be two interval-valued intuitionistic fuzzy numbers, then the Hamming distance between a is defined as follows: (5)

Transcription

1 IOSR Joural of Deal ad Medical Scieces (IOSR-JDMS) e-issn: , -ISSN: Volue 3, Issue 8 Ver. II (ug. 04), PP iosrourals.org Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies Perforace Evaluaio i Our Coury ih Ierval Iuiioisic Fuzzy Iforaio Poovarasa.V ad Kaviyarasu.M ssisa Professor, Deare of Maheaics,Sri VidyaMadir rs & Sciece College, Uhagarai, Tail Nadu, Idia, bsrac: I his aer, e ivesigae he ulile aribue decisio aig (MDM) roblesfor evaluaig he archives ebsies erforace ih ierval iuiioisic fuzzy iforaio.the,based o he TOPSIS ehod, calculaio ses for solvig MDM robles for evaluaig hearchives ebsies erforace ih ierval iuiioisic fuzzy iforaio are give. The eighedhaig disaces roery ha leads o have he eigh haig disaces he relaive closeess degree o he osiive ideal soluio is calculaed o ra all aleraives ad o for os desirable archives ebsie: Keyords:Mulile ribue Decisio-aig (MGM), Ierval Iuiioisic Fuzzy Iforaio, The Cosrucio of rchives Websies, Perforace Evaluaio, Sesiiviy aalysis, TOPSIS echique. I. Iroducio Sice he begiig of he 980s, iforaio Neor of govere affairs has bee oeed i successio i he ay couries. Sudyig o he ebsies erforace evaluaio of govere affairs have bee he ho oic i acadeic circle a hoe ad abroad. Wih he govere iforaio becoig io he oe, he cosrucio of archives ebsies as brough forard. Hoever, e us fid a fe sudy of archives ebsies erforace araisal i our coury. The sudy of archives ebsies erforace evaluaio i "araised ha", "ho o araise" has o fored he uified udersadig ad blidess ad soaeiy coexis i he rocess of oeraig, hich hold bac archives ebsies erforace evaluaio i our coury. Ho o aes usice, fairly ad ubliciy araisal of he cosrucio of archives ebsies, ad guides he cosrucio of archives ebsies o he correc direcio is a quesio ha archives deare is osiively discussig ad hiig. Based o his, he aricle horoughly aalyzes he quesios of archives ebsies erforace evaluaio i our coury ad suarizes he core facors of he cosrucio of archives ebsies[]. The roble of evaluaig archives ebsies erforace ih ierval iuiioisic fuzzy iforaio is he ulile aribue decisio aig (MDM) robles[-5].the ai of his aer is o ivesigae he MDM robles for evaluaig he archives ebsies erforace ih ierval iuiioisic fuzzy iforaio. The, e uilize he ierval iuiioisic raezoidal fuzzy eighed averagig (IITFW) oeraor o aggregae he ierval iuiioisic raezoidal fuzzy iforaio corresodig o each aleraive ad ge he overall value of he aleraives, he ra he aleraives ad selec he os desirable oe(s). Fially, a illusraive exale is give. II. Preliiaries I he folloig, e shall iroduce soe basic coces relaed o iuiioisic raezoidal fuzzy ubers ad ierval iuiioisic raezoidal fuzzy ubers. Defiiio. Le X be a uiverse of discourse, he a fuzzy se is defied as: ={(x,µ (x))/xϵx} Which is characerized by a ebershi fucio µ :X [0,], here µ (x) deoes he degree of ebershi of he elee xo he se [6]. aassov[7, 8] exeded he fuzzy se o he IFS, sho as follos: Defiiio. IFS i X is give by ={(x,µ (x),v (x))/xϵ X} () Where µ :X [0,] ad v (x): X [0,] ih he codiio 0 µ(x)+v (x) xϵx The ubers µ (x) ad v (x) rerese, resecively, he ebershi degree ad o- ebershi degree of he elee o he se [7, 8]. Defiiio 3. For each IFS i X, if π ( x)=- µ (x)- v (x), x ϵx (3) The π ( x) is called he degree of ideeriacy of xo [7, 8]. Defiiio4. Le X be a uiverse of discourse, IVIFS over X is a obec havig he for [9-0]:.iosrourals.org 89 Page

