631 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 Guest Edtors: Peyu Ren, Yancang L, Hupng Song Copyrght 2015, AIDIC Servz S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 The Italan Assocaton of Chemcal Engneerng Onlne at www.adc.t/cet DOI: 10.3303/CET1546106 Performance Management and Evaluaton Research to Unversty Students Shaoyng Yu Department of Musc, Guangdong Unversty of Educaton, Guangzhou, 510303, Chna. yushaoyng@gde.edu.cn For the past decades, conspcuous progress s demonstrated n all felds of Chna, such as economy, scence and technology. Meanwhle, the comprehensve strength of Chna has been enhanced greatly. However, the qualty of hgher educaton should face some dffcultes. It s an mportant Step that how to further realze and enhance the performance of hgher educaton. An assessment framework s essental to be constructed to evaluate the performance of students n the hgher school. Because of the dffculty of expressng the experts' opnons exactly, hestant fuzzy sets are ntroduced to form a multple attrbute decson makng model. A new dstance measure s proposed to solve ths evaluaton problem under the framework of MAGDM. Fnally, a case study s demonstrated to verfy the relablty and applcablty of the proposed method. 1. Introducton From the perspectve of all over the world, the competton of economy and comprehensve natonal strength between each country s ndeed that of the capablty of modern technology. In modern socety, wth the rapd development of knowledge economy, hgher educaton s always a key pont related to the modern technology of a country whether t s a developed country (Tarvd (2015)). Owng to the rapd growth of the number of students n hgher educaton, the management of students s a more complex problem than ever (Yue (2015)). Up to 2014, there are 24,681,000 students n hgher school related to Chna, whch s from Natonal Bureau of Statstcs. The satsfacton for graduates to fnd a good ob s very small. The most mportant ssue of these phenomena s lack of self-percepton for graduates when they are n college. The effectve way to promote self-percepton s to accept assessment from others or themselves (We and Peng (2015); Sheng (2014)). Some hgher educaton nsttute ntroduces Hgher Educaton Informaton System to explore the possblty for predctng the success rate of students n hgher school by usng data mnng technology (Natel and Zwllng (2014)). However, t s not comprehensve to realze the performance of students by hgher educaton nformaton system. Dfferent mnng technology can result dfferent soluton, whch may mss some nformaton. Then, a new assessment framework s essental to construct to help us realze the performance of students comprehensvely. Ths assessment problem can be consdered as a multple attrbute group decson makng (MAGDM) problem n order to ntroduce some MAGDM methods (Lu, Chan and Ran (2013); Feng and La (2014)). The multple attrbute group decson makng problem s a type of mult-obectve and mult-expert decson problem, whch has appled wdely n many felds such as economcs (Mergo, Xu and Zeng (2013)), management (Lang, Pedrycz, Lu and Hu (2015)) and so on (Chen, Zhang and Dong (2015); Sassenberg, Landkammer and Jacoby (2014)). The essence of the MADGM problem s assemblng decson-makng nformaton, sortng and selectng the outcome through defnte means wth multple experts. Most of the proposals for solvng MAGDM found n lterature focus on cases where the nformaton provded by experts represented n precse and accurate assessment values. However, n real-lfe, the experts have dfferent cultural and educatonal backgrounds, experence and knowledge. Then, there