Recommending Life Insurance using Fuzzy Multi Criteria Decision-Making

Transcription

1 Volume 118 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Recommending Life Insurance using Fuzzy Multi Criteria Decision-Making Sipra Sahoo 1 and Bikram Kesari Ratha 2 1 Assistant Professor, Department of CSE, SOA University, Bhubaneswar, , India sipracse@gmail.com 2 Professor & HOD, Department of CSE, Utkal University, Bhubaneswar, , India b ratha@hotmail.com January 16, 2018 Abstract Data has grown tremendously these days due to various reasons like technology adoption and fusion between hardware and software techniques. From this large volumes of data extracting the exact information pose a tough challenge to the researchers. Recommendation systems play a key role in suggesting the best needs based on various parameters. Insurance companies offer a huge deals and offers to lure the customers. Choosing an appropriate policy is a challenging task. In this article, we study how recommender systems can suggest the policies with the help of multi- criteria decision making (MCDM). This type of application would be very helpful to any person for choosing the right policy with right expectations. Key Words : life insurance, multi criteria, decision making, recommender systems

2 1 Introduction These days data has grown tremendously due to technology adoption and fusion of hardware and software techniques. The data has grown in terms of volume, velocity, variety and variability. Adoption of technology: specifically the mobile computing, clouding computing, social networking and internet of things have raised huge data. The fusion of hardware and software has made ease of things in accumulating huge amounts of data with ease ways. Extracting useful information from these huge volumes of data is a challenging task. A recommendation system deals with the specific needs of a person. Mostly the techniques involved are personalization, user profiling and classification. Most of the recommendation systems deal with single criteria [1][2]. Here we study the multicriteria recommendation model.[3][4][5] It is a well understood fact that future is unpredictable and uncertain. Life insurance policy provides the family with assurance that the insured family gets financial support and security even when the insurant is not around anymore. There are a number of companies that offer life insurance. Selecting the best insurance policy is a tough task left with the customer as the companies go with best of the attractions to lure the customer. In this paper, we are focusing on MCDM approach for selecting the best life insurance company for purchasing an online term policy[6]. MCDM method recommends the best alternative among the set of alternatives[7]. To define the decision-making parameters, we used fuzzy set theory. Fuzzy set theory was introduced by Zadeh[8] and it support to vagueness and uncertainty in decision-making. In fuzzy set theory parameters are specified using linguistic terms such as very low, low, medium, high, very high, very poor, poor, fare good, very good instead of exact numerical values. Fuzzy logic may be useful to attempt at mechanization or formalization human capabilities. First the capability to converse, reason and make rational decisions in an environment having of imprecision, uncertainty, conflict, incomplete information. Second the capability of performing a wide variety of physical and mental tasks without any physical measurement and computation. There are some criteria for selecting the best insurance company among a set of companies. Criteria have some weighted values that are in

3 dependent of each other. We evaluate the best insurance company alternative against the set of weighted criteria. We have chosen the company alternative for final implementation which evaluated the best with respect to all other criteria. Jagdal et al.[9] have ranked insurance companies especially in money back insurance policies domain with the help of classical AHP process. In this paper, authors took advices from the specialists in this field and Life Insurance Corporation, State Bank of India, Max Life Insurance, Bajaj Allianz Life Insurance and Aviva Life Insurance as their set of alternatives between which they found LIC to be the best among them using the above mentioned method. Zopounidis [10] has investigated after analyzed different decisionmaking strategies in different financial sectors problem related to insurance, banks, and financial firms, acquisition of firms, risk like bankruptcy risk, country risk and financial planning related problems. In this study, we suggested the different contributions of MCDM in various financial problems and enlightened with possibility of structuring complex evaluation problems and have given different possible solutions. Khodamoradi et al. [11] have studied different insurance companies in Iran and have proposed new hybrid methods consisting DEMATEL and PROMETHEE II method using sample data from insurance companies listed in Tehran Stock Exchange ( ) financial year and have suggested that Alborz Company has the highest and Dana company has the lowest rate. Dominik Ho and Michael Sherris[12] have done the risk analysis and return analysis with the help of Analytical Hierarchy Process (AHP) and ELEC- TRE III method in Insurance Linked Securities (ILS) portfolios in portfolio management. Jain Yogesh[13] have analyzed present and past status of life insurance sector and also discusses about the future strategies of the Indian insurance sector. Hurd and Mc- Garrys[14] have discussed about the unfavorable selection in the purchase of insurance. This paper is organized as follows. Fuzzy set theory is given in section 2. The proposed model for ranking the insurance companies based on MCDM for recommending online term policy is discussed in section 3. Numerical representation and sensitivity analysis and implementation details are given in Section 4. Finally we conclude in section

