Generalized net model of the process of ordering of university subjects

Transcription

1 eventh Int. okshop on Gs, ofia, 4- Juy 006, -9 Geneaized net mode of the pocess of odeing of univesity subjects A. hannon, E. otiova, K. Atanassov 3, M. Kawczak 4, P. Meo-Pinto,. otiov, T. Kim 6 KvB Institute of Technoogy, oth ydney, 060 aane Coege, The Univesity of ew outh aes, 46, Austaia, e-mai: tony@kvb.edu.au Pof. Asen Zataov Univesity, Bougas-8000, Bugaia, e-mai: esotiova@btu.bg 3 CLBME - Bugaian Academy of ciences, Acad. G. Bonchev t., B. 0, ofia-3, Bugaia, e-mai: kat@bas.bg 4 ystems Reseach Institute -- Poish Academy of ciences yzsza zkoa Infomatyki tosowanej i Zazadzania, asaw, Po, e-mai: kawczak@ibs.pan.waw.p CETAV - Univesity of Tas-os-Montes e Ato Douo, Ap. 04, 00-9 Via Rea, Potuga, e-mai: pmeo@utad.pt 6 Institute of cience Education, Kongju ationa Univesity, Kongju 34-70,. Koea, e-mais: taekyun64@hotmai.com. Intoduction The pecise distibution of the ode of the univesity subjects is vey impotant fo the quaity of the taining pocess. Usuay, deveopment of a new taining pan even changes in aeady existing pans cost a ot of time esouces. The pocess takes into consideation diffeent conditions estictions. tudents undetake a ange of vaious discipines coesponding to thei univesity speciaty. In the couse of thei education they ae to be tained as on the espective subjects, as we as given pemises fo futue taining subjects, based of the ent ones. The couses ae sticty connected in an ode that ony makes thei eaning effective. In the pesent pape we constuct a G epesenting the pocess of ogica odeing of the study subjects, accounting on the needs of the students univesity taining. Let us assume that students be tained ove w univesity discipines D, D,., D w. Let discipine D t be epesented by token α t (t,,, w) et it have as paametes:. a ist of pevious discipines (that shoud have been taught befoe the ent one),. duation H D t of the taining pocess ove discipine D t. 3. a ist of modues that D t contains. Each modue is chaacteized by a topic duation (i.e., numbe of ection hous).

2 Let taining at the univesity be done ove q in numbe speciaties,,., q. scpeciaity is intepeted in the G by token β ( =,,, q). The foowing conditions shoud be consideed in the couse of taining in speciaty.. The education takes semestes;. k in numbe discipines ae being taught: D, D,., D k, k w; 3. In the couse of education in speciaty thee have to be undetaken no ess than min max H hous no moe than H.. G mode A definitions eated to the concept of Geneaized nets (G) ae taken fom []. The G, epesenting the pocess of odeing of univesity subjects is shown on Fig.. Initiay, the G consist the foowing tokens: - w in numbe α t -token (in pace ) whit initia ent chaacteistic t x α 0 = D t; ist of pevious discipines; H D t ; ist of modues, t =,,, w; - q in numbe β-token (in pace 3 ) whit initia ent chaacteistic x β 0 = min max ; ; H ; H ; ist of discipines, =,,, q. α- β-tokens wi be at thei paces duing the whoe time of G functioning. hie they may spit into two o moe tokens, the oigina one of those wi aways emain at its pace. Beow, we sha omit these chaacteistics in desciptions of the sepaate tansitions. Token δ with initia chaacteistic t x δ 0 = the name of the speciaty fo which the discipines wi be odeed entes pace. Z Z 4 Z 4 Z Z Fig.. The G mode Geneaized net is pesented by a set of tansitions: 6

3 А= {Z, Z, Z 3, Z 4, Z }, whee tansitions descibe the foowing pocesses: Z Z detemining of the paametes of speciaty ( =,,, q) its paametes. Z 3 Z 4 detemining of the discipines fo the espective speciaty thei paametes. Z ode of the discipines in the semestes. Tansitions of G-mode have the foowing fom. Eveywhee is the speciaty s numbe ( =,,, q); t is the discipine s numbe (t =,,, w). Z =<{, 3 }, {, 3 }, R, (, 3 ) >, whee 3, = peciaty is detemined. R = 3 fase 3, 3, whee Tokens that ente pace obtain chaacteistic min max x = ; ; H ; H ; ist of discipines. β Z =<{, 7 }, { 4,, 6, 7 }, R, (, 7 ) >, R = 7 4 fase 7,4 fase 6 fase 7, 7,4 = The minimum maximum ectue hous pe semeste ae detemined. Tokens that ente paces 4, 6 obtain chaacteistic espectivey: H β min x =, Fo each semeste C, C,..., C β x = H max β x = p 3 x β. of the taining ove speciaty, thee must be H min H max povided at east [ ] ectue hous no moe than [ ] + ectue hous, whee [x] is the intege pat of ea positive numbe x. The token that entes pace 7 does not obtain a new chaacteistic. 7

4 whee Z 3 =<{ 6, }, { 8, 9, 0, }, R 3, ( 6, ) >, R 3 = 6 8 fase,8 8 9 fase,9 0 fase,0,,8 = Thee ae discipines which need no pemise discipines to be taught ;,9 = Detemined ae the discipines, whose pemise discipines have aeady been odeed ;,8 = Detemined ae the discipines that ae dependant on one anothe. The tokens that ente in paces 8, 9 0 obtain chaacteistic espectivey: α t x = D D D,,..., v, α t x = D v+, Dv+,..., D v + u α t x = D v+ u+, Dv+ u+,..., Dv+ u+ z, whee: v numbe of discipines that do not have pevious ones, u numbe of discipines whose pemise discipines have aeady been odeed, z numbe of discipines, dependant on one anothe. whee The token that entes pace (fom pace 6 ) does not obtain a new chaacteistic. Z 4 =<{ 0, 3 }, {, 3 }, R 4, ( 0, 3 ) >, R 4 = 0 3 fase 3, 3, 3, = The discipines, dependant on one anothe, ae divided into goups. The token that entes paces obtains chaacteistic ist: goup, discipines. Discipines fom one the same goup have to be eant in paae in one the same semeste. whee Z =<{ 4,, 8, 9,, }, { 4, }, R, ( ( 4,, 8, 9, ), )>, R = fase fase fase fase fase,4,,4 = The discipines, dependant on one anothe, ae divided into goups.

5 The token that entes pace 4 does not obtain new chaacteistic. The token that entes pace obtains chaacteistic speciaty : semeste C discipines. semeste C discipines semeste C discipines Consion The G-mode is a next step of the authos eseach in the aea of univesity activities modeing (see []). It can be extended with subnets epesenting the pocesses of taining. Refeences: [] Atanassov, K., Geneaized nets, od cientific, ingapoe, ew Jesey, London 99. [] hannon, A., D. Langova-Oozova, E. otiova, I. Petounias, K. Atanassov, M. Kawczak, P. Meo-Pinto, T. Kim. Geneaized et Modeing of Univesity Pocesses. KvB Visua Concepts Pty Ltd, Monogaph o. 7, ydney, 00. 9