TOPSIS Model Based on Entropy and Similarity Measure for Market Segment Selection and Evaluation

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TOPSISmodelbasedonentropy andsimilaritymeasureformarket segmentselectionandevaluation

TruongThiThuyDuong VietnamBankingAcademy,Hanoi,Vietnam,and NguyenXuanThao

FacultyofInformationTechnology,VietnamNationalUniversityofAgriculture, Hanoi,Vietnam

Abstract

Purpose – Thepaperaimstoproposeapracticalmodelformarketsegmentselectionandevaluation.The papercarriesoutatechniqueoforderpreferencesimilaritytotheidealsolution(TOPSIS)approachtomakean operationsystematicdealingwithmulti-criteriadecision-makingproblem.

Design/methodology/approach – Introducingamulti-criteriadecision-makingproblembasedonTOPSIS approach.Anewentropyandnewsimilaritymeasureunderneutrosopicenvironmentareproposedtoevaluate theweightsofcriteriaandtherelativeclosenesscoefficientinTOPSISmodel.

Findings – TheoutcomesshowthattheTOPSISmodelbasedonnewentropyandsimilaritymeasureis effectiveforevaluationandselectionmarketsegment.Profitability,growthofthemarket,thelikelihoodof sustainabledifferentialadvantagesarethemostimportantinsightsofcriteria.

Originality/value – Thispaperputforwardaneffectivemulti-criteriadecision-makingdealingwith uncertaininformation.

Keywords Multi-criteriadecision-making,Marketsegmentselection,Neutrosophicset,Entropy, Similaritymeasure Papertype Researchpaper

1.Introduction

Theselectionandevaluationofmarketsegmentsboostthecompetitiveadvantageof companies.Marketsegmentistosplitthecustomermarketintosmallclustersorsegments basedonvariouscharacteristicssuchaslocations,psychographicsandconsumerbehavior. Thecompanythenevaluateswhichclustersorsegmentstobetargetmarketswiththe highestopportunity.Marketsegmentationmakesmoreadvantagescomparedtomass marking,including:(1)expandfirms’ ownmarketthroughimprovingthecustomer satisfaction(Aghdaie etal.,2013),(2)increaseprofitoreffectivenessofthefirms(Chiu etal., 2009),(3)manufacturemoreappropriateproductsorservicefrommarketsegment.

Eversince Smith(1956) presentedthebenefitsofmarketsegment,numerousstudieshave beeninvestigatedinevaluatingandselectingmarketsegments(McDonaldandDunbar,2004; QuinnandDibb,2010; Aghdaie etal.,2013; Ghorabaee etal.,2017; Duong etal.,2020).Witha

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ThisresearchisfundedbytheVietnamNationalFoundationforScienceandTechnology Development(NAFOSTED)undergrantnumber502.01 – 2018.09.

Market segment selectionand evaluation

Received23December2020 Revised16January2021 Accepted16January2021

AsianJournalofEconomicsand Banking EmeraldPublishingLimited 2615-9821 DOI 10.1108/AJEB-12-2020-0106

viewtoevaluatingavarietyofmarketsegments,decisionmakersarerequiredtotakeinto accountappropriatecriteriaduringtheselectionprocess. Wind(1978) believedthatthe selectionprocedurewascomplextobeaddressedbymanagerswhocarriedoutsome importantfeaturessuchascustomercharacteristics,competitivepotentialsandfeasibility. FreytagandClarke(2001) suggestedsomemainelementsforthisprocess,includingthe expectedprofitincomparisonwiththerelatedrisk,therivals,technology,thelikelihoodof gainingcustomersinthemarket,technology,governmentalandpublicactions,thepotentials toattainacompetitiveadvantage. Ghorabaee etal. (2017) selectthemarketsegmentsusing thePorter’sfiveforceofcompetition. ThaoandDuong(2019) usedtheaspectsofprofitability, marketsize,attractivenessascriteriaformarketsegments.Hence,theselectionand evaluationofmarketsegmentcanbeviewedasamultiplecriteriadecision-making(MCDM) probleminwhichthevagueandimpreciseinformationofexpertsordecisionmakersshould notbeneglected.

