The Qualiflex Method For The Insurance Company Selection Problem

Transcription

1 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN The Quafe Method For The Insurance Company Seecton Probem Ayşegü Tuş Işk, PhD Esra Aytaç Ada, PhD Pamukkae Unversty, Turkey Abstract Insurance s a too for the process of protectng the peope aganst the uncertanty and the oss of ther fe and property. Ths process s operated by an nsurance company under a contract between nsurance hoder and nsurance company. The contract may be sgned for fe, automobe, house etc. and the coverage of the contract may change from nsurance company to company. So the seecton of the most approprate nsurance company s not easy task. Ths seecton may be handed as a MCDM (Mut Crtera Decson Makng) probem. MCDM probems refer to make a decson for the aternatves characterzed by mutpe, usuay confctng, crtera. There are severa methods for sovng MCDM probems. In ths paper, QUALIFLEX (QUALItatve FLEXbe) method, one of the MCDM methods, s apped to the nsurance company seecton probem. Ths method s based on the evauaton of a possbe rankngs (permutatons) of aternatves n terms of concordance and dscordance ndces. The nsurance company aternatves are ranked by ths method and fnay the resuts are dscussed. Keywords: MCDM, QUALIFLEX, nsurance company seecton Introducton Insurance s the protecton aganst fnanca oss arsng on the happenng of unepected events (Vaughan & Vaughan, 2009). Both ndvduas and busnesses have sgnfcant needs for varous types of nsurance to provde protecton for ther heath care, property and ega cams made aganst them by others (Mayer et a., 2012). They get nsurance servces through nsurance companes whch are fnanca nsttutons provde servces as fnanca ntermedares of fnanca markets. In ths manner nsurance companes provde the coverage n the form of compensaton resutng from oss, damages, nury, treatment or hardshp n echange for premum payments (Tadesse, 2014). Gettng nsurance 348

2 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN servces s a technca and compe task because of the varous crtera that nfuence the busnesses to make ths decson. So t s mportant to choose the rght nsurance company for busnesses as we as ndvduas. In the terature, mutpe crtera decson makng methods have been wdey apped n the doman of nsurance decson makng. Amr et a. (2011) apped baanced scorecards and VIKOR method n ratng of nsurance companes. Doumpos et a. (2012) used PROMETHEE II method and regresson anayss for the performance of nonfe nsurers. Yücenur and Demre (2012) anayzed fve Turksh nsurance companes for a foregn nvestor who wants to purchase a oca nsurance company and seected the most approprate aternatve wth the etended VIKOR method. Aenagh (2013) used ANP and PROMETHEE methods for fnanca performance evauaton and rankng of nsurance companes n Tehran Stock Echange. Akhsar (2014) obtaned the fnanca performance rankng of Turksh Insurance companes for the perod wth ANP method. Khodamorad et a. (2014) combned DEMATEL and PROMETHEE II methods for ratng of Iranan nsurance companes sted n Tehran Stock Echange for a perod of Sehhat et a. (2015) ranked the nsurance companes n Iran wth AHP and TOPSIS methods. Krkbesogu et a. (2015) used AHP method for testng the effectveness of nsurance companes to provde nformaton to current and prospectve pocyhoders n two separate nternatona markets; Unted Kngdom (UK) and Turkey. Athough a consderabe numbers of MCDM methods have been empoyed to sove nsurance company seecton probems, QUALIFLEX (QUALItatve FLEXbe) method has not been apped to these probems. In ths paper QUALIFLEX method s used for seectng the most approprate aternatve nsurance company. It s one of the outrankng methods and t depends on the parwse comparsons of aternatves wth respect to each crteron under a possbe permutatons of the aternatves and dentfes the optma permutaton that mamzes the vaue of concordance/dscordance nde (Marte & Matarazzo, 2005; Zhang and Xu, 2015). The rest of ths paper s organzed as foows. The background of QUALIFLEX method s presented. Then the appcaton of ths method s demonstrated wth the nsurance company seecton probem. Lasty the resuts of the appcaton and the recommendatons for future studes are gven. QUALIFLEX Method QUALIFLEX (QUALItatve FLEXbe) method s one of the outrankng methods for sovng MCDM probems. It was deveoped by Paenck (1976, 1977, 1978) and Paenck (1976) generazed Jacquet- Lagreze s permutaton method to deveop a febe method (Chen et a., 349