are subectve and hestant assessments provded by the experts, uncertan and mprecse are the basc characterstcs of ther preferences. For nstance, for a selecton problem of a new computer wth dfferent brand such as Mcrosoft, Lenovo, Thnkpad and others, dfferent experts have dfferent opnons whch have the dsagreements, whch lead the dffculty for the decson maker to select approprate brand. Please cte ths artcle as: Yu S.Y., 2015, Performance management and evaluaton research to unversty students, Chemcal Engneerng Transactons, 46, 631-636 DOI:10.3303/CET1546106
632 In other words, t s dffcult to express the experts' preferences accurately. Because of ths, fuzzy set s ntroduced n MAFDM to solve ths problem. Zadeh defned the basc concept of fuzzy sets based on the theory of fuzzy mathematcs whose man characterstc s that: the membershp functon assgns to each element x n a unverse of dscourse X a membershp n nterval [0,1] and the non-membershp degree equals one mnus the membershp degree. Snce fuzzy set was proposed, t has been a popular method to solve uncertan and mprecse of experts' preferences (Zadeh (1965); Zmmermann (1985)). Up to 2009, Torra and Narukawa asserted t was often dffcult to gve the membershp or non-membershp nto one value and whch may be exst a doubt among a set of dfferent values. Thus, they defned hestant fuzzy sets to deal wth ths problem, whch allows the membershp nto a set demonstrated as several possble values between 0 and 1 (Torra and Narukawa (2009)). Moreover, n 2010, Torra proposed some smple arthmetc and geometrc aggregaton operators of hestant fuzzy sets to aggregate the nformaton of dfferent experts or attrbutes]. Dfferent operaton may result dfferent soluton, so dstance measure s ntroduced n ths paper to aggregate the he nformaton of dfferent experts or attrbutes. The man contrbutons of ths paper nclude the followng: (1) the constructon of the assessment framework of student management; (2) the desgn of expressng expert's preference by hestant fuzzy sets; (3) the ntroducton of Hausdorff dstance measure to aggregate experts' preference; (4) the applcaton of assessment framework based on the proposed method. The rest of ths paper s organzed as follows. In Secton 2, we construct some assessment framework of student management. Secton 3 ntroduces some concepts of hestant fuzzy set and proposes Hausdorff dstance measure to evaluate management performance. A case study s demonstrated n Secton 4. Fnally, Secton 5 concludes ths paper. 2. Proposed method In ths secton, we ntroduce hestant fuzzy multple group decson makng methods to evaluate management performance of students n hgher school. Based on the basc concepts of hestant fuzzy sets, we defne Hausdorff dstance measure to aggregate nformaton n decson matrx. 2.1 Hestant fuzzy sets Torra proposed the concept of hestant fuzzy set whch s n terms of a functon when appled to a fxed set returns a sunset of [0, 1]. Then, n order to easly understood, Xa and Xu expressed the hestant fuzzy set by mathematcal symbol. Defnton 1(Torra and Narukawa (2009)). Let X be a unverse of dscourse, then a hestant fuzzy set H over X s defned as H = { < x, h ( x) > x X }, (1) H where h H (x) s a set of some values n [0, 1], symbolzng the possble membershp degrees of the element x to H. For convenence, we call h = h H (x) a hestant fuzzy element and H the set of all hestant fuzzy elements. 