Smarandache(1998) proposedaneutrosophicsets,whichisoneofthemostpowerfultools formodelinguncertaintyindecision-makingproblems.Theneutrosophicsetsisanextension offuzzysetandintuitionisticfuzzysets.Byusingtheneutrosophicsets,theMCDMapproach canhandlenotonlythevague,impreciseandincompleteinformationbutalsothe indeterminateandinconsistentinformation,whereasthefuzzysetandtheintuitionisticfuzzy setfailtowork.

SeveralpopularMCDMapproachesusingfuzzysets,intuitionisticfuzzysetsand/or neutrosophicsetshavebeenproposedinliteraturetosolvethemarketsegmentselectionand evaluationproblemssuchasatechniqueoforderpreferencesimilaritytotheidealsolution (TOPSIS),analytichierarchyprocess(AHP),qualityfunctiondeployment(QFD)(Dat etal., 2015; Aghdaie,2015; Ghorabaee etal.,2017; Tian etal.,2018). Zandi etal. (2012) evaluatedand selectedmarketsegmentationthroughabi-levelmulti-objectiveoptimizationmodel,which combinesthereturnonassets(ROA)andfuzzycooperativen-persongametheory.The impreciseandvaguedatawererepresentedbyatrapezoidalfuzzynumber. Aghdaie etal. (2013) appliedthefuzzyAHPmethodsinthesenseofChang’sextentanalysis(1992)in calculatingtheweightofeachcriterionandsub-criterion.Thecomplexproportional assessmentwithgrayrelations(COPRAS-G)methodwasusedtorankallthealternatives.In otherresearch, Aghdaie(2015) combinedAHPwithTOPSISforselectingtargetmarketwith threeclustercriteria,includingrelatedsegments,financialandeconomic,technological aspects.Forthispurpose, Ghorabaee etal. (2017) approachedthegeneralizationof combinativedistance-basedassessment(CODAS)utilizingtrapezoidalfuzzynumbers. Tian etal. (2018) proposedahybridsingle-valuedneutrosophicQFDtosupportthemarket segmentevaluationandselection.Manycriteriahavebeenusedtoassessthemarket segment,includingsegmentgrowthrate,expectedprofit,competitiveintensity,capital requiredandleveloftechnologyutilization.

Decision-makingproblemisanoperationsystemdealingwithfindingthebestsolution, whichinvolvesconflictingcriteria.Identifyingtheweightsofcriteriaandtherankingof objectswithrespecttocriteriaaretwokeycomponentsofatypicaldecision-makingmodel. Todeterminetheweightsofcriteria,thefuzzyAHPapproachisoneofthemostpopular techniques.ThefuzzyAHPapproachorganizesthepairwisejudgmentsofcriteriaandsubcriteria,withtheaimofmakingtherelativeprioritiesforasetofalternatives.However,the weaknessoffuzzyAHPistime-consumingduetoalargenumberofpairwisecomparisonbe employed.Toovercomethisproblem,thisstudyproposesanewentropyandnewsimilarity measuresforneutrosophicsetstocalculatetheimportanceweightofcriteriainMCDM approach.ThisstudyfurtherdevelopstheTOPSISapproachbasedonthenewentropyand similaritymeasureforevaluatingthemarketsegment.

Therestofpaperworkisdividedintothreeparts.In Section2,somerelatedworksare introducedthoroughlywhichweinvolvetheneutrosophicset,fundamentalofsimilarity,

entropyandnewentropy.Additionally,anewsimilarity,entropyintheneutrosophicsetsis proposed.AnewTOPSISapproachispresentedin Section3.Anapplicationforselectingthe bestmarketsegmentisallocatedin Section4,andconclusionisthefinalsection.

2.Anewentropyandsimilaritymeasureontheneutrosophicset

Thissectionrecallssomeconceptsofasingle-valuedneutrosophicset(SVNS),whichwas introducedby Wang etal. (2010) aswellasintroduceanewsimilarityandentropymeasureof amSVNS.

