Mathematical and Computational Applications, Vol. 20, No. 3, pp ,

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1 Matheatcal ad oputatoal pplcatos Vol. No. pp MULTIPLE TTRIBUTE DEISION-MKING MODEL OF GREY TRGET BSED ON POSITIVE ND NEGTIVE BULL S-EYE Sha Fu Departet of Iforato Maageet Hua Uversty of Face ad Ecoocs People's Republc of ha bstract- g at coplety ad ucertaty of actual decso-akg evroet ths study proposes a ultple attrbute decso-akg odel of grey target based o postve ad egatve bull s-eye. Frstly t defes that the optal effect vector ad the orst effect vector of grey target decso are respectvely postve egatve bull s-eye of the grey target; secodly coprehesvely cosderg the space proecto dstace betee varous schees ad the postve ad egatve bull s-eye t takes bull s-eye dstace as the bass for space aalyss ad obtas a e tegrated bull s-eye dstace; the accordace th the coprehesve gudeles to e the bull s-eye dstace t costructs goal prograg odel for goal fucto ad thus solves the de eght. Fally through case studes of selectve purchase of forato syste t verfes feasblty ad effectveess of the proposed grey target decso-akg odel. Keyords- postve ad egatve bull s-eye terval grey uber grey target decso-akg tegrated bull s-eye dstace goal prograg. INTRODUTION Grey target decso-akg as a portat part of grey decso-akg ethod has bee dely appled ay felds. coprehesve reve of lterature at hoe ad abroad reveals that ay eperts ad scholars have actvely volved such research ad have ade soe acheveets. For eaple: Eshlaghy ad Ra preseted a tegrated fraeork for proect selecto ad proect aageet approach usg grey-based k-eas ad geetc algorths. The proposed approach of ths study frst cluster dfferet proects based o k-eas algorth ad the raks R&D proects by grey relatoal aalyss odel. Wlla Ho et al. proposed the lterature of the ult-crtera decso akg approaches for suppler evaluato ad selecto. Ths study ot oly provdes evdece that the ult-crtera decso akg approaches are better tha the tradtoal cost-based approach but also ads the researchers ad decso akers applyg the approaches effectvely Mohse et al.. Wa-Yh Wu et al. 6 preseted a alteratve evaluato procedure to help retalers especally hyper arketers ake a locato decso by usg the grey ult-obectve decso ethod. Lu et al. proposed a ovel ult-attrbute grey target decso odel ad deostrated th a practcal case study. Da ad L

2 9 Multple ttrbute Decso-Makg Model Of Grey Target targetg at a class of group decso-akg probles th property value attrbute eght ad polcyaker eghts as terval grey uber troduced cocept of group postve ad egatve bull s-eye ad group devato approachg degree ad proposed group decso-akg ethod for grey ultple attrbute devato approachg degree. he ad Xe 7 studed copatblty proble of tradtoal grey target polarty reversal ad proved probablty of estece ad occurrece of copatblty proble by costructg a specal sequece of oderate value dcator. Wag et al. 9 cosdered the pact of the correlato betee the varous dcators dfferet desos ad dffereces portace o the effect of decso-akg proved tradtoal grey target decso-akg ethod th eghted Mahalaobs dstace ad avoded the pact of the correlato betee the varous dcators dfferet desos ad dffereces portace o the effect of decso-akg as ell as copatblty proble of grey target trasforato. Ma ad Su targetg at estg research results ultple attrbute grey target decso-akg eteded the postve bull s-eye decded by polcyakers deal preferece ad choce preferece de values of certa attrbutes to egatve bull s-eye aalyed dfferet attrbute value preferece s pact o the decso-akg schee dcator ad dealt th polcyakers preferece th geeraled ethod of grey target decso-akg. Fageg ad Zhag 6 costructed a operator reardg good ad pushg bad hch elarges degree of dcator dfferece at udesoalato trasforato of dcators ad establshed eghted grey target decso-akg odel o ths bass. The above studes provde soe deas to solve grey target decso-akg ssues. Hoever t ca also be see that research o grey target decso-akg ssues th decso-akg forato as terval grey uber ad ucerta de eght s relatvely sall. Thus ths paper proposes the correspodg grey target decso-akg odel to eet the eeds of such decso-akg.. MULTIPLE TTRIBUTE DEISION-MKING MODEL OF GREY TRGET. Descrpto of the Proble Suppose ultple attrbute decso-akg proble costtutes aatg decso-akg schee set } th prepared schees evaluato { dees attrbute costtute attrbute set { } schee s attrbute value agast de s [ hch ; ;. The effect saple atr X of schee set agast property set s:

