Hybrid Binary Logarithm Similarity Measure for MAGDM Problems under SVNS Assessments

Transcription

1 Neutosophc Sets ad Systems Vol 0 08 Uvesty of Ne Meco d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssessmets Kalya Modal Suapat amak ad bhas G 3 Depatmet of Mathematcs Jadavpu Uvesty Kolkata: West egal da E mal:kalyamathematc@gmalcom ²Depatmet of Mathematcs Nadalal Ghosh ollege apu O - Naayapu ad Dstct: Noth 4 agaas ode: 7436 West egal da Emal: sua_pat@yahooco 3 Depatmet of Mathematcs Jadavpu Uvesty Kolkata: West egal da Emal: bbhascg@adavpuuvesty bstact: Sgle valued eutosophc set s a mpotat mathematcal tool fo tacklg ucetaty scetfc ad egeeg poblems because t ca hadle stuato volvg detemacy ths eseach e toduce e smlaty measues fo sgle valued eutosophc sets based o bay logathm fucto We defe to type of bay logathm smlaty measues ad eghted bay logathm smlaty measues fo sgle valued eutosophc sets he e defe hybd bay logathm smlaty measue ad eghted hybd bay logathm smlaty measue fo sgle valued eutosophc sets We pove the basc popetes of the poposed measues he e defe a e etopy fucto fo detemg uko attbute eghts We develop a ovel mult attbute goup decso makg stategy fo sgle valued eutosophc sets based o the eghted hybd bay logathm smlaty measue We peset a llustatve eample to demostate the effectveess of the poposed stategy We coduct a sestvty aalyss of the developed stategy We also peset a compaso aalyss betee the obtaed esults fom poposed stategy ad dffeet estg stateges the lteatue Keyods: sgle valued eutosophc set; bay logathm fucto; smlaty measue; etopy fucto; deal soluto; MGDM toducto Smaadache [] toduced eutosophc sets NSs to pave the ay to deal th poblems volvg ucetaty detemacy ad cosstecy Wag et al [] gouded the cocept of sgle valued eutosophc sets SVNSs a subclass of NSs to tackle egeeg ad scetfc poblems SVNSs have bee appled to solve vaous poblems dffeet felds such as medcal poblems [3 5] decso makg poblems [6 8] coflct esoluto [9] socal poblems [0 ] egeeg poblems [- 3] mage pocessg poblems [4 6] ad so o he cocept of smlaty measue s vey sgfcat studyg almost evey pactcal feld the lteatue fe studes have addessed smlaty measues fo SNVSs [7 30] eg et al [3] developed SVNSs based mult attbute decso makg MDM stategy employg M Mult-ttbutve ode ppomato aea ompaso ad smlaty measue OSS echque fo Ode efeece by Smlaty to a deal Soluto ad a e smlaty measue Ye [3] poposed cose smlaty measue based eutosophc multple attbute decso makg MDM stategy ode to ovecome some dsadvatages the defto of cose smlaty measue Ye [33] poposed mpoved cose smlaty measues based o cose fucto sas et al [34] studed cose smlaty measue based MDM th tapezodal fuzzy eutosophc umbes amak ad Modal [35] poposed eghted fuzzy smlaty measue based o taget fucto Modal ad amak [36] poposed tutostc fuzzy smlaty measue based o taget fucto Modal ad amak [37] developed taget smlaty measue of SVNSs ad appled t to MDM Ye ad u [38] studed medcal dagoss poblem usg a SVNSs smlaty measue based o taget fucto a ad Ozguve [39] studed a MDM poblem fo adustg the popotoal-tegal-devatve D coeffcets based o eutosophc Hammg Eucldea set-theoetc Dce ad Jaccad smlaty measues Seveal studes [40 4] have bee epoted the lteatue fo mult-attbute goup decso makg MGDM eutosophc evomet Ye [43] studed the smlaty measue based o dstace fucto of SVNSs ad appled t to MGDM Ye [44] developed seveal clusteg methods usg dstace-based smlaty measues fo SVNSs Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