2.1Single-valuedneutrosophicset

AnSVNS A* in X universalsetischaracterizedby TA* ; IA* ; FA*,whichrepresentthetruth–membership,indeterminacy–membership,falsity–membershipfunction,respectively.For eachelement x of X ,then TA* ðxÞ; IA* ðxÞ; FA* ðxÞ ∈ ½0; 1 ,satisfying TA* ðxÞþ IA* ðxÞ þFA* ðxÞ ≤ 3forall x ∈ X Forconvenience,denoteanSVNSby A* ¼ fðx; TA* ðxÞ; IA* ðxÞ; FA* ðxÞÞjx ∈ X g Thesetof SVNSon X isdenotedby SVNS ðX Þ

2.2Similaritymeasureofneutrosophicsets

Asimilaritymeasurerepresentsthesimilardegreeofobjectsdealingwiththeproblemsin reallifesuchasdecision-making,machinelearning,etc.Unlikesimilarity,entropydetermines thefuzzylevelofobjects.IntheMCDMcontext,similaritymeasureisusedasdistance measuretool,andentropycanbeusedtocalculatetheweightsofattributes.Fortwosets A* ; B* ∈ SVNS ðX Þ,thesimilaritymeasureandentropymeasurearedefinedasfollows

Definition1( BroumiandSmarandache,2013 ). Thefunction s* : SVNS ðX Þ 3SVNS ðX Þ → ½0; 1 iscalledasasimilaritymeasureon SVNS ðX Þ if satisfyingthefollowingconditions:

(1)0 ≤ s*ðA* ; B*Þ ≤ 1; (2) s*ðA* ; B*Þ¼ s*ðB* ; A*Þ; (3) s*ðA* ; B*Þ¼ 1ifonlyif A* ¼ B*;and (4)If A* ⊂ B* ⊂ C * then s*ðA* ; C *Þ ≤ s*ðA* ; B*Þ and s*ðA* ; C *Þ ≤ s*ðB* ; C *Þ:

Definition2(ThaoandSmarandache,2020). Anentropyon SVNS ðX Þ isafunction e*: SVNS ðX Þ → ½0; 1 satisfyingallfollowingconditions:

(1) e*ðA*Þ¼ 0if A* isacrispset,i.e. A*i ¼ðTA* ðxi Þ; IA* ðxi Þ; FA* ðxi ÞÞ¼ð1; 0; 0Þ or A*i ¼ðTA* ðxi Þ; IA* ðxi Þ; FA* ðxi ÞÞ¼ð0; 0; 1Þ forall xi ∈ X : (2) e*ðA*Þ¼ 1if A* ¼ fðxi ; 0:5; 0:5; 0:5Þjxi ∈ X g (3) e*ðAÞ¼ e*ðAC Þ; forall A ∈ SVNS ðX Þ (4) e*ðAÞ ≤ e*ðBÞ ifeither TA ðxi Þ ≤ TB ðxi Þ; IA ðxi Þ ≤ IB ðxi Þ; FA ðxi Þ ≤ FB ðxi Þ whenmaxfTB ðxi Þ; IB ðxi Þ; FB ðxi Þg ≤ 0:5or TA ðxi Þ ≥ TB ðxi Þ; IA ðxi Þ ≥ IB ðxi Þ; FA ðxi Þ ≥ FB ðxi Þ whenminfTB ðxi Þ; IB ðxi Þ; FB ðxi Þg ≥ 0:5: 2.3Proposedentropymeasureofthesingle-valuedneutrosphicset ThissectionproposesanewentropymeasureofanSVNSon X asthefollowing:

Market segment selectionand evaluation

Theorem1. Let A ¼fðxi ; TA ðxi Þ; IA ðxi Þ; FA ðxi ÞÞjxi ∈ X g beanSVNSseton X : Then,the entropymeasureoftheSVNS A isdefinedasfollows:

ET ðAÞ¼ 1 1 n X n i ¼1

jTA ðxi Þ 0 5j þ jFA ðxi Þ 0 5j þ jIA ðxi Þ 0 5j þ maxfjTA ðxi Þ 0 5j; jFA ðxi Þ 0 5j; jIA ðxi Þ 0 5jg 4 (1)

