INTEGRATED APPROACH OF FUZZY MULTI-ATTRIBUTE DECISION MAKING AND DATA MINING FOR CUSTOMER SEGMENTATION

174 2021, XXIV, 4 Ma ke ing and T ade 10.15240/ ul/001/2021-4-011 INTEGRATED APPROACH OF FUZZY MULTI-ATTRIBUTE DECISION MAKING AND DATA MINING FOR CUSTOMER SEGMENTATION Manida a Ray1, Mama a Ray2, Kamalakan a Muduli3, Aud ius Banai is4, Anil Kuma 5 1 Bi la Global Uni e si y, Bi la School o Managemen , India, ORCID: 0000-0002-5614-6469, [email p o ec ed]; 2 Biju Pa naik Uni e si y o Technology, India, ORCID: 0000-0002-5057-8009, [email p o ec ed]; 3 The Papua New Guinea Uni e si y o Technology, Papua New Guinea, ORCID: 0000-0002-4245-9149, [email p o ec ed]; 4 Vilnius Gediminas Technical Uni e si y, Facul y o Ci il Enginee ing, Depa men o Cons uc ion Managemen and Real Es a e, Li huania, ORCID: 0000-0002-3302-1209, [email p o ec ed]; 5 London Me opoli an Uni e si y, Guildhall School o Business and Law, Uni ed Kingdom, ORCID: 0000-0002-1691-0098, [email p o ec ed]. Abs ac : This esea ch wo k ocuses on in eg a ing he mul i a ibu e decision making wi h da a mining in a uzzy decision en i onmen o cus ome ela ionship managemen . The main objec i e is o analyse he ela ion be ween mul i a ibu e decision making and da a mining conside ing a complex p oblem o o de ing cus ome s segmen s, which is based on ou c i e ia o cus ome ’s li e ime alue, iz. leng h (L), ecency (R), equency (F) and mone a y alue (M). The p oposed in eg a ed app oach in ol es uzzy C-means (FCM) clus e analysis as da a mining ool. The expe imen conduc ed using MATLAB 12.0 o iden i ying eigh clus e s o cus ome s. The wo mul i a ibu e decision making ools i.e., uzzy AHP (Analy ic Hie a chy P ocess) and uzzy TOPSIS (Technique o O de P e e ence by Simila i y o Ideal Solu ion) a e used o anking hese iden i ied clus e s. The applicabili y o he in eg a ed decision making echnique is also demons a ed in his pape conside ing he case o Indian e ail sec o . This esea ch collec ed esponses om nine expe s om Indian e ail indus y ega ding hei pe cep ion o ela i e impo ance o ou c i e ia o cus ome li e alue and e alua ed weigh s o each c i e ion using uzzy AHP. T ansac ion da a o 18 mon hs o he case e ail s o e was analysed o segmen 1,600 cus ome s in o eigh clus e s using uzzy c-means clus e ing analysis echnique. Finally, hese eigh clus e s we e anked using uzzy TOPSIS (Technique o O de P e e ence by Simila i y o Ideal Solu ion). The indings o his esea ch could be help ul o i ms in iden i ying he mo e aluable cus ome s o hem and alloca e mo e esou ces o sa is y hem. The indings will be also help ul in de eloping di e en loyal y p og am s a egies o cus ome s o di e en clus e s. Keywo ds: Da a mining, uzzy c-means clus e ing, uzzy AHP, cus ome segmen a ion, uzzy TOPSIS, cus ome li e ime alue (CLV), ma ke ing s a egies. JEL Classi ica ion: C65, L81, D12. APA S yle Ci a ion: Ray, M., Ray, M., Muduli, K., Banai is, A., & Kuma , A. (2021). In eg a ed App oach o Fuzzy Mul i-a ibu e Decision Making and Da a Mining o Cus ome Segmen a ion. E&M Economics and Managemen , 24(4), 174–188. h ps://doi.o g/10.15240/ ul/001/2021-4-011 In oduc ion Recen ad ancemen s in In o ma ion and Communica ion Technologies (ICT) o e ed a ious op ions o he consume s o selec bes goods and se ices acco ding o hei equi emen . As a esul , manu ac u es and EM_4_2021.indd 174 3.12.2021 11:21:58 175 4, XXIV, 2021 Ma ke ing and T ade companies a e expe iencing