2 Neutosophc Sets ad Systems Vol Modal et al [45] poposed se hypebolc smlaty measue fo solvg MDM poblems Modal et al [46] also poposed taget smlaty measue to deal th MDM poblems fo teval eutosophc evomet Lu ad Ye [47] poposed logathmc smlaty measue fo teval valued fuzzy set [48] ad appled t fault dagoss stategy Reseach gap: MGDM stategy usg smlaty measue based o bay logathm fucto ude sgle valued eutosophc evomet s yet to appea Reseach questos: s t possble to defe a e smlaty measue betee sgle valued eutosophc sets usg bay logathm fucto? s t possble to defe a e etopy fucto fo sgle valued eutosophc sets fo detemg uko attbute eghts? s t possble to develop a e MGDM stategy based o the poposed smlaty measues sgle valued eutosophc evomet? he obectves of the pape: o defe bay logathm smlaty measues fo SVNS evomet ad pove the basc popetes o defe a e etopy fucto fo detemg uko eght of attbutes o develop a mult-attbute doup decso makg model based o poposed smlaty measues o peset a umecal eample fo the effcecy ad effectveess of the poposed stategy Havg motvated fom the above eseaches o eutosophc smlaty measues e toduce the cocept of bay logathm smlaty measues fo SVNS evomet he popetes of bay logathm smlaty measues ae establshed We also popose a e etopy fucto to deteme uko attbute eghts We develope a MGDM stategy usg the poposed hybd bay logathm smlaty measues he poposed smlaty measue s appled to a MGDM poblem he stuctue of the pape s as follos Secto pesets basc cocepts of NSs opeatos o NSs SVNSs ad opeatos o SVNSs Secto 3 poposes bay logathm smlaty measues ad eghted bay logathm smlaty measues hybd bay logathm smlaty measue HLSM eghted hybd bay logathm smlaty measue WHLSM SVNSs evomet Secto 4 poposes a e etopy measue to calculate uko attbute eghts ad poves basc popetes of etopy fucto Secto 5 pesets a MGDM stategy based eghted hybd bay logathm smlaty measue Secto 6 pesets a llustatve eample to demostate the applcablty ad feasblty of the poposed stateges Secto 7 pesets a sestvty aalyss fo the esults of the umecal eample Secto 8 coducts a compaatve aalyss th the othe estg stateges Secto 9 pesets the key cotbuto of the pape Secto 0 summazes the pape ad dscusses futue scope of eseach elmaes ths secto the cocepts of NSs SVNSs opeatos o NSs ad SVNSs ad bay logathm fucto ae outled Neutosophc set NS ssume that X be a uvese of dscouse he a eutosophc sets [] N ca be defed as follos: N = {< : N N N > X} Hee the fuctos ad defe espectvely the membeshp degee the detemacy degee ad the o-membeshp degee of the elemet X to the set N he thee fuctos ad satsfy the follog the codtos: : X ] 0 + [ 0 sup N + sup N + sup N 3 + o to eutosophc sets M = {< : M M M > X} ad N = {< N N N > X } the to elatos ae defed as follos: M N f ad oly f M N M N M N M = N f ad oly f M = N M = N M = N Sgle valued Neutosophc sets SVNSs ssume that X be a uvese of dscouse SVNS [] X s fomed by a tuth-membeshp fucto a detemacy membeshp fucto ad a falsty membeshp fucto o each pot X ad [0 ] o cotuous case a SVNS ca be epessed as follos: : X Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

3 4 Neutosophc Sets ad Systems Vol 0 08 o dscete case a SVNS ca be epessed as follos: : X o to SVNSs = {< : > X} ad Q = {< : Q Q Q> X} some deftos ae stated belo: Q f ad oly f Q Q ad Q Q f ad oly f Q Q ad Q = Q f ad oly f = Q = Q ad = Q fo ay X omplemet of e c ={< : > X } 3 Some athmetc opeatos o SVNSs Defto [49] Let ad Q be ay to SVNSs a uvese of dscouse the athmetc opeatos ae stated as follos Q Q Q Q Q Q Q Q Q Q Q Q ; 0 Q Q ; 0 4 ay logathm fucto mathematcs the logathm of the fom log > 0 s called bay logathm fucto [50] o eample the bay logathm of s 0 the bay logathm of 4 s the bay logathm of 6 s 4 ad the bay logathm of 64 s 6 3 ay logathm smlaty measues fo SVNSs ths secto e defe to types of bay logathm smlaty measues ad the hybd ad eghted hybd smlaty measues 3 ay logathm smlaty measues of SVNSs type- Defto Let = < > ad = < > be ay to SVNSs he bay logathm smlaty measue type- betee SVNSs ad ae defed as follos: L = log 3 heoem he bay logathm smlaty measue L betee ay to SVNSs ad satsfy the follog popetes: 0 L L f ad oly f = 3 L L 4 f s a SVNS X ad the L L ad L L oof om the defto of SVNS e te ad ma 0 L oof o ay to SVNSs ad = = = = L ovesely fo L e have 0 0 Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