Proof

(1)If A isacrispset,thenforall xi ∈ X ; thenA 5 (1,0,0)orA 5 (0,0,1);therefore: Ei T ðAÞ¼ jTA ðxi Þ 0 5j þ jFA ðxi Þ 0 5j þ jIA ðxi Þ 0 5j þ maxfjTA ðxi Þ 0 5j; jFA ðxi Þ 0 5j; jIA ðxi Þ 0 5jg 4 ¼ 1

Itimpliesthat ET ðAÞ¼ 0. (2)If A ¼ fðxi ; 0 5; 0 5; 0 5Þjxi ∈ X g,thenEi T ðAÞ¼ 0 Itimplies ET ðAÞ¼ 1. (3)Itiseasytoverifythat E ðAÞ¼ E ðAC Þ forall A ∈ SVNS ðX Þ: (4)Ifeither TA ðxi Þ ≤ TB ðxi Þ; IA ðxi Þ ≤ IB ðxi Þ; FA ðxi Þ ≤ FB ðxi Þ whenmaxfTB ðxi Þ; IB ðxi Þ; FB ðxi Þg ≤ 0 5 orTA ðxi Þ ≥ TB ðxi Þ; IA ðxi Þ ≥ IB ðxi Þ; FA ðxi Þ ≥ FB ðxi Þ whenminfTB ðxi Þ; IB ðxi Þ; FB ðxi Þg ≥ 0:5, then jTB ðxi Þ 0 5j ≤ jTA ðxi Þ 0 5j; jIB ðxi Þ 0 5j ≤ jIA ðxi Þ 0 5j;jTB ðxi Þ 0 5j ≤ jTA ðxi Þ 0:5j; and IBC ðxi Þ 0 5 ≤ IAC ðxi Þ 0 5 forall xi ∈ X

Itmeansthat ET ðAÞ ≤ ET ðBÞ

2.4Proposedsimilaritymeasureofsingle-valuedneutrosphicsets

ThispartintroducesanotherapproachtobuildthesimilaritymeasureofanSVNS.Todothis, thesimilaritymeasureisdeterminedthroughanentropymeasureontheSVNS.Fortwo given A; B ∈ SVNS ðX Þ; defininganewSVSN N ðA; BÞ asfollowing: TN ðA;BÞ ðxi Þ¼ 1 þ jTA ðxi Þ TB ðxi Þj 2 ; IN ðA;BÞ ðxi Þ¼ 1 þ jIA ðxi Þ IB ðxi Þj 2 ; FN ðA;BÞ ðxi Þ¼ 1 þ jFA ðxi Þ FB ðxi Þj 2 (2) forall xi ∈ X Inparticular, TN ðA;BÞ ðxi Þ ≥ 0:5, IN ðA;BÞ ðxi Þ ≥ 0:5and FN ðA;BÞ ðxi Þ ≥ 0:5forall xi ∈ X : Theorem2(ThaoandSmarandache,2020). Thefunction S ðA; BÞ¼ E ðN ðA; BÞÞ determinesasimilaritymeasureof A and B on SVNS ðX Þ ifEisanentropy.

Using equations(1) and (2),thenewsimilaritymeasuresoftwoSVNSs A; B ∈ NS ðX Þ are definedasfollows:

ST ðA; BÞ¼ 1 1 8n X n i¼1

jTA ðxi Þ TB ðxi Þjþ jFA ðxi Þ FB ðxi Þjþ jIA ðxi Þ IB ðxi Þjþ maxfjTA ðxi Þ TB ðxi Þj; jFA ðxi Þ FB ðxi Þj; jIA ðxi Þ IB ðxi Þjg (3)

Ingeneral,if ω ¼ðω1 ; ω2 ;:::; ωn Þ istheweightvectoron X ,thenthesimilaritymeasure generatingfrom equation(3) is:

ST ðA; BÞ¼ 1 X n i¼1

ωi 8 jTA ðxi Þ TB ðxi Þjþ jFA ðxi Þ FB ðxi Þjþ jIA ðxi Þ IB ðxi Þjþ maxfjTA ðxi Þ TB ðxi Þj; jFA ðxi Þ FB ðxi Þj; jIA ðxi Þ IB ðxi Þjg (4)

3.TheexpandofTOPSISmodelbasedonentropyandsimilaritymeasurefor evaluationandselectionmarketsegments