challenges o e aining hei cus ome s and o which hey a e adop ing inno a i e cus ome ela ionship managemen s a egies. Fu he , i is well known by ma ke e s ha , cus ome s ha e a ious kinds o needs and wan s. Hence, hey y o es ablish ce ain c i e ia o be e iden i y and unde s and cus ome g oups and p o ide p e e able p oduc s and se ices o hem in o de o sa is y hei a ying needs and wan s. In his ega d segmen a ion is iewed by hem as an impo an echnique o c ea e p o i able segmen s and alloca e esou ces o espond o he needs o selec ed segmen s based on hei aluableness. Howe e , many ma ke e s ha e di icul y in iden i ying he igh cus ome segmen s o o ganize ma ke ing campaigns. This causes unsuccess ul loyal y p og ams and p omo ions conjunc ion wi h was e o ma ke ing esou ces. Nowadays, companies a e widely employing segmen a ion o cus ome s as a c i ical ool o di e en ia ing hem based on hei buying p e e ence (Sa a i e al., 2016) and unde s anding hei beha iou al esponses in his compe i i e e ail ma ke ing e a. This e en ually helps he o ganiza ions in cus omizing hei se ices o p oduc s as an e o o e ain hei cus ome s (Sa a i e al., 2016; Chiang & Yang, 2018; Egemen e al., 2021; Mok adi e al., 2021). Companies can also ga he he huge amoun o da a ela ed o cus ome s buying beha iou s h ough ICT. Howe e , i has been always a challenge o he companies o handle his massi e consume da a, which is some imes e e ed as Big da a. To handle his massi e da a, Da a Mining (DM) has been eme ged as an e ec i e p ocess ha ex ac s impo an in o ma ion om he same h ough a ious compu ing, s a is ical and ma hema ical, echniques (Chiang & Yang, 2018; Guo e al., 2020). Some o he mos impo an unc ions o he DM includes associa ion, classi ica ion, clus e ing, p edic ion and isualiza ion (Tsai, 2012). Recen ly, he e has been inc eased in e es in in eg a ing ope a ions esea ch echniques wi h DM (Malik e al., 2018; Pé ez-Ma ín e al., 2018; Liao e al., 2019; Gue a d e al., 2021). Mul i-a ibu e decision-making (MADM) is a class o p oblem-sol ing echniques in mul i- c i e ia decision-making (MCDM) which belongs o ope a ions esea ch and i deals wi h mul iple c i e ia in a ious decision en i onmen s, iz. de e minis ic, s ochas ic and uzzy. The li e a u e on MADM-DM in eg a ion shows some new me hodologies in a ious applica ion a eas. Fo example, Pineda e al. (2018) p oposed an in eg a ed model ha combines da a mining and mul i c i e ia decision making echniques, o iden i y and diagnose inancial and ope a ional pe o mance o ai lines. Ami i e al. (2021) p esen ed a new model wi h a iangula uzzy app oach o sus ainable supplie selec ion (SSS) in he supply chain. A abame i e al. (2019) applied ou bi a ia e and mul i a ia e s a is ical (WOE and BLR), da a mining (RF) and mul i c i e ia decision making (TOPSIS) models o g ound wa e po en ial mapping. Ma ques e al. (2020) by combining uzzy cogni i e mapping echniques and he sys em dynamics app oach c ea ed an analysis model ha allows o a mo e holis ic pe spec i e on de e minan s o amily business g ow h, hei cause-and-e ec ela ionships, and hus hei long- e m beha io . Mahdi aji e al. (2019) p oposed a model based on big da a analysis o e alua ion o ma ke ing s a egy using clus e ing-mul i c i e ia decision making app oach. Mohandes e al. (2020) de eloped a no el Risk Assessmen Model (RAM) h ough he in eg a ion o he Fuzzy Bes Wo s Me hod (FBWM) wi h he In e al-Valued Fuzzy