4 Neutosophc Sets ad Systems Vol = oof 3 We have L L oof 4 o e have fo X ; ; L L ad L L 3 ay logathm smlaty measues of SVNSs type- Defto 3 [5] Let = < > ad = < > be ay to SVNSs he bay logathm smlaty measue type- betee SVNSs ad ae defed as follos: L = log ma heoem he bay logathm smlaty measue L betee ay to SVNSs ad satsfy the follog popetes: 0 L L f ad oly f = 3 L L 4 f s a SVNS X ad the L L ad L L oof oofs of the popetes ae sho [5] 33 Weghted bay logathm smlaty measues of SVNSs fo type- Defto 4 Let = < > ad = < > be ay to SVNSs he the eghted bay logathm smlaty measue fo type- betee SVNSs ad ae defed as follos: L = log 3 Hee 0 ad heoem 3 he eghted bay logathm smlaty measues L betee SVNSs ad satsfy the follog popetes: 0 L L f ad oly f = 3 L L 4 f s a SVNS X ad the L L ad L L ; oof om the defto of SVNSs ad e te ad ma L sce oof o ay to SVNSs ad f = the e have = = = Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

5 Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets L t = sce ovesely o L the e have = sce oof 3 o ay to SVNSs ad e have L L fo oof 4 o e have fo X ; ; L L ad L L sce 34 Weghted bay logathm smlaty measues of SVNSs fo type- Defto 5 [5] Let = < > ad = < > be ay to SVNSs he the eghted bay logathm smlaty measue type- betee SVNSs ad s defed as follos: L = ma log 4 Hee 0 ad oof o poof see [5] 33 d bay logathm smlaty measues HLSM fo SVNSs Defto 6 Let = < > ad = < > be ay to SVNSs he hybd bay logathm smlaty measue betee SVNSs ad s defed as follos: L = ma log 3 log 5 Hee 0 heoem 4 he hybd bay logathm smlaty measue L betee ay to SVNSs ad satsfy the follog popetes: L 0 L f ad oly f = 3 L L 4 f s a SVNS X ad the L L ad L L oof om the defto of SVNS e te ad Neutosophc Sets ad Systems Vol

6 Neutosophc Sets ad Systems Vol Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets ma ; L 0 oof o ay to SVNSs ad fo = e have = = = L ovesely fo L e have = oof 3 o ay to SVNSs ad e have L L oof 4 o e have fo X ; ; L L ad L L 34 Weghted hybd bay logathm smlaty measues WHLSM fo SVNSs Defto 7 Let = < > ad = < > be ay to SVNSs he eghted hybd bay logathm smlaty measue betee SVNSs ad s defed as follos: L = ma log 3 log 6 Hee 0 heoem 5 he eghted hybd bay logathm smlaty measue L betee ay to SVNSs ad satsfy the follog popetes: L 0 L f ad oly f = L L 3 4 f s a SVNS X ad the L L ad L L oof om the defto of SVNS e te ad ma ; L 0 oof o ay to SVNSs ad

7 8 Neutosophc Sets ad Systems Vol 0 08 fo = e have = = = L ovesely fo L e have = oof 3 o ay to SVNSs ad e have L L oof 4 o e have fo all X ; ; L L ad L L 4 e etopy measue fo SVNSs Etopy stategy [5] s a mpotat cotbuto fo detemg detemate fomato Zhag et al [53] toduced the fuzzy etopy Vlachos ad Segads [54] poposed etopy fucto fo tutostc fuzzy sets Maumde ad Samata [55] developed some etopy measues fo SVNSs Whe attbute eghts ae completely uko to decso makes the etopy measue s used to calculate attbute eghts ths pape e defe a etopy measue fo detemg uko attbute eghts Defto 8 he etopy fucto of a SVNS = = m; = s defed as follos: m E 7 E E 8 Hee heoem 6 he etopy fucto E follog popetes: E 0 f 0 E f Q Q Q 3 E E Q f ; c 4 E E oof 0 E 0 0 oof E oof 3 Q Q m m Q Q Q Q m m Q Q Q satsfes the m m Q Q Q E Q E oof 4 c Sce e have c E E Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

