute. The sxth step s to calculate the dstance from each scheme to the postve soluton and the negatve soluton. JET Vol. 2, No. 8, 207 4

7 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy n ( d +, a + ) = "(#(" ( rj, aj )" ( r + j, a + j ) wj )) j= n ( d, a ) = "(#(" ( rj, aj )" ( r j, a j ) wj )) j= (26) The seventh step s to calculate the relatve closeness degree from each scheme to the postve soluton. ( ( d, a ) ( d, a ) = "" ( " ( d, a ) + " + + ( d, a ))) (27) The eghth step s to get the rankng results accordng to the relatve closeness degree for the scheme. (25) 4 Experment Before we evaluate the college strength, we need to select the evaluated ndexes. We select these ndexes from fve aspects. The evaluated ndexes are as follows. Unversty comprehensve strength evaluaton Teachng qualty Teacher strength Scentfc research achevements Personnel tranng Peer evaluaton Fg.. College comprehensve evaluaton system We evaluate comprehensvely for fve colleges. Scheme evaluaton table are as follows. Table 4. Scheme evaluaton table Scheme C C 2 C 3 C 4 C 5 A (s 4, 0.6) (s 3, 0.00) (s 2, 0.00) (s 5, 0.6) (s 5, 0.08) A 2 (s 5, 0.08) (s 5, 0.08) (s 4, 0.08) (s 4, 0.6) (s 4, 0.00) A 3 (s 4, 0.00) (s 4, 0.06) (s 4, 0.6) (s 5, 0.00) (s 4, 0.06) A 4 (s 2, 0.08) (s 3, 0.08) (s 5, 0.6) (s 4, 0.6) (s 2, 0.08) A 5 (s 3, 0.00) (s 4, 0.00) (s 3, 0.6) (s 5, 0.00) (s 4, 0.00) 42

8 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy Then we determne the bnary semantc postve deal soluton and the bnary semantc postve deal soluton. O + =(r +, a + )=((s 3, 0.08), (s 4, 0.6),(s 5, 0.00),(s 4, 0.08),(s 5, 0.6)) O - =(r -, a - )=((s 3, 0.00), (s 3, 0.08),(s 4, 0.6),(s 4, 0.00),(s 4, 0.0)) The weght of each ndex s w=(0.4, 0.22, 0.27, 0.3, 0.06). The relatve closeness degree s as follows. (d, a )=(s 4, 0.04), (d 2, a 2 )=(s 4, 0.06), (d 3, a 3 )=(s 5, 0.5), (d 4, a 4 )=(s 3, 0.04), (d 5, a 5 )=(s 5, 0.2), The evaluaton results are A 3 >A 5 >A 2 >A >A 4. 5 Conclusons Colleges and unverstes are the place to tran hgh qualty talents. Through hgher educaton, colleges transport many talents for the communty. Evaluatng the teachng qualty of the hgher educaton can mprove the teachng level of the hgher school. Ths paper apples the mproved Grey-TOPSIS method to evaluate the teachng qualty of the hgher educaton. Ths paper contans the followng works. Frstly, ths paper ntroduces the Grey correlaton model. Secondly, ths paper proposes the mproved Grey-TOPSIS method. Thrdly, ths paper apples the mproved Grey-TOPSIS method to evaluate the teachng qualty of the hgher educaton. The expermental results demonstrate the valdty and the relablty of the method. Evaluatng the college strength comprehensvely can not only gude the college to the scentfc development, but also gude the students to select the colleges. Accordng to the comprehensve evaluaton, each college can mprove the teachng qualty, mprove the level of talent tranng and promote the development of themselves. Accordng to the comprehensve evaluaton, the canddates and ther parents can select better college and more sutable major. Based on ths, ths paper proposes the mproved fuzzy TOPSIS method to evaluate the college comprehensvely. The major contents of ths paper are as follows. Frstly, ths paper brefly ntroduces the present stuaton of the college comprehensve evaluaton. Secondly, based on the fuzzy theory and TOPSIS method, ths paper proposes the mproved fuzzy TOPSIS method. Thrdly, ths paper apples the mproved fuzzy TOPSIS method to evaluate the college comprehensvely. Fnally, the experment verfes the relablty and the valdty of the method. 6 References [] Bergsmann, E., Schultes, M.T., Wnter, P., Schober, B., Spel, C. (205). Evaluaton of competence-based teachng n hgher educaton: From theory to practce. Evaluaton and Program Plannng, 52: JET Vol. 2, No. 8,