OneofthemostpopularMCDMmodelsisTOPSIS,whichwasproposedby HwangandYoon (1981).ThefundamentalconceptoftheTOPSISmethodisthatthemostalternativeisbyall meansneartothepositiveidealsolutionandsimultaneouslyfarthestnegativeidealsolution. Sofar,thismodelhasgainedattentionofresearchersforitseffectiveness.Theweighted determinationofcriteriaandthedistancemeasurearetwomainstepsintheTOPSISmodel. Inthispart,wecarryoutanextensionoftheTOPSISmodeltocopewiththeMCDMissue. UnlikethetraditionalTOPSISmodelusingtheEuclideanorHammingdistancesfor calculationthedistancefromeachalternativetoidealsolution,thismodelusesthenew similaritymeasureunderaneutrosophicenvironment.Aninnovativeentropyisalsotaken intoconsiderationforaccomplishingtheweightsofcriteria. Initially,consider m marketsegments A ¼ fA1 ; A2 ;:::; Am g versus n criteria C ¼ fC1 ; C2 ;:::; Cn g withthesupportofdecisionmakers.Theprocessofextension TOPSISisoutlinedasfollows:

3.1Determinethedecisionmatrix

Executethesingle-valuedneutrosophicdecisionmatrixofalternativesundercriteriainform of D ¼½xij mn inwhichtheneutrosophicnumber xij ¼ðTij ; Iij ; Fij Þ isusedtoexternalizethe judgmentofalternatives Ai ði ¼ 1; 2;:::; mÞ withrespecttocriteria Cj

3.2Determinetheweight ωj ofcriteriaC j

Thepriorpreferencedeterminationisgivenbydecisionmakersfortherelativeimportanceof criteria,whichcanleadtosubjectiveidentify.Theevaluationofeachalternativeunder featureshaveputforwardtogaintheobjectiveweightsofcriteria.Let Cj ¼ fxj1 ; xj2 ; :::; xjm jj ¼ 1;:::; ng istheimportanceweightofcriteria Cj Using equation(1),theentropy measures ej of Cj ; j ¼ 1; 2;:::; n arecalculated.Theweight ωj ofeachcriterion Cj isdetermined by: ωj ¼ 1 ej P n j¼1 ð1 ej Þ (5) forall j ¼ 1; 2;:::; n.

Market segment selectionand evaluation

3.3Identifythebestsolutionandtheworstsolution

Thebestsolution A* andtheworstsolution A* aretakendependingonthetypeofattribute, costorbenefitcriterion.Theneutrosophicnumbersareusedforrepresentationofthebest andworstsolutionasfollows: A* ¼ n Cj ; T * j ; I * j ; F * j Cj ∈ C o

min i ¼1;:::;m Fij Þ if Cj isabenefitcriterion (7)

3.4Determinetherelativeclosenesscoefficient

ThetraditionalTOPSISapproachesdistancefunctionsuchasHammingdistance,Euclidean distanceforachievementgeometricdistancefromalternativestopositiveidealsolution A* andnegativeidealsolution A*.Inthisstudy,theproposedsimilaritymeasureisapplied. Foreachmarketsegment,thesimilaritymeasuresof S þ i and Si from Ai to A* and A* are calculatedbyusing equation(4).Then,therelativeclosenesscoefficientof Ai ði ¼ 1; 2;:::; mÞ isdefinedasfollows(HwangandYoon,1981):

CCi ¼ S þ i S þ i þ Si (8) S þ i and Si aresimilaritymeasuresfrom Ai to A* and A* forall i ¼ 1; 2;:::; m

3.5Rankingofmarketsegments

Thebestmarketsegmentisnearest A* andfarthest A*,thereforetherankingofmarket segments A ¼ fA1 ; A2 ;:::; Am g with Ai ≻ Ak if CCi ≻ CCk forall i ; k ¼ 1; 2;:::; m:

4.Resultanddiscussion

Inthissection,weapplytheproposedmodelfortheevaluationandselectionmarketsegment infoursegmentations A1, A2, A3, A4.Fordemonstrationoftheproposedmodel,thedatawere gainedby ThaoandDuong(2019) witheightbenefitcriteriaforassessmentmarketsegments, includingidentifyprofitability(C1),thegrowthofthemarket(C2),sizeofmarket(C3),likely customersatisfaction(C4),salesvolume(C5),likelihoodofsustainabledifferentialadvantage (C6),developmentopportunities(C7)andthedifferentiationofproduct(C8).Themodelis implementedasfollows:

Thedecisionmakersdeterminemarketsegmentswithrespecttocriteriausinglinguistic variables.TheSVNSisemployedfortransferringtheratingscaleoflinguisticvariables, whichisshowedin Table1 (Tian etal.,2018).