4 2 Fuzzy set theory The fuzzy sets are represented by linguistic terms that consist one or more linguistic variables, i.e. The linguistic variables have their possible states defined in a universe of discourse, represented by these linguistic terms. A fuzzy set F can be represented as, F = (x, µ F (x)) x X Where F (x) is the Membership Function (MF) for the fuzzy set F. X is called as Universe of Discourse that is represented as linguistic values. Each element of X has membership grade between 0 and 1. Membership functions (MF) are different types i.e. Triangular, Trapezoidal, Sigmoidal, Gaussian etc. 2.1 Triangular MF A triangular MF (fig.1) is represented by the three parameters (a,b,c) 0, x a, x a, a x b, b a c x c b, b x c, (1) 0, c x Parameters (a,b,c) are the real number and the value of these parameters specify the x coordinates of the three corners of the triangular MF. Fig. 1. Triangular Fuzzy number 4 738

5 Table 1: T able 1. Linguistic variables to define the criteria ratings. Linguistic variable Membership function Very Low (VL) 1,1,3) Low (L) (1,3,5) Medium (M) (3,5,7) High (H) (5,7,9) Very High (VH) (7,9,9) Table 2: Table 2. Linguistic variable to define the ratings of alternatives. Linguistic variable Membership function Very Poor (VP) (1,1,3) Poor (P) (1,3,5) Fair (F) (3,5,7) Good (G) (5,7,9) Very Good (VG) (7,9,9) 2.2 Distance between fuzzy triangular numbers Let (X) = (X 1, X 2, X 3 )and(y ) = (Y 1, Y 2, Y 3 ) are triangular fuzzy numbers. The distance between two triangular fuzzy numbers calculated by using vertex method is given below. d( x, 1 y) = [(x 3 1 y 1 ) 2 + (x 2 y 2 ) 2 + (x 2 y 3 ) 2 ] (2) 2.3 Linguistic variables: Linguistic variable is described by a quintuple, which is consist a variable name, term set, universe of discourse, syntactic rule and semantic rule. In fuzzy set theory, transformation scale is needed to convert the fuzzy numbers from linguistic variable [13-15]. In this paper we will apply a 1-9 transformation scale for rating the alternatives and criteria. Linguistic variable for criteria ratings are represented in Table.1 and linguistic term for alternatives ratings are represented in Table

6 3 Proposed model for ranking of insurance companies The proposed model for ranking of insurance companies consists of five different steps and these are depicted below. 3.1 Process for election of insurance policy There are several types insurance policy are available in market such as term insurance plans, pension plan, health plan, endowment plan, child plan, money back plan. One of the popular plans is term insurance plan. Online term policy is a combine application of e-commerce and financial market. Now-a-days it is combined to the insurance sector and produces a new insurance product that is online term plan. There are lot of attractive facilities are available under this plan, where we can buy this type of plan directly without any help of an agent. In this paper we have chosen only the online term plan and finally ranking the insurance companies for purchasing an online term plan. [15] 3.2 Process for selection of criteria There are lot of criteria exist for recommending an insurance policy. We have chosen the 10 criteria that is described in table 3. These criteria are taken from literature survey and consult with some experience person of this field. Criterias are categorized in to two types i.e. cost criteria and benefit criteria. In cost criteria, lower value is more preferable for alternative selection and for benefit criteria; higher value is more preferable for alternative selection [20]. In table 3, the criteria are denoted by C 1-C 10, here C 4 and C 6 are the cost criteria and all other criteria are the benefit criteria