9 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy [2] Peng, R.Z., Wu, W.P., Fan, W.W. (205). A comprehensve evaluaton of Chnese college students ntercultural competence. Internatonal Journal of Intercultural Relatons, 47: [3] Yn, Z.M. (2005). Research on the ndcator system of college ntegrated evaluaton n Chna. Wuhan Unversty, Informaton management. [4] Xu, M. (200). Research on the evaluaton of unversty knowledge management. Harbn Insttute of Technology, Management scence and Engneerng. [5] L, B.F. (20). Applcaton of fuzzy comprehensve evaluaton method based on set valued teraton n comprehensve strength evaluaton of Unversty. Scence & Technology nformaton, 2: [6] Huang, Q.S. (2007). Research on evaluaton of unverstes comprehensve strength n Guangx. Guangx Normal Unversty, Hgher educaton management. [7] Wang, X.Y. (200). Research on hgher schools teachng evaluaton method based on comprehensve fuzzy judgment. Journal of Boha Unversty, 9: [8] L, W.X., Q, D.L., Zheng, S.F., Ren, J.C., L, J.F., Yn, X. (205). Fuzzy mathematcs model and ts numercal method of stablty analyss on rock slope of opencast metal mne. Appled Mathematcal Modellng, 39: [9] Chatterjee, A., Mukherjee, S., Kar, S. (204). Poverty Level of Households: A Multdmensonal Approach Based on Fuzzy Mathematcs. Fuzzy Informaton and Engneerng, 6: [0] Hüllermeer, E. (205). Does machne learnng need fuzzy logc? Fuzzy Sets and Systems, 28: [] Godo, L., Gottwald, S. (205). Fuzzy sets and formal logcs. Fuzzy Sets and Systems, 28: [2] Gao, Y.B., L, H.Y., Wu, L.G., Karm, H., Lam, H. (206). Optmal control of dscretetme nterval type-2 fuzzy-model-based systems wth -stablty constrant and control saturaton. Sgnal Processng, 20: [3] Ulu, C. (205). Exact analytcal nverson of nterval type-2 TSK fuzzy logc systems wth closed form nference methods. Appled Soft Computng, 37: [4] Chang, W., Hsu, F.L. (206). Sldng mode fuzzy control for Takag Sugeno fuzzy systems wth blnear consequent part subject to multple constrants. Informaton Scences, 327(0): [5] Zhang, J., L, X.M., Zhao, T.Y., Da, W. (205). Expermental study on a novel fuzzy control method for statc pressure reset based on the maxmum damper poston feedback. Energy and Buldngs, 08: [6] Chen, S.M., Cheng, S.H., Chou, C.H. (206). Fuzzy multattrbute group decson makng based on ntutonstc fuzzy sets and evdental reasonng methodology. Informaton Fuson, 27: [7] Xu, Z., Zhao, N. (206). Informaton fuson for ntutonstc fuzzy decson makng: An overvew. Informaton Fuson, 28: [8] Aghajan, M.M., Tahere, G.P., Sulaman, N.M.N., Basr, N.E.A., Saher, S., Mahmood, N.Z., Jahan, A., Begum, R.A., Aghamohammad, N. (206). Applcaton of TOPSIS and VIKOR mproved versons n a mult crtera decson analyss to develop an optmzed muncpal sold waste management model. Journal of Envronmental Management, 66(9):

10 Paper Research on the Comprehensve Strength Evaluaton for Unverstes based on the Fuzzy [9] Blbao-Terol, A., Arenas-Parra, M., Cañal-Fernández, V., Antoml-Ibas, J. (204). Usng TOPSIS for assessng the sustanablty of government bond funds. Omega, 49: [20] Wanke, P., Barros, C., Macanda, N.P.J. (206). Predctng Effcency n Angolan Banks: A Two Stage TOPSIS and Neural Networks Approach. Research n Internatonal Busness and Fnance, 36(3): [2] Oztays, B. (204). A decson model for nformaton technology selecton usng AHP ntegrated TOPSIS-Grey: The case of content management systems. Knowledge-Based Systems, 70: 44-54, [22] Huang, W., Huang, Y.Y. (202). Research on the Performance Evaluaton of Chongqng Electrc Power Supply Bureaus Based on TOPSIS. Energy Proceda, 4: [23] Choudhary, D., Shankar, R. (202). An STEEP-fuzzy AHP-TOPSIS framework for evaluaton and selecton of thermal power plant locaton: A case study from Inda. Energy, 42: [24] Guo, S., Zhao, H.R. (205). Optmal ste selecton of electrc vehcle chargng staton by usng fuzzy TOPSIS based on sustanablty perspectve. Appled Energy, 58: [25] Alon, D., Dulmn, R., Mnnno, V. (204). A peer IF-TOPSIS based decson support system for packagng machne selecton. Expert Systems wth Applcatons, 4: Author Fuqn Yue receved the master degree from X'an Jao Tong Unversty. Her research s manly on nvestment and fnancng management; engaged n fnance and nvestment research and teachng(yuefuqn@26.com). Artcle submtted 3 May 207. Publshed as resubmtted by the author 7 June 207. JET Vol. 2, No. 8,