Fromtheevaluationofeachexpertforeachmarketsegmentusingtheneutrosophic number,theintegratedvalueisimplementedforthefinalassessmentofeachmarketsegment usingthebasicoperatorsin Wang etal. (2010).Theneutrosophicdecisionmatrixisshownin Table2,theintegratedvaluesareshowninthelastcolumnof Table2.

From Table2,theweightvectoriscalculatedfollowing equations(1) and (5),whichis ω ¼ð0 1549; 0 151; 0 1317; 0 066; 0 0832; 0 159; 0 1278; 0 1264Þ.Accordingtotheweightsof criteria,identifyprofitabilityandlikelihoodofsustainabledifferentialadvantagecriteria, whichareseenasthetwomostheavilyusedcriteriaforselectionmarketsegment,followed bythegrowthofthemarket,sizeofmarket.Intermsofbusinessside,profit,growthandsize ofthemarketarethemostmarketattractivenessfactorsformarketsegment.Theseare consistentwiththefindingof SimkinandDibb(1998)

Using equations(6) and (7),theSVNSbestsolution A* andtheSVNSworstsolution A* are shownin Table3

Thesimilaritymeasures S þ i and Si from Ai to A* and A* aregainedbyusing equation(4), whicharedescribedin Table4.

Therelativeclosenesscoefficientof Ai ; ði ¼ 1; 2;:::; 5Þ using equation(8) isshownin Table5.Foursegmentsarerankedby A3 ≻ A1 ≻ A4 ≻ A2 AccordingtothecharacteristicofTOPSIS,thesegment A3 hasthehighestrelative closenesscoefficientallocatedatthefirstposition,followedby A1, A4, A2.Therefore,the segment A3 isthemostappropriateoneforinvestment.Thisorderissuitablewiththe rankingfourmarketsegmentcomparingtoThaoandDuong’soutcome(2019);thisconfirms toselect A3 withhighdegreeofreliability,anditalsoshowsthatourmodelisvalid.

Market segment selectionand evaluation

LinguisticscaleforperformanalternativesIntervalintuitionisticfuzzyscale

Verylow(Vl)(0.1,0.85,0.9) Low(L)(0.2,0.75.0.8) Medium(M)(0.5,0.5,0.45) Good(H)(0.8,0.2,0.15) Verygood(Vh)(0.9,0.1,0.05)

CriteriaSegment Decision makersAveragedvaluesSegment Decision makersAveragedvalues

C1 A1 Vh,Vh,H,H(0.85,0.15,0.1) A3 H,H,H,Vh(0.825,0.175,0.125) C2 H,H,Vh,Vh(0.85,0.15,0.1)Vh,Vh,Vh, Vh (0.9.0.1.0.05)

C3 H,Vh,H,F(0.75,9.25,0.2)Vh,Vh,H,H(0.85,0.15,0.1) C4 F,H,F,F(0.575,0.425,0.375)H,Vh,Vh,Vh(0.875,0.125,0.075)

C5 H,F,F,F(0.575,0.425,0.375)Vh,Vh,Vh, Vh (0.9,0.1,0.05)

C6 Vh,H,Vh,Vh(0.875,0.125,0.075)H,H,Vh,H(0.825,0.175,0.125)

C7 H,H,Vh,H(0.825,0.175,0.125)H,H,Vh,Vh(0.85,0.15,0.1)

C8 H,H,Vh,Vh(0.85,0.15,0.1)H,Vh,Vh,H(0.85,0.15,0.1)