2.2 Dstance measures 1. Dstance measure s fundamentally mportant n a varety of scentfc felds such as decson makng, pattern recognton, machne learnng and marker predcton, lots of studes have been done on ths ssue. 2. By takng nto account the dscrete element of hestant fuzzy sets, and followng the basc lnes of reasonng on whch the defnton of dstances between ntutonstc fuzzy sets are based, we defne the Hausdorff dstance measure between the hestant fuzzy sets. Defnton 2 Let M = {x, h M (x) x X}and N = {x, h N (x) x X} be two hestant fuzzy sets n X={x 1, x 2,..., x n }, we defne the generalzed weghted Hausdorff dstance measure between M and N as follows: d g (M, N) = { max } ( ) ( ( ) ) 1 n w hm x hn ( x) λ = 1 σ σ λ (2) where λ > 0, whch can be obtaned accordng to the decson maker's rsk atttude. Defnton 3 Let M = {x, h M (x) x X}and N = {x, h N (x) x X}be twol hestant fuzzy sets n X={x 1, x 2,..., x n }, we defne the weghted Eucldean- Hausdorff dstance between M and N as follows: d e (M, N) = { max } ( ) ( ( ) ) ( ) 2 12 n σ σ w hm x hn x = 1 (3)
633 Defnton 4 Let M = {x, h M (x) x X}and N = {x, h N (x) x X}be twol hestant fuzzy sets n X={x 1, x 2,..., x n }, we defne the weghted Hammng- Hausdorff dstance between M and N as follows: d h (M, N) = ( ) ( { max ( ) ) ( ) n σ σ w hm x hn x } = 1 (4) Obvously, when λ=1, d g reduces to d h ; when λ=2, d g reduces to d e. Defnton 5. Let M and N be two hestant fuzzy sets on X = {x 1, x 2,..., x n }, then the dstance measure between M and N s defned as d(m, N), whch satsfes the followng propertes: 1. (1) 0 d(m, N) 1; 2. (2) d(m, N) = 0, f and only f M = N; 3. (3) d(m, N) = d(n, M). 2.3 Decson method When Hwang and Yoon proposed TOPSIS(technque for order preference by smlarty to an deal ), whose basc prncple s to choose the alternatve wth the shortest dstance from the postve deal soluton(pis) and the farthest dstance from the negatve deal soluton(nis), t has been acqured great attenton n MAGDM problems. In ths paper, based on the characterstc of hestant fuzzy sets, we use the deal of TOPSIS to select the alternatve wth the shortest dstance from the postve deal soluton (PIS). Under hestant fuzzy envronment, the hestant fuzzy PIS, denoted by A + can be defned as follows: k {,max 1,2,, } A + = x h = n (5) In order to smplfy computaton, the Eq. (6) s appled nstead of the Eq. (5) as follows. { 1, 0 1, 2,, } A + = = n (6) 4. The relatve closeness coeffcent of an alternatve A wth respect to the hestant fuzzy PIS A + and A - s expressed as follows: CC = d +, (7) where 0 CC 1, = 1,2,... m. Obvously, when an alternatve A s closer to the hestant fuzzy PIS, CC wll be closer to 1. Thus, based on the closeness coeffcent CC, the rankng of all alternatves can be determned and the best alternatve can be selected 2.4 Procedure of assessment model Based on the framework demonstrated n secton 2, we can propose a procedure to solve ths problem, where attrbute values take the form of the hestant fuzzy values Step 1. For a assessment problem, we frstly construct a decson matrx D= [ h ] m n, where all the arguments h ( = 1, 2,..., m; = 1, 2,..., n) are the hestant fuzzy numbers, provded by the experts. As for every alternatve A ( = 1, 2,..., m), the experts s nvted to express evaluaton or preference accordng to each attrbute C ( = 1, 2,..., n) by a hestant fuzzy number h ( = 1, 2,..., m; = 1, 2,..., n) and gves the relatve weghts of the n attrbutes denoted as w = (w 1, w 2,, w n ) T wth 0 w 1 ( = 1, 2,..., n) and n w = 1 = 1. Step 2. Accordng to preference of the decson maker, the decson makng matrx s obtaned as follow: D h11 h12 h1 n h h h hm1 hm2 hmn 21 22 2n m n= (8) Step 3: Utlze Eq.(6) to determne the correspondng hestant fuzzy PISA + and the dual hestant fuzzy NISA -. Step 4: Accordng to Eq. (7), the closeness coeffcent of each alternatve s acqured.