8 Neutosophc Sets ad Systems Vol MGDM stategy based o eghted hybd bay logathm smlaty measue fo SVNSs ssume that m be the alteatves be the attbutes of each alteatve ad {D D D } be the decso makes Decso makes povde the atg of alteatves based o the pedefed attbute Each decso make costucts a eutosophc decso mat assocated th the alteatves based o each attbute sho Equato 9 Usg the follog steps e peset the MGDM stategy see fgue based o eghted hybd bay logathm smlaty measue WHLSM Step : Deteme the elato betee the alteatves ad the attbutes t fst each decso make pepaes decso mat he elato betee alteatves = m ad the attbute = coespodg to each decso make s peseted the Equato 9 D [ ] = D D D D D D D D D D D D D D D D D D D D D D D D D D D m m m m m m m m m m 9 Hee D D = m; = s the D sgle valued eutosophc atg value of the alteatve th espect to the attbute coespodg to the decso make D Step : Deteme the coe decso mat We fom a e decso mat called coe decso mat to combe all the decso make s opos to a goup opo oe decso mat mmzes the basess hch s mposed by dffeet decso makes ad hece cedblty to the fal decso ceases he coe decso mat s peseted Equato 0 D [ ] = m 0 Dt Dt Dt t Dt Dt Dt t D D D t t t t Dt Dt Dt t Dt Dt Dt t D D D t t t t Step 3: Deteme the deal soluto Dt Dt Dt t Dt Dt Dt t D D D t t t t he evaluato of attbutes ca be categozed to beeft attbute ad cost attbute deal alteatve ca be detemed by usg a mamum opeato fo the beeft attbutes ad a mmum opeato fo the cost attbutes fo detemg the best value of each attbute amog all the alteatves deal alteatve [4] s peseted as follos: * = { * * m*} hee the beeft attbute s * ma m m ad the cost attbute s * m ma ma Step 4: Deteme the attbute eghts Usg Equato 8 deteme the eghts of the attbute Step 5: Deteme the WHLSM values Usg Equato 6 calculate the eghted smlaty measues fo each alteatve Step 6: Rakg the poty ll the alteatves ae pefeece aked based o the deceasg ode of calculated measue values he hghest value eflects the best alteatve Step 7: Ed 6 llustatve eample Suppose that a state govemet ats to costuct a ecotousm pak fo the developmet of state tousm ad especally fo metal efeshmet of chlde fte tal sceeg thee potetal spots amely spot- spot- ad spot-3 3 ema fo futhe selecto team Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

9 0 Neutosophc Sets ad Systems Vol 0 08 of thee decso makes amely D D ad D 3 has bee costucted fo selectg the most sutable spot th espect to the follog attbutes Ecology osts echcal faclty 3 aspot 4 Rsk factos 5 he steps of decso-makg stategy to select the best potetal spot to costuct a eco-tousm pak based o the poposed stategy ae stated belo: 6 Steps of MGDM stategy We peset MGDM stategy based o the poposed WHLSM usg the follog steps Step : Deteme the elato betee alteatves ad attbutes he elato betee alteatves ad 3 ad the attbute set { 3 4 5} coespodg to the set of decso makes {D D D 3} ae peseted Equatos 3 4 ad 5 D [ ] D [ ] D [ ] Step : Deteme the coe decso mat Usg Equato 0 e costuct the coe decso mat fo all decso makes sho Equato 6 D[ ] Step 3: Deteme the deal soluto Hee 3 ad 4 deote beeft attbutes ad ad 5 deote cost attbutes Usg Equatos ad e calculate the deal solutos as follos: * Step 4: Deteme the attbute eghts Usg Equato 8 e calculate the attbute eghts as follos: [ 3 4 5] = [ ] Step 5: Deteme the eghted hybd bay logathm smlaty measues Usg Equato 6 e calculate smlaty values fo alteatves sho able Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