C1 A2 H,F,H,H(0.725,0.275,0.225) A4 Vh,Vh,H,H(0.85,0.15,0.1)

C2 H,F,F,F(0.575,0.425,0.375)Vh,Vh,H,H(0.85,0.15,0.1)

C3 F,H,H,F(0.65,0.35,0.3)H,H,H,Vh(0.825,0.175,0.125)

C4 F,F,F,F(0.5,0.5,0.45)F,F,F,F(0.5,0.5,0.45)

C5 H,F,F,F(0.575,0.425,0.375)H,F,F,F(0.575,0.425,0.375)

C6 H,H,H,F(0.725,0.275,0.225)Vh,Vh,H,H(0.85,0.15,0.1)

C7 H,H,F,F(0.65,0.35,0.3)F,F,H,H(0.65,0.35,0.3)

C8 H,F,F,H(0.65,0.35,0.3)F,L,L,L(0.275,0.688,0.713)

Table1. Linguisticvariablesfor ratingscaleonmarket segment

Table2. Theneutrosophic decisionmatrix

Table3. Thepositive idealsolution A* andthe negativeideal solution A*

5.Conclusion

Marketsegmentevaluationandselectionisoneofthemostimportantproblemsthatneedto bethoroughlysolvedtodeterminearightmarketingstrategyinroughlycompetitive environments.Itisbettertoutilizeeconomicsegmentationmethodsbeforeusingthecostly marketingmixedpart.SincethefirstdebaseofSmithaboutthebenefitsofmarketsegment, varioussegmentexcogitationswereemployed.However,managershavedifficultieshowto choosethebestappropriatesegmenttoserve.Therefore,amathematicalsystemallows simplechoice,whichbringsmanyadvantages.Themultipleconflictingcriteriaalongwith subjectiveandimpreciseassessmentcausedifficultyinthetargetmarketselectionprocess.In thispaper,wehavescrupulouslyextendedaTOPSISmodelbasedontheentropyand similaritywithintheneutrosophicenvironment.Theneutrosophichasbeenrecognizedasan effectiveandflexibletooltoshedlightonuncertain,inconsistentinformation.Acombination ofneutrosophicsetandMCDMmodelcontributestoimprovethemodelaccuracybothin termsofresearchandpractice.Inthiswork,anovelentropyandnovelsimilaritymeasureis proposedforaneutrosophicset.Entropytacklesandidentifiestheweightsofcriteria; meanwhile,theaforementionedsimilarityallowstherelativeclosenesscoefficientaim.The findingshowsthatprofitability,growthofthemarket,thelikelihoodofsustainable differentialadvantagesarethemostimportantinsightsofcriteria.Fourmarketsegmentsas wellaseightcriteriaareappliedtoselectthebestmarketsegment.Theproposedmodelcan bemodifiedtoapplyforarbitrarymarketsegmentnumberswithvariousconflictingcriteria. Inaddition,themodelextendsthescopenotonlyformarketsegmentbutalsoforotherreal practices.

(0.9,0.1,0.05)(0.575,0.425,0.375) C3 (0.85,0.15,0.1)(0.65,0.35,0.3) C4 (0.85,0.125,0.075)(0.5,0.5,0.45) C5 (0.9,0.1,0.05)(0.575,0.425,0.375) C6 (0.85,0.125,0.075)(0.725,0.275,0.225) C5 (0.85,0.125,0.075)(0.65,0.35,0.3) C6 (0.85,0.15,0.1)(0.275,0.6875,0.7125)

References

Aghdaie,M.H.(2015), “Targetmarketselectionbasedonmarketsegmentevaluation:amultiple attributedecisionmakingapproach” , InternationalJournalofOperationalResearch,Vol.24, pp.262-278.

Aghdaie,M.H.,Zolfani,S.H.andZavadskas,E.K.(2013), “Marketsegmentevaluationandselection basedonapplicationoffuzzyAHPandCOPRAS-Gmethods” , JournalofBusinessEconomics andManagement,Vol.14,pp.213-233.

Broumi,S.andSmarandache,F.(2013), “Severalsimilaritymeasuresofneutrosophicsets” , NeutrosophicSetsandSystems,Vol.1No.1,pp.54-62.