Technique o O de o P e e ence by Simila i y o Ideal Solu ion (IVFTOPSIS). Liou e al. (2021) p oposed a no el hyb id MCDM model, ha in eg a es he suppo ec o machine (SVM), he uzzy bes wo s me hod (FBWM) and, he uzzy echnique o o de p e e ence by simila i y o an ideal solu ion (FTOPSIS) app oaches o selec he mos sui able g een supplie s. Ozkaya e al. (2021) used a hyb id model o da a mining and mul i c i e ia decision making me hods o p opose an indica o ha measu es science, echnology and inno a ion (STI) policies o o y coun ies o each hei sus ainable de elopmen goals. Ray and Manga aj (2016) e alua ed CLV in e ms o leng h, ecency, equency, mone a y (LRFM) a iables and employed AHP o ob ain ela i e weigh s o hese a iable based on mul iple expe s. They segmen ed cus ome s in o clus e s by K-means algo i hm using Da is- Bouldin (DB) index o a e aile o design p omo ional s a egies o imp o ing e aile - cus ome s ela ionship. Wu and Olson (2006) de eloped a TOPSIS based DM echnique o classi y c edi sco e da a in o g oups o high expec ed epaymen and low expec ed epaymen . Aghdaie e al. (2014) p oposed an app oach ha included K-means clus e EM_4_2021.indd 175 3.12.2021 11:21:58 176 2021, XXIV, 4 Ma ke ing and T ade analysis as a DM ool along wi h SWARA and VIKOR as wo MADM ools o ank he clus e s o supplie s. The cu en pape p oposes a new hyb id MADM-DM app oach o e alua e CLV in e ms o LRFM a iables in a uzzy decision en i onmen . Fo he same, AHP as well as uzzy AHP (FAHP) a e used o ob ain ela i e weigh s o hese a iables om a g oup o expe s. To employ uzzy C-means (FCM) clus e ing o segmen cus ome s and la e , ank hese clus e s o cus ome s using a uzzy TOPSIS (FTOPSIS) me hod. Sec ion 1 p esen s a discussion abou cus ome li e ime alue o loyal y as he composi e cons uc o segmen cus ome s and o design ma ke ing s a egies acco dingly. In sec ion 2, p oposed in eg a ed MADM-DM me hodology in a uzzy decision en i onmen is discussed. Sec ion 3 demons a es he applicabili y o he sugges ed in eg a ed DM app oach in Indian e ail sec o . Sec ion 4 p esen s a discussions and implica ions, and inally, he las sec ion concludes he pape . 1. Cus ome Li e-Time Value (CLV) Cus ome alue analysis is a ype o analy ic ool o unde s and a cus ome om beha iou al poin o iew. Acco ding o Ko le (2003), cus ome s a e b oadly classi ied by wo dimensions, iz. cus ome cha ac e is ics and beha iou . Demog aphics, psychog aphic and geog aphic a iables a e included in cus ome cha ac e is ics, whe eas a i udes owa ds he p oduc and he esponse shown by he cus ome s explains he beha iou al dimension. Cus ome alue also e med as ‘li e ime alue (LTV)’ o ‘cus ome li e ime alue (CLV)’ o ‘cus ome equi y (CE)’ o e en ‘cus ome p o i abili y (CP)’ is assessed by e alua ing he p esen alue o he u u e p o i s eam which is expec ed o e a gi en ime ho izon o ansac ing wi h he cus ome . Wiesel e al. (2011) s a es i as he u u e cash low alue o be p oduced om a cus ome in CRM ha also de e mines he p esen alue o cus ome s b ough o an o ganiza ion du ing cus ome s’ li e cycle. Hence, i is no mally used o ecognize bene icial cus ome s and o mula e app op ia e s a egies o di e en cus ome s’ segmen s (Khaj and e al., 2011). Howe e , o he a eas o applica ion o CLV includes cus ome s e alua ion whe e he segmen a ion scheme helps he ma ke e o make a decision whe he i is be e o acqui e ew la ge cus ome s (who may be isky) o a la ge numbe o small cus ome