3 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN , Wang et a., 2015). Its febty comes from the abty of handng cardna and ordna nformaton smutaneousy n the decson makng process (Zhang & Xu, 2015). The QUALIFLEX method s based on a metrc procedure namey the method performs the parwse comparsons of aternatves wth respect to each crteron under a possbe permutatons (rankngs) of the aternatves. Then a concordance and dscordance ndces are computed for each coupe of aternatves of permutatons. Fnay optma permutaton of the aternatves that mamzes the vaue of concordance/dscordance nde and the most preferred aternatve among aternatves are determned (Marte & Matarazzo, 2005; Anezhad & Esfandar, 2012). In the terature QUALIFLEX method and ts etensons have been empoyed to sove MCDM probems. Anezhad and Esfandar (2012) soved sutabe ste seecton probem for budng a dam wth QUALIFLEX and VIKOR methods. The authors deveoped the senstvty anayss of these methods and proposed a method based on changes n the weghts. Chen and Tsu (2012) performed a mut crtera decson anayss reated wth medca decson makng probem by combnng optmstc and pessmstc estmatons wth ntutonstc fuzzy QUALIFLEX method. Chen et a. (2013) deveoped an etended QUALIFLEX method based on nterva type- 2 trapezoda fuzzy numbers and apped the etended QUALIFLEX method to a medca decson makng probem. Wang et a. (2015) proposed a kehood-based QUALIFLEX method for handng mut crtera decson makng probems wthn the nterva type-2 fuzzy decson envronment. The proposed method was apped to a medca decson makng probem. Zhang and Xu (2015) proposed a hestant fuzzy QUALIFLEX method wth a sgned dstance-based comparson method for sovng a green supper seecton probem of an automobe manufacturng company. Zhang (2015) combned the QUALIFLEX method wth nterva-vaued hestant fuzzy decson envronment then the new method was caed nterva-vaued hestant fuzzy QUALIFLEX method. They apped the new method to the probem of Zhang and Xu (2015). Xue et a. (2016) soved robot seecton probems by a new ntegrated ngustc MCDM approach usng hestant 2-tupe ngustc term sets and an etended QUALIFLEX method. The appcaton steps of QUALIFLEX method are presented n the foowng (Chen & Tsu, 2012; Anezhad & Esfandar, 2012; Xue et a., 2016): Step 1: A mutpe crtera decson makng probem s formuated. It s assumed that there s a set of m feasbe aternatves, A (=1,2,,m), aganst to a fnte set of evauaton crtera C (=1,2,,n). Then the decson matr X s formed. It shows the performance of dfferent aternatves wth respect to varous crtera. 350

4 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN X = [ ] mn = m m2 1n 2n mn ( = 1,2,m; = 1,2,,n) (1) presents the performance vaue of th aternatve on th crteron, m and n are the numbers of aternatves and crtera respectvey. Step 2: A possbe permutatons of rankng of the aternatves are sted. The number of these permutatons s m!. Let P denote the th permutaton as: P = (, A,, A, ) = 1, 2,, m! (2) where the aternatve A s ranked hgher than or equa to A. Step 3: For each coupe of aternatves of permutatons, a concordance and dscordance ndces are computed whch refects the concordance and dscordance of ther ranks and ther evauaton preorder derved from the decson matr. Ths nde s frsty computed at the eve of snge crteron and then at a comprehensve eve wth respect to a possbe rankngs. The concordance/dscordance nde I (A,A ) for each par of aternatves ( A,A ) at the eve of preorder wth respect to th crteron and the rankng correspondng th permutaton s computed as: I = I ( A,A ) (3) where A,A A I (A, A ) = There are concordance and dscordance f A and A are ranked or not ranked n the same order wthn the preorder and permutaton respectvey. If they have the same rank, then the stuaton s e aequo. Step 4: Sometmes decson makers want to gve more mportance to a crteron than the others. If the mportance weght of a crteron s taken nto account, n ths step the weghted concordance/dscordance s cacuated as: I = I ( A,A ) w (5) A,A A 1 f there s concordance 0 f there s aequo -1 f there s dscordance w denotes the weght of th crteron. (4) 351