7 Table 3: Table 3. policy Criteria for recommendation of an insurance Criteria Definition Criteria type Total number of death Average claim ratio (1) claim settled Benefit Entry age (2) Age of insured person at the beginning of policy Benefit Policy term (3) The benefit amount that is received by the policy holder or nominee either Benefit death or contract stipulation Maturity (4) Period of coverage provided by a policy Cost Sum assured (5) Financial cost of a policy that is paid by the insured Benefit Premium (6) Pre-decide amount, that insurer Cost pay to the insured. Premium payment Duration for the policy holder term (7) to pay the premium Benefit Premium payment Number of times to pay frequency (8) the premium Benefit Rebate on large sum assured (9) Discount on large sum assured Benefit Riders (10) Additional benefit that can be enhance the coverage Benefit 3.3 Process for selection of alternatives There are 24 Life insurance companies in India under the IRDA (Insurance Regulatory and Development Authority of India)[16]. At first we have chosen some companies which has better claim ratio. It is an important criterion for an insurance company. It refers to the ratio of total number of death claim received and the total number of death claim settled. For an example, if a life insurance company receives 1000 death claim and settles 970, then the claim ratio of this company would be 97%. After that the claim ratio of each company has been evaluated for last 4 years ( ) and then the average claim ratio has been calculated

8 Those companies which has more than 70% claim ratio have been considered. Finally we have chosen 12 insurance companies which has online term plan facility. In table 4, the alternatives of insurance companies are denoted by A 1-A 12. Table 4. Name of the alternatives. 3.4 Ranking Insurance companies using fuzzy TOPSIS We used a MCDM technique, called Fuzzy TOPSIS for choosing the best insurance company against some selected weighted criteria. TOPSIS helps to find the best alternative which is farthest from the Negative Ideal Solution (NIS) and very near to the Positive Ideal Solution (PIS). A NIS is consists of the minimum values of each alternative and PIS is consist of the maximum values of each alternative. The several steps of fuzzy TOPSIS are discussed as follows.[16][17][19][21]. Step 1. Evaluation of performance assignment to the criteria and the alternatives. Let is a set alternatives, where = ( 1, 2, 3,..., ), is a set of criteria, where = ( 1, 2, 3,..., ) and is number of decision maker, where (=1,2,..,). The value of alternatives is to calculated against criteria. The weights for each criterion are represented by (=1,2,3,...,). The performance assignment of each decision maker for each alterative with respect to each criterion is represented by P k = y ijk (=1,2,3,..,;=1,2,3,..,;=1,2,3,..,) with membership function µ P k (). Step 2. Calculate the aggregate fuzzy assignment for criteria and alternatives. Triangular fuzzy number is used to express the fuzzy assignment of all decision makers P k = (,, ),=1,2,..,. The aggregated fuzzy rating is calculated as P k =(,,), where x = min k {x k }, y = 1 K k k=1 y k, z = max k {z k } (3) 8 742

9 If the effective weight of the decision maker and fuzzy assignment are cw ijk = (cw jk1, cw jk2, cw jk3 ) and y ijk = (x jk1, y jk2, z jk3 ) respectively, then the aggregated fuzzy ratings ( y ij ) of alternatives with respect to each criterion are given by where y ij = (x ij, y ij, z ij ) where, x ij = min k {x ijk }, y ij = 1 K k k=1 y ijk, z ij = max k {z ijk } (4) The aggregated fuzzy weights ( cw ij ) of each criterion are calculated as cw j = (cw j1, cw j2, cw j3 ) where, cw j1 = min k {cw}, cwj2 = K k=1 cw jk2, cw j3 = max k {cw jk3 } (5) 1 k Step 3. Calculate the fuzzy decision matrix. Fuzzy decision matrix for the criteria and the alternatives is formed as bellows: Step 4. Fuzzy decision matrix should be normalized Normalization should be required for transforming the raw data into normalized data. We normalized the fuzzy decision matrix is denoted by P, which is given by P = [ P ij ] m n, =1,2,,; =1.2., for cost criteria P ij = ( x j z ij, x j y ij, x z ij ), x j = min i (x ij ) (6) and for benefit criteria P ij = ( x ij, y ij zj, z ij z zj ), z j = max i (z ij ) (7) Step 5. Calculate the weighted normalized fuzzy decision matrix. The weighted normalized fuzzy decision matrix() is calculated by multiplying the weights()of criteria with the normalized fuzzy 9 743