Chang,D.Y.(1992), “Extentanalysisandsyntheticdecision” , OptimizationTechniquesand Applicatons,Vol.1,pp.352-355.

Chiu,C.-Y.,Chen,Y.-F.andKuo,I.-T.K.(2009), “Anintelligentmarketsegmentationsystemusing k-meansandparticleswarmoptimization” , ExpertSystemswithApplications,Vol.36, pp.4558-4565.

Dat,L.Q.,Phuong,T.T.,Kao,H.P.,Chou,S.Y.andNghia,P.V.(2015), “AnewintegratedfuzzyQFD approachformarketsegmentsevaluationandselection” , AppliedMathematicalModelling, Vol.39,pp.3653-3665.

Duong,T.T.T.,Phong,L.T.,Hoi,L.Q.andThao,N.X.(2020), “Anovelmodelbasedonsimilarity measureandqualityfunctiondeploymentonintervalneutrosophicsetsforevaluationand selectionmarketsegments” , JournalofIntelligentandFuzzySystems,Vol.38,pp.5203-5214.

Freytag,P.andClarke,A.(2001), “Businesstobusinessmarketsegmentation” , IndustrialMarketing Management,Vol.3No.6,pp.473-486.

Ghorabaee,M.K.,Amiri,M.,Zavadskas,E.K.,Hooshmand,R.andAntuchevicien _ e,J.(2017), “Fuzzy extensionoftheCODASmethodformulti-criteriamarketsegmentevaluation” , Journalof BusinessEconomicsandManagement,Vol.8No.1,pp.1-19.

Hwang,C.L.andYoon,K.(1981), MultipleAttributeDecisionMakingMethodsandApplication:AState oftheArtSurvey,SpringerVerlag.

McDonald,M.andDunbar,I.(2004), MarketSegmentationHowtoDoitHowtoDoProfitfromit, ElsevierButterworth-Heinemann.

Quinn,L.andDibb,S.(2010), “Evaluatingmarket-segmentationresearchpriorities:targeting re-emancipation” , JournalofMarketingManagement,Vol.26Nos13-14,pp.1239-1255.

Simkin,L.andDibb,S.(1998), “Prioritizingtargetmarkets” , MarketingIntelligenceandPlanning, Vol.16,pp.407-417.

Smarandache,F.(1998), Neutrosophy:NeutrosophicProbability,Set,andLogic.AnalyticSynthesis SyntheticAnalysis.AmericanResearchPress.

Smith,W.(1956), “Productdifferentiationandmarketsegmentationasalternativemarketing strategies” , JournalofMarketing,Vol.21No.1,pp.3-8.

Thao,N.X.andDuong,T.T.T.(2019), “Selectingtargetmarketbysimilarmeasuresininterval intuitionisticfuzzyset” , TechnologicalandEconomicDevelopmentofEconomy,Vol.25, pp.934-950.

Thao,N.X.andSmarandache,F.(2020), “Applynewentropybasedsimilaritymeasuresofsingle valuedneutrosophicsetstoselectsuppliermaterial” , JournalofIntelligentandFuzzySystems, Vol.39No.1,pp.1005-1019.

Tian,Z.P.,Wang,J.Q.andZhang,H.Y.(2018), “Hybridsingle-valuedneutrosophicMCGDMwithQFD formarketsegmentevaluationandselection” , JournalofIntelligentandFuzzySystems,Vol.34, pp.177-187.

Wang,H.,Smarandache,F.,Zhang,Y.andSunderraman,R.(2010), “SinglevaluedSVNSsets” , Multisp Multistruct,Vol.4,pp.410-413.

Market segment selectionand evaluation

Wind,Y.(1978), “Issueandadvancesinsegmentationresearch” , JournalofMarketingResearch, Vol.15,pp.317-337.

Zandi,F.,Tavana,M.andO’Connor,A.(2012), “AStrategiccooperativegame-theoreticmodelfor marketsegmentationwithapplicationtobankinginemergingeconomies” , Technologicaland EconomicDevelopmentofEconomy,Vol.18,pp.389-423.

Correspondingauthor

TruongThiThuyDuongcanbecontactedat: thuyduongktv@yahoo.com.vn

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