5 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN Step 5: The overa concordance/dscordance nde ( I ) for the permutaton P s computed as: n ( A,A ) I = I w (6) = 1 A,A A The fna rankng order of a aternatves s obtaned from the overa concordance/dscordance nde of each permutaton. The bgger the overa concordance/dscordance nde vaue, the better rankng of the aternatves. Appcaton In ths secton, an nsurance company seecton probem n a tete company s performed to demonstrate the appcabty of QUALIFLEX method. The tete company has purchased automobes for ther managers. The modes and features of the automobes are same. The company wants to have ther new automobes nsured so the company searches the best nsurance company. A commttee from the purchasng department s nterested n ths task as a decson maker. Frsty the commttee dentfes the evauaton crtera as C 1 (nsurance premum n TRY), C 2 (nsurance coverage n TRY), C 3 (dscounts n %), C 4 (reputaton) and C 5 (servce quaty). The data for C 1, C 2 and C 3 are quanttatve whereas data for the C 4 and C 5 are quatatve. 5 pont scae (5: Eceent, 4: Very good, 3: Good, 2: Far, 1: Poor) s used whe evauatng the aternatves for C 4 and C 5. Aso C 2, C 3, C 4 and C 5 are benefca crtera where hgher vaues are desrabe; C 1 s non-benefca crteron where smaer vaue s aways preferred. Consderng these crtera the commttee determnes 4 dfferent nsurance company aternatves (A 1, A 2, A 3, A 4 ) for ther automobes and receves nsurance proposas from these nsurance company aternatves. The decson matr shown n Tabe 1 s formed by these proposas. Tabe 1. Decson matr A 1 A 2 A 3 A 4 C 1 921,82 966, ,89 918,11 C C C C Consderng the data n Tabe 1, the rankng of aternatves wth respect to each crteron s gven n Tabe

6 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN Tabe 2. Rank evauaton of aternatves A 1 A 2 A 3 A 4 C C C C C The QUALIFLEX method begns wth stng a possbe permutatons of rankng of the aternatves. 4! permutatons of aternatves rankng are possbe for ths probem. > sgn n the permutatons means s preferred to. The permutatons are generated as: P 1 = A 1 >A 2 >A 3 >A 4 P 9 =A 2 >A 3 >A 1 >A 4 P 17 = A 3 >A 4 >A 2 >A 1 P 2 = A 1 >A 2 >A 4 >A 3 P 10 = A 2 >A 3 >A 4 >A 1 P 18 = A 3 >A 4 >A 1 >A 2 P 3 =A 1 >A 3 >A 2 >A 4 P 11 = A 2 >A 4 >A 1 >A 3 P 19 = A 4 >A 2 >A 3 >A 1 P 4 = A 1 >A 3 >A 4 >A 2 P 12 = A 2 >A 4 >A 3 >A 1 P 20 = A 4 >A 2 >A 1 >A 3 P 5 = A 1 >A 4 >A 2 >A 3 P 13 = A 3 >A 2 >A 1 >A 4 P 21 =A 4 >A 3 >A 2 >A 1 P 6 = A 1 >A 4 >A 3 >A 2 P 14 = A 3 >A 2 >A 4 >A 1 P 22 = A 4 >A 3 >A 1 >A 2 P 7 = A 2 >A 1 >A 3 >A 4 P 15 =A 3 >A 1 >A 2 >A 4 P 23 = A 4 >A 1 >A 2 >A 3 P 8 = A 2 >A 1 >A 4 >A 3 P 16 = A 3 >A 1 >A 4 >A 2 P 24 = A 4 >A 1 >A 3 >A 2 The concordance/dscordance nde for each par of aternatves at the eve of preorder wth respect to th crteron and the rankng correspondng th permutaton s computed by Eq. (3) (4). For nstance the necessary operatons are presented for the frst permutaton (P 1 ): P 1 : A 1 >A 2 >A 3 >A 4 C 1 C 2 C 3 C 4 C 5 A 1 >A 2 1 A 1 <A 2-1 A 1 >A 2 1 A 1 >A 2 1 A 1 <A 2-1 A 1 >A 3 1 A 1 >A 3 1 A 1 >A 3 1 A 1 =A 3 0 A 1 <A 3-1 A 1 <A 4-1 A 1 >A 4 1 A 1 =A 4 0 A 1 >A 4 1 A 1 <A 4-1 A 2 >A 3 1 A 2 >A 3 1 A 2 <A 3-1 A 2 <A 3-1 A 2 =A 3 0 A 2 <A 4-1 A 2 >A 4 1 A 2 <A 4-1 A 2 <A 4-1 A 2 >A 4 1 A 3 <A 4-1 A 3 >A 4 1 A 3 <A 4-1 A 3 >A 4 1 A 3 >A 4 1 Ony the computatona resuts of the concordance and dscordance ndces for the frst permutaton are presented n Tabe 3 because of the page constrant. Then the weghted concordance and dscordance ndces are computed by Eq. (5). In ths paper t s assumed that crtera are weghted equay as 1/5. 353