634 Step 5: Rank all alternatves A based on the closeness coeffcent CC, where the greater the value CC, the better the alternatve A. 3. Case study In ths secton, we desgn a case study to demonstrate the applcablty of the proposed method. 4 professors from dfferent maor are nvted as the experts. A vce-presdent s nvted as the decson maker chooses any fve students as the alternatves denoted A 1, A 2, A 3, A 4, A 5 and four attrbutes (examnaton performance, campus actvtes, Evaluaton and Socal actvty). Frstly, the decson maker wth the experts gve the weght vector of these four attrbutes denoted as w = (0.3, 0.2, 0.2, 0.3) T. Secondly, they gve ther preferences of every student on each attrbute, respectvely. Thus, the decson maker combnes the opnons of these experts to provde a hestant fuzzy decson matrx D= [ h ] 5 4 demonstrated n Table1. Table 1: Transposton of orgnal hestant fuzzy decson matrx A 1 A 2 A 3 A 4 A 5 C 1 {0.1,0.3} {0.5,0.6, 0.8} {0.1,0.4, 0.5} {0.3,0.5} {0.5,0.7} C 2 {0.5,0.6,0.7} {0.2,0.4,0.7} {0.1,0.4} {0.3,0.4,0.6} {0.4,0.5} C 3 {0.4,0.6,0.8} {0.1,0.3} {0.2,0.3 } {0.2,0.5,0.6} {0.3,0.6,0.8} C 4 {0.4,0.5,0.8} {0.3, 0.6} {0.1,0.3,0.4} {0.5} {0.3,0.6} Based on Eqs. (6) and (7), t can be obtaned dstance of each alternatve and the hestant fuzzy PISA + n Fgures 1. Table 2: Dstance measure between each alternatve and the hestant fuzzy PISA+ d + λ = 1 λ= 2 λ= 6 λ= 8 α 1 0.67 0.6422 0.6101 0.5824 α 2 0.7 0.6915 0.6823 0.6778 α 3 0.88 0.8511 0.8369 0.8127 α 4 0.66 0.6337 0.6285 0.617 α 5 0.62 0.605 0.582 0.573
635 Fgure 1: Dstance of each alternatve to postve deal soluton In order to demonstrate the relatonshp of parameter λ wth the rank-order, we select λ [1, 8] to demonstrate the rule. It s obvous that dfferent parameter λ has dfferent rank. So, we ntervew these experts to realze ther preference. Based on the most experts' preference, we select = 2. Therefore, accordng to Eqs. 6-7 and parameter =2, the closeness coeffcent and rank-order can be computed as (0.6422, 0.6915, 0.8511, 0.6337, 0.605). As mentoned above, the rank-order s demonstrated as A 3 A 2 A 1 A 4 A 5. It s obvously to select A 3 s the optmal student. Ths result consderng the professors' rsk atttude can help the students further realze themselves and understand the gap between them wth the optmal student. After ths, the student can acqure more motvaton to enhance ablty of not only examnaton but also socal skll. 4. Conclusons and further study Recently, wth the fast development of hgher school, student management has become an mportant ssue for our country. As mentoned n secton 1, to construct a new assessment framework s useful way to help us promote student management. The key problem of t s the actual expresson of the experts' preference. Thus, accordng to exstng studes, we ntroduce hestant fuzzy set wth multple attrbute group decson makng method ncludng dstance measure of TOPSIS to handle ths assessment problem. Based on the case study, t can further show the contrbutons and nnovatons of the assessment framework ncludng the followng aspects: (1) the constructon of the assessment framework of student management; (2) the demonstraton of expressng expert's preference by hestant fuzzy sets; (3) the ntroducton of Hausdorff dstance measure to aggregate experts' preference; (4) the applcaton of assessment framework based on the proposed method. Although the method s useful to evaluate management preference of students n hgher school, t cannot solve the problems wth more complex problems such as hestant fuzzy lngustc nformaton. In the future, we wll extend the method to solve more complex problems. References Cheng Y. S. What are students' atttudes towards dfferent management strateges: A cross-regonal study [J]. Proceda-Socal and Behavoral Scences, 2014(141), 188-194. Chen X., Zhang H. J., Dong Y. C., 2015, The fuson process wth heterogeneous preference structures n group decson makng: A survey [J]. Informaton Fuson, (24): 72-83. Feng B., La F. J.. Mult-attrbute decson makng wth aspratons: A case study [J]. Omega, 2014(44): 136-147. Lang D. C., Pedrycz W., Lu D., Hu P., 2015, Three-way decsons based on decson-theoretc rough sets under lngustc assessment wth the ad of group decson makng [J]. Appled Soft Computng, (29), 256-269. Lu S., Chan F. T. S., Ran W. X., 2013, Mult-attrbute group decson-makng wth mult-granularty lngustc assessment nformaton: An mproved approach based on devaton and TOPSIS [J]. Appled Mathematcal Modelng, (37), 10129-10140.
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