s (Benoi & Van den Poel, 2009); p oduc ecommenda ion o each cus ome g oup (Liu & Shih, 2005) e c. Li e a u e shows ha he e a e se e al modelling app oaches o s udy CLV. These app oaches include RFM models, econome ic models, p obabili y models, pe sis ence models, compu e models, di usion/g ow h models e c. Measu ing RFM is an impo an me hod o assessing CLV. RFM sco ing model using RFM da a was p oposed by Hughes (1994) which di e en ia ed cus ome s om a la ge da a- base by hese h ee a iables, so ha di e en ma ke ing s a egies could be adop ed o di e en g oups o cus ome s. RFM model was also used o assessing CLV alue by Sa a i e al. (2016). The au ho s u he employed uzzy clus e ing and uzzy AHP app oach o segmen ing he cus ome s and anking he clus e s espec i ely. Ani ha and Pa il (2019) in hei esea ch aimed a segmen ing cus ome s based on hei CLV alue also conside ed RFM a iables. Howe e , ew esea che s a gue ha RFM a iable based assessmen o CLV ails o iden i y cus ome s based on hei ansac ional leng h (Za e & Emadi, 2020). Hence, an ex ended RFM model was p oposed by adding ano he dimension he cus ome ansac ional leng h (L) o i which is known as LRFM model (Chang & Tsay, 2004). The addi ional a iable in LRFM model ep esen s he ime in e al be ween he i s and las exchanges wi h he cus ome . Wei e al. (2012) applied LRFM model and used sel -o ganizing maps o segmen pa ien s and a ge ed impo an pa ien s in a child en’s den al clinic. I is o be no ed ha , hese a iables emain independen in bo h he RFM (Liu & Shih, 2005) and LRFM (Seyed Hosseini e al., 2010) models. Rega dless o he numbe o a iables a e conce ned in he CLV cons uc , he e a e wo schools o hough conce ning assignmen o weigh s o a iables in he modelling p ocess. Hughes (1994) conside ed equal impo ance o R, F, M a iables, and hence equal weigh s o hem. On he o he hand, some esea che s ha e used he weigh ed models (Liu & Shih, 2005; Seyed Hosseini e al., 2010) in hei s udies. Howe e , assignmen o weigh s o hese c i e ia emains a di icul ask, al hough some au ho s (Liu & Shih, 2005; Rad e al., 2011; Ray & Manga aj, 2016) ha e used AHP EM_4_2021.indd 176 3.12.2021 11:21:58 177 4, XXIV, 2021 Ma ke ing and T ade as a sys ema ic me hod o weighing hese a iables. Concep ually, AHP de e mines ela i e weigh s o al e na i es wi h espec o one consis en expe whose subjec i e opinions a e conside ed in a pai -wise compa ison ma ix. In he e en o mul iple expe s, we use a i hme ic mean o a e aging hese weigh s ob ained om mul iple compa ison ma ices associa ed wi h consis en expe s. Bu in his pape , he dis ibu ion o judgemen s con ained in hose compa ison ma ices a e accoun ed and ep esen hem as a iangula uzzy numbe in an agg ega ed compa ison ma ix. Hence, ins ead o mul iple pai wise compa ison ma ices consis ing o judgemen s ei he in a scale o 1 o 9 o an in e se scale 1 o 1/9, we ge a ma ix o iangula uzzy numbe s (TFNs), whose e alua ion needs a FAHP o he de e mina ion o weigh s. The de ailed p ocedu e in he nex sec ion. 2. The P oposed Model This sec ion desc ibes he p oposed MADM- DM modelling app oach o anking cus ome segmen s using L, R, F and M sco es. This equi es p epa a ion o cus ome CLV ile o gene a ing L, R, F and M da a o each cus ome by accessing s o e’s da a-base o a pa icula ime pe iod looking o da a such as ca d numbe , cus ome name, and da e o isi o he s o e and pu chase amoun . The cus ome eco d in his espec is gene