10 Neutosophc Sets ad Systems Vol 0 08 Step 6: Rakg the alteatves Rakg ode of alteatves s pepaed as the descedg ode of smlaty values Hghest value dcates the best alteatve Rakg esults ae sho able fo dffeet values of Step 7 Ed 7 Sestvty aalyss ths secto e dscuss the vaato of akg esults see able fo dffeet values of om the esults sho ables e obseve that the poposed stategy povdes the same akg ode fo dffeet values of 8 ompaso aalyss ths secto e solve the poblem th dffeet estg stateges [ ] Outcomes ae fushed the able ad fgue 9 otbutos of the poposed stategy We popose to types of bay logathm smlaty measues ad the hybd smlaty measue fo SVNS evomet We have poved the basc popetes o calculate uko eghts stuctue of attbutes SVNS evomet e have poposed a e etopy fucto We develop a decso makg stategy based o the poposed eghted hybd bay logathm smlaty measue WHLSM We have solved a llustatve eample to sho the feasblty applcablty ad effectveess of the poposed stategy 0 ocluso oclusos the pape ae cocse as follos: We have poposed hybd bay logathm smlaty measue ad eghted hybd bay logathm smlaty measue fo dealg detemacy decso makg stuato We have defed a e etopy fucto to deteme uko attbute eghts 3 We have developed a e MGDM stategy based o the poposed eghted hybd bay logathm smlaty measue 4 We have peseted a umecal eample to llustate the poposed stategy 5 We have coducted a sestvty aalyss 6 We have peseted compaatve aalyses betee the obtaed esults fom the poposed stateges ad dffeet estg stateges the lteatue he poposed eghted hybd bay logathm smlaty measue ca be appled to solve MGDM poblems clusteg aalyss patte ecogto pesoel selecto etc 7 utue eseach ca be cotued to vestgate the poposed smlaty measues eutosophc hybd evomet fo tacklg ucetaty cosstecy ad detemacy decso makg he cocept of the pape ca be appled pactcal decsomakg supply cha maagemet data mg cluste aalyss teache selecto etc able Rakg ode fo dffeet values of Smlaty measues Measue values Rakg ode L * 00 L * 0946 ; L * 0933; L * L * 05 L * ; L * 0996; L * L * 040 L * 0953; L * ; L * L * 055 L * ; L * 0949; L * L * 070 L * ; L * 0948 ; L * L * 090 L * ; L * 09565; L * Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

11 Neutosophc Sets ad Systems Vol 0 08 able Rakg ode fo dffeet estg stateges Smlaty measues Measue values fo ad 3 Rakg ode Modal ad amak [37] Ye [33] sas et al [56] Ye ad u [38] oposed stategy WHLSM based decso makg stategy Decso makg aalyss phase Detemato of the elato betee alteatves ad attbutes Step- Deteme the coe decso mat Step- Deteme deal soluto Step- 3 Deteme the attbute eghts Step-4 alculate the WHLSM values Step-5 Rakg the alteatves Step- 6 g : Decso makg phases of the poposed appoach Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

12 Neutosophc Sets ad Systems Vol g : Rakg ode of dffeet stateges Refeeces [] Smaadache ufyg feld logcs eutosophy: eutosophc pobablty set ad logc Rehoboth meca Reseach ess 998 [] H Wag Smaadache Y Q Zhag ad R Sudeama Sgle valued eutosophc sets Multspace ad Multstuctue [3] Y Guo Zhou H ha hughta J We L M Hadsk E Kazeoo utomated teatve eutosophc lug segmetato fo mage aalyss thoacc computed tomogaphy Medcal hyscs do: 08/48679 [4] K M m Shah Y Guo ovel beast tumo classfcato algothm usg eutosophc scoe featues Measuemet [5] Y X Ma J Q Wag J Wag X H Wu teval eutosophc lgustc mult-ctea goup decso-makg stategy ad ts applcato selectg medcal teatmet optos Neual omputg ad pplcatos [6] J Ye mpoved coss etopy measues of sgle valued eutosophc sets ad teval eutosophc sets ad the multctea decso makg stateges ybeetcs ad fomato echologes [7] J J eg J Q Wag X H Wu J Wag X H he Mult-valued eutosophc sets ad poe aggegato opeatos th the applcatos mult-ctea goup decso-makg poblems teatoal Joual of omputatoal tellgece Systems [8] R Şah ad Lu Mamzg devato stategy fo eutosophc multple attbute decso makg th complete eght fomato Neual omputg ad pplcatos [9] J Ye Smplfed eutosophc hamoc aveagg poecto-based stategy fo multple attbute decso makg poblems teatoal Joual of Mache Leag ad ybeetcs [0] h Lu eteded OSS method fo the multple attbute decso makg poblems based o teval eutosophc set Neutosophc Sets ad Systems [] sas S amak ad G Etopy based gey elatoal aalyss method fo mult-attbute decso makg ude sgle valued eutosophc assessmets Neutosophc Sets ad Systems [] sas S amak ad G e methodology fo eutosophc mult-attbute decso makg th uko eght fomato Neutosophc Sets ad Systems [3] sas S amak ad G ggegato of tagula fuzzy eutosophc set fomato ad ts applcato to mult-attbute decso makg Neutosophc Sets ad Systems [4] sas S amak ad G Value ad ambguty de based akg method of sgle-valued tapezodal Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