10 decision matrix P ij W C = [ W C ij ]m n, =1,2,,; =1.2..., where W C = W C ij = pij (.)cw j (8) Step 6. Calculate the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) The FNIS and FPIS of the alternatives are calculated as follows, F + = (wc + 1, wc +,,..., wc + n ) where wc + j = max j (wc ij3 )), i = 1, 2,...m; j = 1, 2,...n (9) F = (wc 1, wc,,..., wc n ) where wc j = min j (wc ij1 )), i = 1, 2,...m; j = 1, 2,...n (10) Step 7. Calculate the distance from FNIS and FPIS for each alternative. The distance(v + i, v i ) of each alternative i=1,2,...,m from the FPIS and the FNIS is calculated as follows: v + i v i = n j=1 v t( t ij, t + j ), i = 1, 2,..., m (11) = n j=1 v t( t ij, t j ), i = 1, 2,..., m (12) where vt( x, y) is the distance between two fuzzy numbers x and y. Step 8. Calculate the closeness coefficient of each alternative. The closeness coefficient (S i ) denoted the distances to the FPIS (F + ) and the FNIS (F )simultaneously. The S i of each alternative is computed as S i = v i, (13) v i +v+ Step 9. Ranking of the alternatives. Ranking of alternatives are made according the value of closeness coefficient (S i ) in decreasing order. Choose the best alternative which has heights (S i )value

11 3.5 Sensitivity analysis Sensitivity analysis is a technique and it is used to determine the sensitiveness of the overall decision if we make changes in the input values. In this paper we have consider the assessment values of criteria as input [18]. It is also used to test the robustness of the model where uncertainties exist for different factors. We observe that how much effect on the decision if we slightly change the values of the weights of criteria? We used the sensitivity analysis on our model in the order to notice that the effectiveness of weights of the criteria in resolving the best insurance company for purchasing an online term. 4 Numerical representation Let us consider that someone is interested to buy an online term policy. There are so many companies available. So problem is that how to determine the best company for buying a policy. A committee is formed which consist of three decision makers D 1, D 2, D 3 for choosing the best choice. The alternatives available for purchasing an online term policy is defined in Table 4. There are several criteria used for purchasing an online term policy which is define in Table 3, that is Average claim ratio (C 1), Entry age (C 2), Policy term (C 3), Maturity (C 4), Sum assured (C 5), Premium (C 6), Premium payment term (C 7), Premium payment frequency (C 8), Rebate on large sum assured (C 9), Riders (C 10). Criteria C 4 and C 6 are the cost criteria and rest of the criteria are benefit criteria. The committee of 3 decision makers provide the linguistic judgment for the 10 criteria using the rating scale that is define in Table 1 and the 12 alternatives of insurance companies for each of the 10 criteria that is defined in Table2. Linguistic judgment for the criteria and alternatives are defined in Table 5 and Table

12 Table 5. Linguistic judgement for the criteria Criteria (D 1 ) (D 2 ) (D 3 ) Average claim ratio (C 1 ) VH VH VH Entry age (C 2 ) H H VH Policy term (C 3 ) VH VH VH Maturity (C 4 ) VH H VH Sum assured (C 5 ) H VH VH Premium (C 6 ) VH VH VH Premium payment term (C 7 ) H H VH Premium payment frequency (C 8 ) M H H Riders (C 9 ) M H M Rebate on large sum assured (C 1 0) M M M Table 6. Linguistic judgement for the alternatives