7 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN Tabe 3. The concordance and dscordance ndces for the frst permutaton P 1 C 1 C 2 C 3 C 4 C 5 I1(A1,A2) I1(A1,A3 ) I1(A1, A4 ) I1(A2, A3) I1(A2, A4 ) I1(A3, A4 ) Tabe 4. The weghted concordance and dscordance ndces for the frst permutaton I (A, A ) 1 I (A, A ) I (A, A I (A, A I (A,A P 1 0 0,8-0,2 0,2-0,2 Tabe 5. The overa concordance and dscordance ndces for the a permutatons P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 I 0,6 0,2 0,6 1 0,6 0,6 0,2-0,2 P 9 P 10 P 11 P 12 P 13 P 14 P 15 P 16 I -0,6-0,6-0,2-1 -0,6-0,6-0,2 0,2 P 17 P 18 P 19 P 20 P 21 P 22 P 23 P 24 I -0,2 0,2-0,6 0,2-1,4-0,2 0,6 0,6 Fnay the overa concordance/dscordance nde for the permutaton P s computed by Eq. (6) and resuts are gven n Tabe 5. Accordng to Tabe 5, permutaton 4 (P 4 ) s greater than the others so A 1 s the best aternatve. Concuson Athough automobe nsurance s made optonay, companes want to get the automobe nsurance for ther automobes n order to protect themseves aganst the potenta rsks that may arse. In ths paper, choosng the rght nsurance company of a tete company s eamned regardng the mportant crtera nfuencng the decson and QUALIFLEX method, whch s one of the outrankng methods, s apped. The obectve of ths paper s to fnd out overa rankng of automobe nsurance companes aternatves under the evauaton crtera. In ths manner frsty the nsurance company seecton probem of the tete company s defned by determnng the 354

8 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN crtera and aternatves. Then the necessary data are gathered. After formng a permutatons of aternatves rankng, a concordance and dscordance ndces are computed for each coupe of aternatves of permutatons at the snge crteron eve and the comprehensve eve. Fnay the best permutaton of aternatves rankng and the best aternatve are determned accordng to the overa concordance/dscordance ndces. Permutaton 4 (P 4 ) and aso A 1 are the best for ths probem. The QUALIFLEX method provdes some advantages to the decson makers. Frsty the mathematca background of QUALIFLEX method s not compe so t s easy understandabe and appcabe. The method s febe n terms of handng both cardna and ordna data of the probem. The method s sutabe for the probems where the number of crtera eceeds the number of aternatves (Chen et a., 2013). But the number of permutatons ncreases when the number of aternatves ncreases. In ths stuaton the computatona procedure becomes tme consumng and tedous. Ths s the man dsadvantage of the method. Ths stuaton may be overcome by deveopng a software whch performs QUALIFLEX method steps. Ths paper shows that the QUALIFLEX method s performed effcenty for the nsurance company seecton probem. In future studes, the number of crtera and aternatves may be changed for the same seecton probem. The weghts of the crtera may be derved from dfferent weghtng methods. The rankng of the aternatves may be performed wth other MCDM methods and the obtaned resuts may be compared. The QUALIFLEX method may aso be apped to other seecton probems. Aso fuzzy etenson of ths method may be apped to the same probem or other seecton probems. Acknowedgments Ths paper was fnancay supported by the Scentfc Research Proects Coordnaton Unt of Pamukkae Unversty. References: Akhsar, I. (2014). Performance rankng of Turksh nsurance companes: the ANP appcaton. Fnansa Araştırmaar ve Çaışmaar Dergs, 6 (11), 1-13 Aenagh, R. S. (2013). Performance evauaton and rankng of nsurance companes n Tehran Stock Echange by fnanca ratos usng ANP and PROMETHEE. European Onne Journa of Natura and Soca Scences, 2 (3), Anezhad, A. & Esfandar, N. (2012). Senstvty anayss n the QUALIFLEX and VIKOR methods. Journa of Optmzaton n Industra Engneerng, 5(10),

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10 European Scentfc Journa August 2016 /SPECIAL/ edton ISSN: (Prnt) e - ISSN Wang, J. C., Tsao, C. Y. & Chen, T. Y. (2015). A kehood-based QUALIFLEX method wth nterva type-2 fuzzy sets for mutpe crtera decson anayss. Soft Computng, 19, Xue, Y. X., You, J. X., Zhao, X. & Lu, H. C. (2016). An ntegrated ngustc MCDM approach for robot evauaton and seecton wth ncompete weght nformaton. Internatona Journa of Producton Research, DOI: / Yücenur, G. N., & Demre, N. Ç. (2012). Group decson makng process for nsurance company seecton probem wth etended VIKOR method under fuzzy envronment. Epert Systems wth Appcatons, 39(3), Zhang, X. & Xu, Z. (2015). Hestant fuzzy QUALIFLEX approach wth a sgned dstance-based comparson method for mutpe crtera decson anayss. Epert Systems wth Appcatons, 42, Zhang, Z. (2015). Mut-crtera decson-makng usng nterva-vaued hestant fuzzy QUALIFLEX methods based on a kehood-based comparson approach. Neura Comput & Appc, DOI /s