a ed consis ing o he ields, iz. ca d numbe and name o he cus ome along wi h his alue o R, L, F and M wi h e e ence o a pa icula da e. This becomes he da a p epa a ion s age which hen leads o he applica ion o he in eg a ed model o assess cus ome ’s alue o he s o e based on his buying beha io by employing FCM, FAHP and FTOPSIS in a sequen ial manne as shown in Fig. 1. De ails o hese models a e explained in he ollowing sub-sec ions. 2.1 Fuzzy C-Mean (FCM) Clus e ing Fo cus ome s g ouping in o segmen s and as a DM echnique, clus e ing a e used. Wi h he help o clus e ing he na u al g oups can be iden i ied om a la ge se o da a wi h LTV o example K-means, kohonen ne wo k/sel - o ganizing map and uzzy c-means. K-means clus e ing is a me hod equen ly used o ca ego ize da a in o K numbe o g oups (Rad e al., 2011). I s algo i hm pe o ms based on c isp pa i ioning which means each da um belongs o jus one clus e . Hence, he membe ship deg ee o each da um in a clus e is ei he 0 o 1. Howe e , o a da um ha ing ambiguous cha ac e is ics, he membe ship unc ion akes a alue in he ange 0 o 1. Hence, he concep o uzzy se is used in clus e ing o so pa i ioning o he objec s in o g oups he eby esul ing in uzzy c-means (FCM) clus e ing. FCM clus e ing was p oposed by Dunn (1973) and u he de eloped by Bezdek e al. (1984) ha allowed one piece o da a o belong o wo o mo e clus e s. By his me hod, we allow a piece o da a ha can exis in mul iple clus e s whe e i explains i s belongingness o each clus e o a ce ain deg ee in he ange 0 o 1. Hence, we minimize he ollowing objec i e unc ion: (1) He e N ep esen s he numbe o da a se and C ep esen s numbe o clus e s; xi deno es i h da a alue, Cj symbolizes j h clus e ’s cen e ; Uij deno es membe ship deg ee o xi belonging o he clus e j; ||*|| Euclidean ec o no m exp essing he dis ance be ween j h clus e ’s cen e and i h da a. Bu , in case o FCM clus e ing, an i e a i e op imiza ion o he Jm is done h oughou wi h he upda e o Um ij and Cj by ollowing o mulas (2) and (3) espec i ely. , (2) . (3) I , hen he i e a ion will be discon inued, whe e δ is a p esc ibed accu acy le el be ween 0 and 1, while k is he i e a ion s ep. This p ocedu e con e ges o a local minimum o a saddle poin o Jm. In ou wo k, we use his me hod o clus e cus ome s wi h simila LTV. 2.2 Fuzzy AHP (FAHP) o Ranking LRFM Though Analy ic AHP has been employed by many esea che s o assigning weigh s o he a iables L, R, F, M (Ray & Manga aj, 2016), ye he p oposed Fuzzy AHP me hod o he EM_4_2021.indd 177 3.12.2021 11:21:58 178 2021, XXIV, 4 Ma ke ing and T ade Fig. 1: Model o uzzy MADM in da a mining o cus ome segmen a ion Sou ce: own EM_4_2021.indd 178 3.12.2021 11:22:00 179 4, XXIV, 2021 Ma ke ing and T ade same as he la e allows eedom o decision make s o p o ide hei opinion h ough na u al languages (Muduli & Ba e, 2015; Shen e al., 2015). This equi es o mula ion o a uzzy compa ison ma ix ob ained om consis en compa ison ma ices om a se o AHPs depending upon he numbe o decision-make s (DMs). To ca y ou his, nine expe s om sales depa men ha include h ee expe s om each o he h ee di e en managemen laye s we e selec ed and eques ed o p o ide hei judgemen using a 9 poin scale desc ibed in Tab. 1, abou how impo an hey pe cei e one a iable in compa ison o he o he . These sco es we e used o de elop he pai wise compa ison ma ices. 2.3 E alua ion o Weigh s o LRFM a iables The s eps ollowed o assess he weigh s o he