13 By using Eq(5), we calculate the aggregated fuzzy weight for each criterion. Let us take an example, the aggregated fuzzy weight for Average claim ratio (C 1 ) is given by ( cw j = cw j1, cw j2, cw j3 ) where cw j1 = min k {7, 7, 7}, cw j2 = k=1 ( ), cw j3 = max k {9, 9, 9} cw j = (7, 9, 9) This way we calculate the aggregated fuzzy weight for rest of all criteria and that is define in Table 7. Table 7. Aggregated fuzzy weight for criteria Criteria (D 1 ) (D 2 ) (D 3 ) Aggregated fuzzy weight Average claim ratio (C 1 ) (7,9,9) (7,9,9) (7,9,9) (7,9,9) Entry age (C 2 ) (5,7,9) (5,7,9) (7,9,9) (5,7.66,9) Policy term (C 3 ) (7,9,9) (7,9,9) (7,9,9) (7,9,9) Maturity (C 4 ) (7,9,9) (5,7,9) (7,9,9) (5,8.33,9) Sum assured (C 5 ) (5,7,9) (7,9,9) (7,9,9) (5,8.33,9) Premium (C 6 ) (7,9,9) (7,9,9) (7,9,9) (7,9,9) Premium payment term (C 7 ) (5,7,9) (5,7,9) (7,9,9) (5,7.66,9) Premium payment frequency (C 8 ) (3,5,7) (5,7,9) (5,7,9) (3,6.33,9) Riders (C 9 ) (3,5,7) (5,7,9) (3,5,7) (3,5.66,9) Rebate on large (3,5,7) (3,5,7 sum(3,5,7) assured (C 10 ) )(3,5,7) (3,5,7) we also calculate the aggregated fuzzy weight for each alternative by using Eq. (4). Let us take an example, the aggregated fuzzy weight for alternative A 1 for criterion C 1 is yij = (x ij, y ij, z [ ij]) x ij = min k {7, 7, 7}, y ij = k=1 ( ), z ij = max k {9, 9, 9} Similarly we calculate the aggregated fuzzy weight for all the alternatives with respect to the ten criteria and that is presented in Table

14 Table 8. Aggregated fuzzy weight for alternatives Then we calculate the normalized fuzzy decision matrix for the alternatives by using Eqs. (6) and (7). Let us take an example, the normalized fuzzy rating of alternative A 1 for Average claim ratio (C 1 ) (benefit criteria) is calculated as zj = max j (9, 9, 9)

15 pij = ( 7, 9, 9 ) = (0.778, 1, 1) The normalized fuzzy rating of alternative A 1 for Maturity (C 4 ) (cost criteria) is calculated as x j = min j (1, 1, 1) pij = ( 1, 1, 1 ) = (0.11, , 0.2) Similarly normalized fuzzy decision matrix is calculated for all the alternatives with respect to each criteria and that is presented in Table 10.Minimum value for cost criteria and maximum value for benefit criteria is presented in Table 9, that is used for calculating the normalized fuzzy decision matrix. Table 9. Minimum value for cost criteria and maximum value for benefit criteria Table 10. Normalized fuzzy decision matrix

16 The next step is compute the normalized fuzzy decision matrix for all the alternatives by using Eq. (8). The values of r ij that is present in Table. 10 and the values of that is present in Table. 7 are required to compute the weighted normalized fuzzy decision matrix. Let us take an example, the weighted normalized fuzzy assessment of alternative A 1 for Average claim ratio (C 1 ) is given by wcij = (0.778, 1, 1)(7, 9, 9) = (5.4444, 9, 9) Similarly we calculate the weighted normalized fuzzy decision matrix for all the alternatives with respect to each criteria and that is presented in Table 11. Table 11. Weighted Normalized fuzzy decision matrix

17 Then we compute the FPIS and FNIS by using Eqs. (9) and (10). For an example, the FPIS (F + ) and FNIS (F ) for Average claim ratio (C 1 )is given by F + =(9,9,9) and F =(0.7778,0.7778,0.7778) Similarly we calculate the FPIS and FNIS for all the criteria that is presented in Table. 12. Table 12. FPIS(F + ) and FNIS (F )

18 Now we calculate the distance vt(.) for each alternatives from FPIS (F + ) and FNIS (F ) by using Eqs. (2), (11), and (12). For an example the distances (vt,a + 1 ) and(vt,a 1 ) of alternative A 1 for Average claim ratio (C 1 ) are computed as follows (v t, A + 1 ) = 1 3 [( )2 + (99) 2 + (99) 2 ] = (v t, A 1 ) = 1 3 [( )2 + ( ) 2 + ( ) 2 ] = This way we calculate the distances for all the criteria and all the alternatives that are presented in Table. 13 and 14. Table 13. Distance vi(a i, F + ) for alternatives Table 14. Distance vi(a i, F ) for alternatives Then we calculate the distances v + i andv i using Eqs. (11) and (12). Let us take an example, the distances v + i andv i of alternative A 1 for Average claim ratio (C 1 ) are computed as follows