13 4 Neutosophc Sets ad Systems Vol 0 08 eutosophc umbes ad ts applcato to mult-attbute decso makg Neutosophc Sets ad Systems [5] sas S amak ad G Mult-attbute goup decso makg based o epected value of eutosophc tapezodal umbes Ne eds Neutosophc heoy ad pplcatos-vol- os Edtos ussells 07 ess [6] sas S amak ad G No-lea pogammg appoach fo sgle-valued eutosophc OSS method Ne Mathematcs ad Natual omputato 07 ess [7] S amak S Dalapat ad K Roy Logstcs cete locato selecto appoach based o eutosophc multctea decso makg Ne eds Neutosophc heoes ad pplcatos os-edttos ussels [8] K Modal ad S amak Neutosophc decso makg model of school choce Neutosophc Sets ad Systems [9] S amak K Roy Neutosophc game theoetc appoach to do-ak coflct ove Jammu-Kashm Neutosophc Sets ad Systems [0] S amak ad S N hackabat study o poblems of costucto okes West egal based o eutosophc cogtve maps teatoal Joual of ovatve Reseach Scece Egeeg ad echology [] K Modal ad S amak study o poblems of Has West egal based o eutosophc cogtve maps Neutosophc Sets ad Systems [] J Ye ault dagoses of steam tube usg the epoetal smlaty measue of eutosophc umbes Joual of tellget ad uzzy Systems [3] K Hu J Ye E a S She L Huag J ovel obect tackg algothm by fusg colo ad depth fomato based o sgle valued eutosophc cossetopy Joual of tellget ad uzzy Systems [4] Y Guo Şegü ovel mage segmetato algothm based o eutosophc smlaty clusteg ppled Soft omputg [5] D Koudal S Gupta S Sgh utomated deleato of thyod odules ultasoud mages usg spatal eutosophc clusteg ad level set ppled Soft omputg [6] D Koudal S Gupta S Sgh Speckle educto stategy fo thyod ultasoud mages eutosophc doma E mage ocessg [7] J Ye Multctea decso-makg stategy usg the coelato coeffcet ude sgle-valued eutosophc evomet teatoal Joual of Geeal Systems [8] J Ye Sgle valued eutosophc clusteg algothms based o smlaty measues Joual of lassfcato [9] S oum Smaadache Neutosophc efed smlaty measue based o cose fucto Neutosophc Sets ad Systems [30] S amak sas G d vecto smlaty measues ad the applcatos to mult-attbute decso makg ude eutosophc evomet Neual omputg ad pplcatos [3] X eg J Da ppoaches to sgle-valued eutosophc MDM based o M OSS ad e smlaty measue th scoe fucto Neual omputg ad pplcatos 06 6 do: [3] J Ye Vecto smlaty measues of smplfed eutosophc sets ad the applcato multctea decso makg teatoal Joual of uzzy Systems [33] J Ye mpoved cose smlaty measues of smplfed eutosophc sets fo medcal dagoss tfcal tellgece medce [34] sas S amak ad G ose smlaty measue based mult-attbute decso-makg th tapezodal fuzzy eutosophc umbes Neutosophc Sets Systems [35] S amak ad K Modal Weghted uzzy Smlaty Measue ased o aget ucto ad ts pplcato to Medcal Dagoss teatoal Joual of ovatve Reseach Scece Egeeg ad echology [36] K Modal ad S amak tutostc fuzzy smlaty measue based o taget fucto ad ts applcato to mult-attbute decso makg Global Joual of dvaced Reseach [37] K Modal S amak Neutosophc taget smlaty measue ad ts applcato to multple attbute decso makg Neutosophc sets ad systems [38] J Ye J u Mult-peod medcal dagoss stategy usg a sgle valued eutosophc smlaty measue based o taget fucto ompute Methods ad ogams omedce [39] M S a O Ozguve D tug th eutosophc smlaty measue teatoal Joual of uzzy Systems [40] K Modal S amak Mult-ctea goup decso makg appoach fo teache ecutmet hghe educato Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets

14 Neutosophc Sets ad Systems Vol [4] ude smplfed eutosophc evomet Neutosophc Sets ad Systems [4] Lu eg eteded ODM stategy fo multple attbute goup decso-makg based o - dmeso uceta lgustc vaable omplety [43] S amak S Dalapat S lam Smaadache K Roy NS-oss Etopy-ased MGDM ude Sgle-Valued Neutosophc Set Evomet fomato ; do:390/fo [44] J Ye Multple attbute goup decso-makg stategy th completely uko eghts based o smlaty measues ude sgle valued eutosophc evomet Joual of tellget ad uzzy Systems [45] J Ye lusteg methods usg dstace-based smlaty measues of sgle-valued eutosophc sets Joual of tellget Systems [46] K Modal S amak ad G Sgle valued eutosophc hypebolc se smlaty measue based stategy fo MDM poblems Neutosophc Sets ad Systems 9 08 EED [47] K Modal S amak ad G teval eutosophc taget smlaty measue ad ts applcato to MDM poblems Neutosophc Sets ad Systems 9 08 EED [48] Z Lu J Ye Logathmc smlaty measue betee teval-valued fuzzy sets ad ts fault dagoss method fomato do: 390/fo [49] shta Haghghad Maku G Motaze Eteso of fuzzy OSS method based o tevalvalued fuzzy sets ppled Soft omputg [50] J Ye mult-ctea decso-makg method usg aggegato opeatos fo smplfed eutosophc sets Joual of tellget & uzzy Systems [5] J N Mtchell ompute multplcato ad dvso usg bay logathms RE asactos o Electoc omputes [5] K Modal S amak G Smaadache J Ye d logathm smlaty measue based MGDM stategy ude SVNS evomet epts do:00944/pepts080303v [53] E Shao edcto ad etopy of pted Eglsh ell Labs echcal Joual [54] H Zhag W Zhag Me Etopy of teval-valued fuzzy sets based o dstace ad ts elatoshp th smlaty measue Koledge-ased Systems [55] K Vlachos G D Segads tutostc fuzzy fomato applcatos to patte ecogto atte Recogto Lettes [56] Maumda S K Samata O smlaty ad etopy of eutosophc sets Joual of tellgece ad uzzy Systems [57] sas S amak ad G OSS method fo mult-attbute goup decso-makg ude sglevalued eutosophc evomet Neual omputg ad pplcatos [58] bdel-asset M Mohamed M Smaadache & hag V 08 Neutosophc ssocato Rule Mg lgothm fo g Data alyss Symmety [59] bdel-asset M & Mohamed M 08 he Role of Sgle Valued Neutosophc Sets ad Rough Sets Smat ty: mpefect ad complete fomato Systems Measuemet Volume 4 ugust 08 ages [60] bdel-asset M Guasekaa M Mohamed M & Smaadache ovel method fo solvg the fully eutosophc lea pogammg poblems Neual omputg ad pplcatos - [6] bdel-asset M Maogaa G Gamal & Smaadache 08 hybd appoach of eutosophc sets ad DEMEL method fo developg supple selecto ctea Desg utomato fo Embedded Systems - [6] bdel-asset M Mohamed M & hag V 08 NMD: fameok fo evaluatg cloud computg sevces utue Geeato ompute Systems 86-9 [63] bdel-asset M Mohamed M Zhou Y & Hezam 07 Mult-ctea goup decso makg based o eutosophc aalytc heachy pocess Joual of tellget & uzzy Systems [64] bdel-asset M; Mohamed M; Smaadache Eteso of Neutosophc H SWO alyss fo Stategc lag ad Decso-Makg Symmety Receved : Mach 9 08 ccepted : pl 9 08 Kalya Modal Suapat amak ad bhas G d ay Logathm Smlaty Measue fo MGDM oblems ude SVNS ssesmets