2 Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies. x, ( x), v ( x) / x X (4) Where ( x ) [ 0,] ad v ( x ) [0,] are ierval ubers, ad 0 su( ( x) )+su v ( x )), xϵ X For coveiece, le ( x) =[a, b], v ( x ) =[c,d], so ([ a, b],[ c, d]) Defiiio 5.Lea ([ a, b ],[ c, d]) ad a ([ a, b],[ c, d]) be o ierval-valued iuiioisic fuzzy ubers, he he Haig disace beee a ([ a, b ],[ c, d]) ad a ([ a, b ],[ c, d]) is defied as follos: a a b b c c d d d( a, a) (5) III. roach o rchives Websies Perforace Evaluaio i Our Coury ih Ierval Iuiioisic Fuzzy Iforaio The folloig assuios or oaios are used o rerese he MDM robles for evaluaig archives ebsies erforace ih ierval iuiioisic fuzzy iforaio. Le ={,,, M } be a discree se of aleraives. Le G={ G, G,,G } be a se of aribues. The iforaio abou aribue eighs is coleely o. Le ={,,, } be he eigh vecor of aribues, here 0. Suose ha R ( r i ) ([ ai, bi ],[ ci, di ]) is he ierval iuiioisic fuzzy decisio arix, here,[a i,b i ] idicaes he degree ha he aleraive i saisfies he aribue G give by he decisio aer,,[c i,d i ] idicaes he degree ha he aleraive i does saisfy he aribue G give by he decisio aer,[ a, b ] [0,],[ c, d ] [0,], b d, i,,...,,,,...,.. I he folloig, e i i i i i i aly he TOPSIS ehod o MDM robles for evaluaig he archives ebsies erforace ih ierval iuiioisic fuzzy iforaio. The ehod ivolves he folloig ses: Se. Deerie he osiive ideal ad egaive ideal soluio based o ierval-valued iuiioisic fuzzy iforaio. r a b, c d, a b c d,..., a b c d (6) r a b, c d, a b c d,..., a b c d (7) here a b, c d ax ai, ax bi, i ci, i di i i i i a b, c d ax ai,ax bi, i ci,i di,...,. i i i i Se. Calculae he eighed haig disaces. The eighed haig disaces of each aleraive fro he ideal soluio is give as,, d r r d r r i ai a bi b ci c di d l, i,,... Siilarly, he eighed haig disaces fro he egaive ideal soluio is give as,, d r r d r r i ai a bi b ci c di d l, i,,... The basic ricile of he TOPSIS ehod is ha he chose aleraive should have he shores disace fro he osiive ideal soluio ad he farhes disace fro he egaive ideal soluio. (9) (8).iosrourals.org 90 Page

3 Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies. Obviously, for he eigh vecor give, he saller d r, r ad he larger d r, r, he beer aleraive i. Se 3. Calculae he relaive closeess o he ideal soluio. The relaive closeess of he aleraive i ih resec o r d is defie as ri, r c ri, r, i,,...,. (0) d r, r d r, r i i Se 4. Ra all he aleraives i (i=,,.)ad selec he bes oe(s) i accordace ih (i=,,.). c r, r IV. Develoig a Ne Mehod for Sesiiviy alysis of MDM Probles Earlier researches o he sesiiviy aalysis of MDM robles ofe focused o deeriig he os sesiive aribue. They also focused o fidig he leas value of he chage. Hoever, a e ehod for sesiiviy aalysis of MDM robles is cosidered i his aricle ha calculaes he chagig i he fial score of aleraives he a chage occurs i he eigh of oe aribue. 4.. The effec of chage i he eigh of oe aribue o he eigh of oher aribues The vecor for eighs of aribues is W,,..., herei eighs are oralized ih a su of, ha is: () Wih hese assuios, if he eigh of oe aribue chages, he he eigh of oher aribues chage accordigly, ad he e vecor of eighs rasfored io W,,..., The ex heore deics chages i he eigh of aribues. Theore 4... I he MDM odel, if he eigh of he P h aribue, chages by aribues chage by, here:. ;,,...,, Proof: If he e eigh of he aribue is The, he e eigh of he oher aribues ould chage as ;,,...,, d because he su of eighs us be he: 0 ad he e eigh of he P h aribue chages as: (5) Therefore: Where:. ;,,...,, Sice:. (8) Mai resul. I a MDM roble, if he eigh of he P h aribue chages fro The, he eigh of oher aribues ould chage as:, he he eigh of oher (6) o as: (9) () (3) (4) (7) i.iosrourals.org 9 Page

4 Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies...,,...,, (0),,...,, Sice, for e have:.. ().. ;,,...,, W The, e vecor for eighs of aribues ould be,,...,, ha is:.,,,..., if,,...,, if The su of e eighs of aribues ha are obaied i (3) is,because:. Theore 4.. I he MDM odel of TOPSIS, if he eigh of he P h aribue chages by i,,..., score of he is aleraive, ould chage as belo: d ri, r c ri, r, i,,..., (6) d r, r d r, r Where d ri, r, d ri, r i i,, d r r d r r,,, are calculaed as follo: i d r r d r r ai a bi b ci c di d, i,,... i (3) (4) () (5), he he fial (8) ai a bi b ci c di d, i,,... The values d ri, r, d ri, r i equaios (7), (8) are calculaed by heir older values d ri, r, d ri, r, he value of chage i he eigh of he P h aribue,, ad oher available iforaio i (7).iosrourals.org 9 Page