3 S. Fu 9 The above atr ca be coverted to: [ [ [ [ [ [ [ [ [. Dstace ad Possblty Degree Forula of Iterval Grey Nubers I the grey systes theory the uber th oly lkely rage ko but ot the eact value s called grey uber. Grey uber s the basc ut of grey systes. Grey uber th both loer boud a ad upper boud a s called terval grey uber deoted by a [ a a B Zeg et al.. Defto : Suppose to terval grey ubers a [ a a ad b [ b b k s a postve real uber the: a b [ a b a b ; a b [{ ab ab ab ab} a{ ab ab ab ab} ; ka [ ka ka ; k a [ k a k a. Defto : Suppose to terval grey ubers a [ a a ad b [ b b the the dstace betee terval grey uber a ad b s Sog et al. : L a b [ a b a b Defto : For terval grey uber a [ a a ad b [ b b

4 9 Multple ttrbute Decso-Makg Model Of Grey Target deote l a a a b b the l b p { l l a a b} l l a b a b s possblty degree of a b. a b. Establshet of Multple ttrbute Decso-Makg Model of Grey Target.. Noraled Process of Decso Matr I order to elate the effect of ter-property o decso-akg result due to dfferet desos the follog forula ca be adopted to orale the decso atr ad obta oraled decso atr. I ultple attrbute decso-akg probles the coo attrbute types are effcecy odel ad cost odel. For effcecy attrbute the bgger value the better; but cost attrbute s opposte. Suppose I respectvely deotes subscrpt set of effcecy cost type. For the effcecy attrbute: Where ; I For cost attrbute: / / / / Where ; I.. Grey Target Decso-Makg of Postve ad Negatve Bull s-eye Defto : Suppose a{ / } { } ad deote ts correspodg decso value as [ the { } {[ [ [ } s optal effect vector of grey target decso-akg ko as postve bull s-eye Luo ad Wag. Defto : Suppose { / } { } ad deote

5 S. Fu 9 ts correspodg decso value as [ the } [ [ {[ } { 6 s orst effect vector of grey target decso-akg ko as egatve bull s-eye. Where de eght ad. Defto 6: Refer to [ 7 s postve bull s-eye dstace of effect vector. Refer to [ 8 s egatve bull s-eye dstace of effect vector. Defto 7: Refer to [ 9 s postve ad egatve bull s-eye dstace. ccordg to defto lterature Luo dstace fall o the sae le or for a tragle. ccordg to the la of coses t ca be ko that cos Sce the postve bull s-eye dstace ad egatve bull s-eye dstace are vectors cosder proecto of bull s-eye dstace o the le betee the postve ad egatve bull s-eye the the tegrated bull s-eye dstace s: cos Itegrated bull s-eye dstace coprehesvely cosders the postve ad egatve bull s-eye ad uses the bull s-eye dstace as a vector for ore scetfc ad ratoal decso-akg forato... Deterato of Ide Weght If the de eght sequece s uko the the sequece

6 9 Multple ttrbute Decso-Makg Model Of Grey Target s a sequece of grey cootato ad grey etropy ca be defed as: H l ccordg to the prcple of au etropy should be adusted to reduce the ucertaty of sequece aely to proote aato of H. t the sae te adust the eght so that the overall tegrated bull s-eye dstace s al. For ths ed a ult-obectve optato odel as follos could be establshed: a H l s. t. To solve the ult-obectve optato odel based o far copetto of varous schees the above ult-obectve optato odel ca be coverted to a sgle-obectve optato odel. s. t. l Where. Takg to accout far copetto of opted obectve fucto. s geerally preferable. Solve the odel by Vsual ++ prograg ethod obta the de eght sequece substtute t to forula 8 ad obta tegrated bull s-eye dstace Sahu et al.. ccordg to the se of ore ecellet the correspodg schee s. value sort the alteratve schee. The saller s the

7 S. Fu 9. Step of Multple ttrbute Grey Target Decso-Makg I suary specfc steps of ultple attrbute grey target decso-akg based o postve ad egatve bull s-eye are as follos: Step Use equato ad for oraled process of decso atr X ad obta oraled decso atr Z; Step Use equato ad 6 to respectvely detere the postve ad egatve bull s-eye of grey target decso-akg; Step Use equato 7 ad 8 to respectvely detere the postve ad egatve bull s-eye dstace of effect vector ; Step Solve the sgle obectve optato odel sho equato th softare prograg ethod ad obta de eght sequece ; Step Use equato to detere tegrated bull s-eye dstace ad sort the varous alteratve schees accordg to the se of value.. PPLITION EXMPLE Prove applcato of the aforeetoed ultple attrbute decso-akg ethod th decso attrbute value as terval grey uber ad ucerta attrbute eght forato syste selecto proble by ay of eaple. eterprse plas fve alteratve forato syste selectve purchase schees accordg to the eed of forato costructo. There are three a evaluato dees attrbutes. Where represets product perforace represets after-sale servce represets product prce. Eperts evaluate the fve alteratve schees ad orgaed data s sho Table. Try to detere the optal forato syste that polcyakers should select. Table. Decso Matr X [ [8.8.9 [ [8.8.9 [7.8.7 [ [ [8.89. [ [8.8. [7 8 [6 [9 [8 9 [ For the above attrbutes are effcecy attrbutes s cost attrbute.