LRFM a iables wL, wR, wF and wM a e as ollows: S ep 1: De elopmen o pai -wise compa ison ma ix This asks he decision-make s o make pai - wise compa ison o he LRFM a iables using he scale as p esen ed in Tab. 1. We show his compa ison as a 4 x 4 judgmen ma ix o each DM. Fo example, he judgmen ma ix R1 o expe 1 wi h espec o he LRFM c i e ia could be p esen ed as shown in o mula (4). (4) In his ma ix, 1,11 = 1,22 = 1,33 = 1,44 and 1,ij. 1,ji = 1, whe e i = j = 1, 2,.., 4 and 1,ij is a alue in he abo e scale whe e i ≠ j. S ep 2: Assess he consis ency o pai wise compa ison While making pai wise compa ison, some DMs may make inconsis en judgmen s. This can be known by measu ing he deg ee o inconsis ency o all he DMs, whe e no inconsis ency ep esen s pe ec consis ency. As pe ec consis ency is a ely achie ed in such a si ua ion, an inconsis ency index alue o less han 0.1 is accep able o a judgmen ma ix as a consis en . In his way, we ge all he consis en judgmen ma ices o he consis en DMs. S ep 3: Cons uc he uzzy e alua ion ma ix We agg ega e all hese ma ices o a uzzy e alua ion ma ix whe e he elemen s o he ma ix a e he TFNs (lijk, mijk, uijk) o k numbe o DMs. We de e mine he alues o lijk, mijk, and uijk using o mulas (5), (6) and (7) espec i ely. (5) Compa a i e impo ance Desc ip ion Explana ion 1Equally impo an Bo h he a iable ha e equal con ibu ion owa ds he objec i e 3Weakly impo an One a iable is pe cei ed sligh ly impo an in compa ison o o he 5 S ongly impo an Impo ance o one a iable wi h espec o goal is s ong in compa ison o o he as pe he expe ’s pe cep ion 7 Ve y s ongly impo an One a iable is pe cei ed o ha e e y s ong impo ance in compa ison o o he 9 Ex emely impo an One a iable is pe cei ed ex emely impo an in compa ison o o he The impo ance le els 2, 4, 6 and 8 ep esen he in e media e alues. Fo example, 2 signi ies in e media e be ween equally and weakly impo ance whe e judgmen is be ween equally and sligh ly a o ing one a iable o e ano he . Sou ce: own Tab. 1: Rela i e deg ee o compa ison o pai wise compa ison o L, R, F and M a iables EM_4_2021.indd 179 3.12.2021 11:22:00 180 2021, XXIV, 4 Ma ke ing and T ade (6) (7) Fo each alue o i and j, mijk gi es he maximal g ade o he membe ship unc ion μx, e e o o mula (8), whe e lijk and uijk a e he lowe and uppe bounds ha limi he ield o possible e alua ion (Chang, 1996). Hence, o each i and j. . (8) Hence, we cons uc he uzzy e alua ion ma ix o k numbe o DMs using o mula (9). (9) S ep 4: Ob ain he weigh s o LRFM c i e ia Ex en analysis o FAHP p oposed by Chang (1996) was conduc ed o ob ain no malized non- uzzy weigh o he LRFM a iables wL, wR, wF and wM, whose sum is equal o one. 2.4 Fuzzy TOPSIS (FTOPSIS) o Ranking Clus e s Technique o O de P e e ence (TOPSIS) is also a popula MCDM echnique and used o de e mine ela i e weigh s o a se o al e na i es based on a ini e numbe o decision c i e ia (Tian e al., 2018; Bha i, 2020; Juan e al., 2021; Liao e al., 2020) as shown in Fig. 2. Howe e , unlike a compa ison ma ix o alues o al e na i es wi h espec o a c i e ion, his me hod is based on a ma ix o ac ual alues o al e na i es o a se o weigh ed c i e ia. As ge s he weigh s o LRFM a iables by FAHP, look o ac ual alues o he cus ome clus e s ha ing simila LTV wi h espec o LRFM c i e ia in o de o ge he ela i e weigh s o hese clus e s. The mos ideal op ion e alua ion h ough FTOPSIS is based on he compu a ion o sho es dis ance o he ideal solu ion (Wailoni e al., 2022). Hence, a posi i e ideal solu ion (PIS) needs o be calcula ed om he ma ix as well as he weigh ed c i e ia. Simila ly, a nega i e ideal solu ion (NIS) also compu ed. In his case, The PIS is a ou -dimensional co-o dina e ou o which wo a e he weigh ed maximum alues o hese clus e s o he equency and mone a y alue c i e ia, whe eas he o he wo a e he weigh ed minimum alues o he same clus e s o ecency and leng h c i e ia. The bes clus e is he one, which is closes o he PIS and a he same ime, a hes om he NIS. In his wo k, we employ uzzy TOPSIS (FTOPSIS) as he minimum, a e age and maximum alues o LRFM a iable o di e en clus e s a e ob ained by FCM clus e ing app oach and hence, a e exp essed as TFNs in he c i e ia- al e na i e ma ix. The s eps ollowed o de elop he FTOPSIS model a e as ollows: 1. Clus e o cus ome s is ob ained by FCM clus e ing app oach. 2. Weigh o each LRFM c i e ion is calcula ed employing FAHP. 3. Es ablishing he da a ma ix o he FTOPSIS as p esen ed in Tab. 2. In Tab. 2, each cell alue ep esen s a TFN. Fo example, (Lil, Lim, Liu) o i = 1, 2, …, s deno es TFN, whe e Lil, Lim and Liu a e he lowe , a e age and uppe alues o he a iable L ob ained by FCM clus e ing analysis ac oss he gene a ed clus e s. Fo each a iable c isp alues a e ob ained using o mula (10). (10) whe e i = 1, 2, ..., s. Hence, we ge maximal g ade o he membe ship unc ion o L, i.e. 1 a Lim. Simila ly, Lil and Liu a e he poin s o ze o sa is ac ion o he same unc ion. As discussed in he p e ious sub-sec ion, we deno e wL, wR, wF and wM a e he ela i e weigh s o he LRFM a iables. EM_4_2021.indd 180 3.12.2021 11:22:01 181 4, XXIV, 2021 Ma ke ing and T ade 4. We no malize he da a ma ix [(xij, xim, xiu)]sX4, whe e x = L, R, F and M and ge i as: D = [( ij, im, iu)]sX4, whe e ; ; 5. We compu e he weigh ed ma ix V = [( ij, im, iu)]sX4, whe e ij = wj . ij ; im = wj . im : iu = wj . iu and i = 1, 2, 3, …, s. 6. We de e mine he posi i e ideal poin A+ and he nega i e ideal poin A– as: A+ = ( 1 +, 2 +, 3 +, 4 +) and A– = ( 1 –, 2 –, 3 –, 4 –), whe e j + = maxi( ij) and j – = mini( ij): i = 1, 2, 3 … s 7. We ind ou he dis ance o each clus e Ci = ( i1, i2, i3, i4) : i = 1, 2, 3 … s om A+ and A– as di + and di – espec i ely, whe e and 8. We compu e he ela i e closeness o each clus e om he ideal solu ions as: Hence, highe alue o Ri implies be e CLV sco e o i h clus e . 3. A Case S udy o a Re ail S o e Fo he e alua ion o he p oposed model, a eal-li e case s udy o Indian e ail i m is chosen. The i m has se e al s o es loca ed in di e en pa s o he coun y i.e., India and has hund eds o egula cus ome s. Howe e , his wo k conside ed he e ail s o e loca ed a Bhubaneswa , Odisha, India. The eason o choose his pa icula s o e o expe imen al wo k is ha i is close o he median alue o he cus ome s a e conce ned. A e discussion wi h he i m managemen o an imp o ed CRM, decided o implemen a ion o he p oposed modelling app oach o i s cus ome s da abase o he segmen ing o he cus ome s in o de o ha e di e en p omo ional measu es, as an impo an componen o i s ma ke ing s a egy. The s o e’s sales da abase is designed ha ing name, ca d numbe , da e o pu chase and amoun o pu chase as he a ibu es ela ed o cus ome s. Then ou o ha L, R, F and M alues o a pa icula cus ome s ansac ions in las 18 mon hs a e iden i ied. The size o he cus ome s da abase is 1,600, who isi ed he s o e mul iple in las 18 mon hs. Fo segmen ing hese cus ome