5 Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies. he odel. These equaios ca be used i he sofare ha use TOPSIS echique for solvig MDM robles o obai e resuls i ligh of chage i he eigh of oe aribue. V. Nuerical exale Le us suose here is a ivese coay, hich as o ives a su of oey for archives ebsies cosrucio. There is a ael ih five ossible archives ebsies ( i =,,,5) o ives he oey. I order o evaluae archives ebsies erforace of five archives ebsies, he ivese coay us ae a decisio accordig o he folloig four aribues: () G is he eor ifrasrucure (The eor ifrasrucure is alicaio syse, icludig he suor lafor ih he ebsie file eor ifrasrucure sadard, eor srucure, ouer e, irae); () G is he hardare eviroe(hardare eviroe is archives faciliy, icludig he ai hard equie ad hardare aieace rocedures); (3) G 3 is he sofare eviroe(sofare eviroe ebsie file is he effecive oeraio of he guaraee, icludig he oeraig syse, daabase syse, eor aagee syse ad he busiess sofare); (4) G 4 is he oeraios aagee(oeraios aagee refers o he rocess of oeraio ebsie file i he ileeaio of he aagee, aily icludig rocess aagee, securiy syse aagee, busiess oeraio aagee, ersoel aagee ad syse aagee). The five ossible archives ebsies( i =,,,5)are o be evaluaed usig he ierval iuiioisic fuzzy iforaio by he decisio aer uder he above four aribues hose eighig vecor =(0.800,0.900,0.3300,0.000) T, as lised i G G G3 G4 he folloig arix: 0.3,0.6, 0., ,0.7, 0.,0.3 0.,0.5, 0.3, ,0.5, 0.,0. 0.4,0.8, 0.,0. 0.5,0.8, 0.,0. 0.,0.7, 0., ,0.6, 0.,0.4 R 3 0.,0.6, 0.,0.3 0.,0.4, 0.,0.5 0.,0.6, 0.3,0.4 0.,0.4, ,0.4, 0.3, ,0.7, 0.,0. 0.3,0.6, 0., ,0.6, 0., ,0.5, 0.3, ,0.6, 0., , 0., ,0.6, 0.3,0.4 The, e uilize he aroach develoed o evaluae archives ebsies erforace of five archives ebsies. Case: Se. Deerie he osiive ideal archives ebsie ad egaive ideal archives ebsies r [ 0.4,0.8], [0.,0.], [0.5,0.8],[0.,0. ], [0.4,0.7],[0.,0.3], [0.5,0.6], [ 0.,0.] r 0.,0.4, 0.3,0.6, 0.,0.4, 0.,0.5, 0.,0.5, 0.3,0.4, 0.,0.4, 0.3,0.5 Se:. Calculae he eighed haig disaces of each archives ebsie fro he osiive ideal archives ebsies ad egaive ideal archives ebsie by uilizig he eigh vecor, resecively. d r, r 0.635, d r, r , d r, r , d r, r , d r, r d r, r 0.85, d r, r 0.49, d r, r 0.4, d r, r 0., d r, r 0.35 Se:3Calculae he relaive closeess o he osiive ideal archives ebsie c r, r 0.596, c r, r 0.894, c r, r 0.438, c r, r 0.40, c r, r Se: 4. Ra all he archives ebsies i (i=,,3,4,5) i accordace ih he relaive closeess c r, r (i=,,3,4,5): > 5 > > 4 > 3 ad hus he os desirable archives ebsie is. Case: Se: No e assue ha he eigh of he 4 h aribue icreased by ad be The by equaio (3), he eigh of oher aribues chage as (9): 4. ;,,3 4 (0., 0.45, 0.475, ). (9) Se: Calculae he eighed haig disaces of each archives ebsie fro he osiive ideal archives ebsies ad egaive ideal archives ebsie by uilizig he e eigh vecor, resecively. d r, r 0.076, d r, r 0.37, d r, r , d r, r 0.674, d r, r d r, r 0.36, d r, r , d r, r 0.099, d r, r 0.665, d r, r i.iosrourals.org 93 Page