8 96 Multple ttrbute Decso-Makg Model Of Grey Target Weght forato of each attrbute s ko:. Uder coplete certa forato eght rage of each attrbute s: ; ad. Step Use equato ad for oraled process of decso atr X ad obta oraled decso atr Z as sho Table ; Table. Noraled Decso Matr Z [.7.76 [..7 [.9. [..9 [..6 [.. [.98. [.8.6 [.8.9 [..8 [.68.8 [.8. [..6 [.. [.9. Step Use equato ad 6 to respectvely calculate the postve ad egatve bull s-eye of grey target decso-akg. + = { [..7 [.8.6 [.68.8 } - = { [.7.76 [.98. [.8. } Step Use equato 7 ad 8 to respectvely detere the postve ad egatve bull s-eye dstace of effect vector ; The postve bull s-eye dstace: [.87.8 [.7. [.9 [.7.. [...8 The egatve bull s-eye dstace: [.6 [.87.

9 S. Fu 97 [ [..8.9 [... Space betee postve ad egatve bull s-eye: [ Step Solve the sgle obectve optato odel detered by equato th softare prograg ad obta de eght Step Use equato to detere tegrated bull s-eye dstace ad sort the varous alteratve schees accordg to the se of value Thus. So sortg results of the varous schees are as follos:. Through coputatoal aalyss the result obtaed ths study s cosstet th lterature Su ad Zhag hch proves feasblty ad effectveess of the ethod. reve of specfc steps ad processes reveals that copared to ethod proposed lterature of the sae type the ethod s ore practcal ad reasoable.. ONLUSION Grey target decso-akg s oe portat ay to solve ultple attrbute decso-akg probles. Ths study costructs a ultple attrbute grey target decso-akg odel based o postve ad egatve bull s-eye ad troduces the cocepts of postve ad egatve bull s eye ad postve ad egatve bull s eye dstace of grey target. Based o ths t cobes spatal aalyss ad proposes calculato ethod of tegrated bull s-eye dstace ad sorts the pros ad cos of each schee by the se of tegrated bull s-eye dstace. It provdes a scetfc practcal decso-akg ethod to solve grey target decso-akg proble th decso-akg forato as terval grey uber ad verfes feasblty ad effectveess of the costructed odel by eaple aalyss.

10 98 Multple ttrbute Decso-Makg Model Of Grey Target. KNOWLEDGEMENTS Ths study as supported by the Scetfc Research Fud of Hua Provcal Educato Departet No. 8 by the Hua Provce Phlosophy ad Socal Scece Foudato No. YB6 ad also supported by Hua Provce Scece ad Techology Progra Proect No. GK. Supported by the costruct progra of the key dscple Hua provce. 6. REFERENES.. T. Eshlaghy F. F. Ra hybrd grey-based k-eas ad geetc algorth for proect selecto Iteratoal Joural of Busess Iforato Systes W. Ho X. Xu P. K. Dey Mult-crtera decso akg approaches for suppler evaluato ad selecto: lterature reve Europea Joural of Operatoal Research 6.. M. J. Soghor M. Tavaa. adeh M. H. Khakba suppler selecto ad order allocato odel th ultple trasportato alteratves The Iteratoal Joural of dvaced Maufacturg Techology W. Wu. Ba O. K. Gupta hyperarket ste selecto odel usg the grey ult-obectve decso ethod Iteratoal Joural of Logstcs Systes ad Maageet S. Lu B. Xu J. Forrest Y. he O Ufor Effect Measure Fuctos ad a Weghted Mult-attrbute Grey Target Decso Model The Joural of Grey Syste D. We-Zha L. Ju-Lag Off-target devato degree ethod for grey ult-attrbute group decso-akg Systes Egeerg Theory & Practce Yog-Mg X. Ha-Yg. Test of the cosstecy proble o Deg's grey trasforato by sulato Systes Egeerg ad Electrocs Z.X Wag Y.G Dag H. Yag Iproveets o decso ethod of grey target Systes Egeerg ad Electrocs M. Jsha S. Jg Grey Target Decso Method for Postve ad Negatve Target eters Based o Decso Maker s Prefereces Scece ad Techology Maageet Research J. Fag H. Zhag Grey target odel apprasg fr's facal status based o lta coeffcets The Joural of Grey Syste B Zeg S. F. Lu L J. M. he Grey target decso akg odel of terval grey uber based o cobeb area Systes Egeerg ad Electrocs

11 S. Fu S. Je D. Yao-Guo W. Zheg-X Z. Ke Ne decso odel of grey target th both the postve clout ad the egatve clout Systes Egeerg Theory & Practce D. Luo X. Wag The ult-attrbute grey target decso ethod for attrbute value th three-paraeter terval grey uber ppled Matheatcal Modellg L. Dag Mult-obectve grey target decso odel based o postve ad egatve clouts otrol ad Decso N. K. Sahu S. Datta S. S. Mahapatra Decso akg for selectg PL servce provder usg three paraeter terval grey ubers Iteratoal Joural of Logstcs Systes ad Maageet H. Su Q. Zhag. Iterval-valued Fuy VIKOR Method Fuy Systes ad Matheatcs -8.