19 (v + i ) = 1 3 [( )2 + (99) 2 + (99) 2 ]+ 1 3 [(2.7789)2 + ( ) 2 + (99) 2 ] [(19)2 + (2.7789) 2 + ( ) 2 ] = (v i ) = 1 3 [( )2 + ( ) 2 + ( ) 2 ]+ 1 3 [( )2 + ( ) 2 + ( ) 2 ]...+ = [( )2 + ( ) 2 + ( ) 2 ] We compute the closeness coefficient (S i ) buy using distances v + i andv i for all the alternatives that is given by Eq. (13). Let us take an example the S i of alternative A 1 is given by S i = = Similarly we compute the CC i for all alternatives, that is presented in Table. 15. Table 15. Closeness coefficients(s i ) of the alternatives Finally we rank the alternatives by comparing the CC i value, that is given in Table. 15. We find that LIC (2)> SBI(4)> ICICI (1)> HDFC(3)> BAJAJ ALIANZ(6)> MAX(5)>KOTAK MAHIN- DRA (10)> BHARTI AXA (7)> AVIVA(12)> RELIANCE(9)> AEGON RELIGARE (8)> CANARA HSBC (11). So LIC (2) is recommended as best insurance company for an online term plan. Ranking of all the alternatives are presented in figure

20 4.1 Sensitivity analysis We conducted a sensitivity analysis to find the influence of weights of criteria on the best insurance company choosing for purchasing an online term policy. 25 experiments were conducted, which are presented in Table. 16. In the first two experiments, all of the criteria weights we are assigned to (7,9,9) and (5,7,9), that is presented in Table. 16. In third and fourth experiment, we set the weight of criterion C 1=(7,9,9) and the rest of criteria have weight=(5,7,9) and (3,5,7) respectively. In fifth experiment, we set the weight of criterion C 1=(5,7,9) and the rest of criteria have weight=(3,5,7). In experiment 6-9, we set the weight of all criteria = (7,9,9) except the cost criteria C 4 and C 6. The weights of C 4 and C 6 for the experiments 6-9 are respectively (5,7,9), (3,5,7), (1,3,5) and (1,1,3). In experiment 10-13, we set the weight of all criteria = (5,7,9) except the cost criteria C 4 and C 6. The weights of C 4 and C 6 for the experiments are respectively (7,9,9), (3,5,7), (1,3,5) and (1,1,3). In experiment 14 and 15, we set the weight of all criteria = (3,5,7) except the cost criteria C 4 and C 6. The weights of C 4 and C 6 for the experiments 14 and15 are respectively (1,3,5) and (1,1,3). In experiment 16, we set the weights of criteria C 1 and C 2=(7,9,9), and all other criteria weights=(5,7,9). In experiment 17, we set the weights of criteria C 1, C 2 and C 3=(7,9,9), and all other criteria weights =(5,7,9). In experiment 18-20, all criteria have weights (3,5,7), (1,3,5) and (1,1,3) respectively. In experiment 21 and 22,

21 we set the weight of all criteria = (3,5,7) except the cost criteria C 4 and C 6. The weights of C 4 and C 6 for the experiments 21 and 22 are respectively (7,9,9) and (5,7,9). In experiment 23, we set the weight of criterion C 1=(3,5,7) and all other criteria weights =(1,3,5). In experiment 24, we set the weights of criteria C 1 and C 2=(3,5,7) and all other criteria weights =(1,3,5). In experiment 25, we set the weights of criteria C 1, C 2 and C 3=(3,5,7) and the rest of criteria have weight=(1,3,5). Out of 25 experiments, LIC (A 2) is selected as best insurance company in first 17 experiments. However SBI (A 4) is selected as best insurance company in last 8 experiments. Table 16. Experiment for sensitivity analysis 5 Conclusion Increase in data resulted in techniques to extract useful information from large amount of data. A case study on life insurance policy was taken where one can choose a policy online. Since a number of companies offer a vide variety of policies, a recommender system which works on multi-criteria is devised to rank the life insurance