6 Sesiiviy alysis of TOPSIS Techique: roach o rchives Websies. Se:3Calculae he relaive closeess o he osiive ideal archives ebsie c r, r 0.60, c r, r 0.743, c r, r 0.74, c r, r 0.499, c r, r Se:4 Ra all he archives ebsies i (i=,,3,4,5) i accordace ih he relaive closeess (i=,,3,4,5): > > 5 > 4 > 3 ad hus he os desirable archives ebsie is. c r, r VI. Coclusio I his aer, a ovel of he ulile aribues decisio aig (MDM) robles for evaluaig he archives ebsies erforace ih ierval iuiioisic fuzzy iforaio.the, based o he TOPSIS ehod, calculaio ses for solvig MDM robles for evaluaig he archives ebsies erforace ih ierval iuiioisic fuzzy iforaio are give. The eighed Haig disaces roery ha leads o have he eigh haig disaces he relaive closeess degree o he osiive ideal soluio is calculaed o ra all aleraives ad o for os desirable archives ebsie: Refereces []. Ch. Zhag, Sudy o he quesios of archives ebsies erforace evaluaio i our coury, Xiaga Uiversiy, 006. []. X.H. Wag, "Model for Touris Maagee ih -ule Liguisic Iforaio", ISS : dvaces i Iforaio Scieces ad Service Scieces, Vol. 3, No. 4, , 0. [3]. X.F. Li, D. Li, "TOPSIS Mehod for Chiese College Teacher Perforace raisal Syse ih Ucerai Iforaio", ISS: dvaces i Iforaio Scieces ad Service Scieces, Vol. 3, No. 6, , 0. [4]. G.W. Wei, H. Ta, "IFLOWHM Oeraor ad is licaio o Mulile ribue Grou Decisio Maig", JCIT: Joural of Covergece Iforaio Techology, Vol. 6, No. 7, , 0. [5]. P.D. Liu, Y. Su, The exeded TOPSIS based o raezoid fuzzy liguisic variables, Joural of Covergece Iforaio Techology, vol. 5, o. 4,.38-53, 00. [6]. H. Ta, G.W. Wei, "OWCLCO Oeraor ad is licaio o Corehesive Evaluaig Modelig of Brad Exesio i Ucerai Liguisic Seig", JCIT: Joural of Covergece Iforaio Techology, Vol. 6, No. 7, , 0. [7]. G. W. Wei, Soe iduced geoeric aggregaio oeraors ih iuiioisic fuzzy iforaio ad heir alicaio o grou decisio aig, lied Sof Couig, vol. 0, o., , 00. [8]. Z. S. Xu ad R. R. Yager, Soe geoeric aggregaio oeraors based o iuiioisic fuzzy ses, Ieraioal Joural of Geeral Syse, vol.35, o.6, , 006. [9]. Z. S. Xu, Iuiioisic fuzzy aggregaio oeraors, IEEE Trasaios o Fuzzy Syses, vol.5, o.6,.79-87, [0]. Z. S. Xu, Models for ulile aribue decisio-aig ih iuiioisic fuzzy iforaio, Ieraioal Joural of Uceraiy, Fuzziess ad Koledge-Based Syses vol.5, o.3,.85-97, 007. []. G.W. Wei, FIOWHM oeraor ad is alicaio o ulile aribue grou decisio aig, Exer Syses ih licaios, vol. 38, o. 4, , 0. []. D.F. Li, Muliaribue decisio aig odels ad ehods usig iuiioisic fuzzy ses, Joural of Couer ad Syse Scieces, vol.70, o.3,.73-85, 005. [3]. G. W. Wei, Soe geoeric aggregaio fucios ad heir alicaio o dyaic ulile aribue decisio aig i iuiioisic fuzzy seig, Ieraioal Joural of Uceraiy, Fuzziess ad Koledge-Based Syses, vol. 7, o., , 009. [4]. G.W. Wei, ehod for ulile aribue grou decisio aig based o he ET-WG ad ET- OWG oeraors ih -ule liguisic iforaio, Exer Syses ih licaios, vol. 37, o., , 00. [5]. K. aassov, More o iuiioisic fuzzy ses, Fuzzy Ses ad Syses, vol.33, o.5,.37-46, 989. [6]. K. aassov ad G. Gargov, Ierval-valued iuiioisic fuzzy ses, Fuzzy Ses ad Syses, vol. 3, o.7, , 989. [7]. K. aassov, Oeraors over ierval-valued iuiioisic fuzzy ses, Fuzzy Ses ad Syses, vol.64, o., , 994. [8]. H. Barro, C. P. Schid, Sesiiviy alysis of addiive uli aribues values odels. Oeraios Research, 46, -7, 00. [9].. Eshlaghy, N. R. Paydar, K. Joda, N.R. Paydar, Sesiiviy aalysis for crieria values i decisio aig arix of SW ehod. Ieraioal Joural of Idusrial Maheaics,, 69-75, 009. [0]. E. S. Soofi, Geeralized eroy based eigh for uli aribue value odels. Oeraios Research, 38, , 990. i.iosrourals.org 94 Page