s in o mul iple g oups along L, R, F and M alues. The same alues used in FCM clus e ing analysis by MATLAB 12.0. Ob ained eigh clus e s wi h hei co esponding minimum, a e age and maximum alues o L, R, F and M c i e ia as p esen ed in Tab. 3. Based on he de ini ion o L, R, F and M c i e ia o de ining CLV as explained in sec ion 2, his wo k e alua ed he ela i e impo ance o each o hem wi h espec o nine expe s om he s o e. These expe s included chie ma ke ing manage , business manage , sales’ manage , logis ic manage and adminis a i e manage o he s o e. They p o ided hei indi idual pai - wise compa ison o he da a o hese c i e ia in he 9-poin scale as desc ibed in Tab. 1. When assessed o hei consis ency, ou o hem we e ound o be consis en while he i h one was asked o e ise his da a. A e ge ing he consis en ma ices, cons uc ed he uzzy e alua ion ma ix as discussed in s ep 3. Then employed ex en analysis o handle his ma ix o ob ain he no malized non- uzzy ela i e weigh s o he c i e ia as shown in Tab. 3. A e ge ing he ela i e impo ance o he L, R, F and M c i e ia as well as hei minimum, a e age and maximum alues o eigh clus e s, cons uc ed he uzzy da a ma ix o hese clus e s wi h Clus e s Leng h (wL) Recency (wR)F equency (WF) Mone a y alue (wM) Clus e 1 (L1l, L1m, L1u) (R1l, R1m, R1u)(F1l, F1m, F1u) (M1l, M1m, M1u) Clus e 2 (L2l, L2m, L2u) (R2l, R2m, R2u)(F2l, F2m, F2u) (M2l, M2m, M2u) …………… …………… Clus e S (Lsl, Lsm, Lsu) (Rsl, Rsm, Rsu)(Fsl, Fsm, Fsu) (Msl, Msm, Msu) Sou ce: own Tab. 2: Da a ma ix o FTOPSIS i i EM_4_2021.indd 181 3.12.2021 11:22:01 182 2021, XXIV, 4 Ma ke ing and T ade espec o he L, R, F and M c i e ia whe e each cell ep esen ed a alue o a clus e exp essed as iangula uzzy numbe . Thus, o ganized he L, R, F and M alues o hese clus e s as an 8 x 4 ma ix o FTOPSIS analysis as discussed in sec ion 2.3. The decision a iables in his p oblem ha e di e en uni s o measu emen . Hence, o coun e his issue a no malized da a ma ix was de i ed om Tab. 3 ollowing s ep 4 discussed in sec ion 2.4, and shown in Tab. 4. The no malized da a ma ix is hen con e ed o a weigh ed no malized da a ma ix as shown in Tab. 5 by using he weigh s o LRFM a iables. Compu a ional p ocedu e is discussed in s ep 5 in sec ion 2.4. Following compu a ional p ocedu e discussed in s eps 6 and s ep 7 o sec ion 2.4, FNIS and FPIS a e calcula ed om using Tab. 5 alues and a e shown in Tab. 6 and Tab. 7 espec i ely. Fig. 2: Mul i a ibu e decision making p ocess Sou ce: own Clus e No. Leng h (0.1120) Recency (0.1971) F equency (0.2446) Mone a y alue (0.4463) No. o cus ome s Highes alue Lowes alue A e age alue Highes alue Lowes alue A e age alue Highes alue Lowes alue A e age alue Highes alue Lowes alue A e age alue 1360 340 349 190 151 162 12 6 9 233,898 233,898 233,898 400 2724 307 453 400 22 273 30 11 24 377,487 242,280 225,840 370 3693 342 483 361 123 229 23 14 18 261,963 29,945 176,691 402 4724 307 491 400 163 306 22 1 10 209,155 25,863 103,290 311 5724 307 508 400 61 268 21 1 9 377,257 165,804 297,820 3 6724 311 566 319 5 99 30 5 22 348,549 26,101 125,440 9 7724 307 597 297 5 101 30 1 10 377,590 35,034 261,710 84 8695 307 442 237 5 119 19 1 9 259,665 24,909 112,820 21 To al 5,368 2,528 3,889 2,604 535 1,557 187 40 111 2,445,564 783,534 1,537,509 1,600 A e age 486.125 194.625 13.875 192,188.625 Sou ce: own Tab. 3: Clus e s c ea ed by uzzy c-means echnique h ough MATLAB 12.0 EM_4_2021.indd 182 3.12.2021 11:22:02