22 policies and rank them. The customers can be recommended the insurance based on the ranks. References [1] Sahoo, Sipra, and Ratha Bikram Kesari, Location based Personalized Recommendation Systems for the Tourists in India, IJRASET,Vol-5(10), [2] Sahoo, Sipra, and Ratha Bikram Kesari. A Study on Similarity Metrics for Recommendations., International Journal of Computer Science, Information Technology, & Security (IJCSITS), Vol-6(5),Oct-2016, pp [3] Aruldoss, M., Lakshmi, T.M. and Venkatesan, V.P., A Survey on Multi Criteria Decision Making Methods and Its Applications, American Journal of Information Systems, 2013,Vol. 1, No. 1, pp [4] Mishra, R.A, Fuzzy Approach for Multi Criteria Decision Making in Web Recommendation System for E-Commerce, 11th International Conference on ICT and Knowledge Engineering (ICT&KE), IEEE, 2013, pp.1-4. [5] Adomavicius, G., Manouselis, N., and Kwon, Y. Multi- Criteria Recommender Systems Handbook,Part5, Springer (2011), pp [6] Adomavicius G. and Kwon Y., New Recommendation Techniques for Multi-Criteria Rating Systems, IEEE Intelligent Systems, vol. 22, no.3 (2007). [7] L. Kleanthi, T. Stelios, and M. Nikolaos, UTA-Rec: a recommender system based on multiple criteria analysis, in Proceedings of the 2008ACM conference on Recommender systems, Switzerland, 2008,pp [8] Zadeh, L.A., Fuzzy sets,information and Control 8, 1965, pp

23 [9] Jagdale, S., Jagdale, A., Venkataraman, K. and Gupta, V.B., Multi-Criterion Decision Approach in Ranking of Money Back Insurance Policies, 18 National Conference on Mapping for Excellence Challenges Ahead (Management), 2014, pp [10] Zopounidis C., Multicriteria decision aid in financial management. European Journal of Operational Research, 1999 Dec 1;119(2): [11] Khodamoradi S, Safari A, Rahimi R. A hybrid multi-criteria model for insurance companies rating, International Business Research May 27;7(6):150. [12] Ho D, Sherris M. Portfolio, Selection for Insurance Linked Securities: An Application of Multiple Criteria Decision Making, 2012 Mar 12. [13] Jain Y. Economic reforms and World economic crisis: Changing Indian life insurance market place, ISOR Journal of Business and Management. 2013;8(1): [14] Hurd, M. D. and McGrarry, K., Medical insurance and the use of health care services by the elderly, Journal of HealthEconomics 16, 1997, pp [15] Upadhyay, P, Satisfaction of the Policy Holders Protection in Insurance Sector:A Case Study, International Journal of Advanced Research in Computer Science and Software Engineering, 2013, Vol.3, pp [16] Insurance Regulatory and Development Authority (IRDA), India. [17] Awasthi, A. and Chauhan, S.S., A hybrid approach integrating Affinity Diagram, AHP and fuzzy TOPSIS for sustainable city logistics planning, Applied Mathematical Modelling36,2011, pp [18] Saaty, T.L., The Analytic Hierarchy Process, McGraw-Hill, NewYork (1980)

24 [19] Memariani, A., Amini, A. and Alinezhadc, A., Sensitivity Analysis Simple Additive Weighting Method (SAW): The Results of Change in the Weight of One Attribute on the Final Ranking of Alternatives, Journal of Industrial Engineering, 2009, vol-4, pp [20] Sevkli, M., Zaim, S., Turkylmaz, A. and Satr, M., An Application of Fuzzy Topsis Method for Supplier Selection, International conference on Fuzzy Systems, IEEE, 2010, pp.1-7. [21] D. Singh, B.K. Pattanayak, Performance Analysis of Shortest Time Regional Head Path Protocol (STRHP) in Wireless Sensor Networks, Far East Journal of Electronics and Communication, Volume 17(6), 2017, pp

25 759

26 760