key: cord-0961382-r3k7phph authors: Ecer, Fatih; Pamucar, Dragan title: MARCOS technique under intuitionistic fuzzy environment for determining the COVID-19 pandemic performance of insurance companies in terms of healthcare services date: 2021-02-18 journal: Appl Soft Comput DOI: 10.1016/j.asoc.2021.107199 sha: 234d4edd82c9c5309525e4969f4851adf62ba9db doc_id: 961382 cord_uid: r3k7phph Assessing and ranking private health insurance companies provides insurance agencies, insurance customers, and authorities with a reliable instrument for the insurance decision-making process. Moreover, because the world’s insurance sector suffers from a gap of evaluation of private health insurance companies during the COVID-19 outbreak, the need for a reliable, useful, and comprehensive decision tool is obvious. Accordingly, this article aims to identify insurance companies’ priority ranking in terms of healthcare services in Turkey during the COVID-19 outbreak through a multi-criteria performance evaluation methodology. Herein, alternatives are evaluated and then ranked as per 7 criteria and assessments of 5 experts. Experts’ judgments and assessments are full of uncertainties. We propose a Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) technique under an intuitionistic fuzzy environment to rank insurance companies. The outcomes yielded ten insurance companies ranking in terms of healthcare services in the era of COVID-19. The payback period, premium price, and network are determined as the most crucial factors. Finally, a comprehensive sensitivity analysis is performed to verify the proposed methodology’s stability and effectiveness. The introduced approach met the insurance assessment problem during the COVID-19 pandemic very satisfactory manner based on sensitivity analysis findings. Insurance has an important place in modern society's daily life [1] . Insurers play a fundamental role in economies since they manage risks for individuals and firms, and countries. Thanks to insurance, further, people do not have to worry about unexpected events [2] . Health insurance ensures the expenses for the treatment of policyholders in case of illness and/or injuries resulting from an accident during the insurance period [3] . In private health insurance, one of the alternative financing methods of healthcare services, the reimbursement institution is private health insurance, and individuals or institutions insure their health risks [4] . Turkey's health insurance covers illness, private health, health for foreigners, emergency health, health, and travel health products [5] . Since the beginning of the 1990s, there have been some crises in Turkey regarding health financing. As a result, radical changes were made in the health system with the Health Transformation Program, which started in 2003, and one of them was the Social Security Reform. With this reform, the general health insurance system was implemented as well as access of all citizens to health services has become more comfortable. Thus, the regulations associated with the delivery and financing of health services have gained momentum, especially after 2003, and financing and the provision of services, both radical changes, have taken place [6] . In 2012, all citizens in Turkey had been general health insurance coverage. In Turkey, further, public health insurance is made mandatory against the risk of illness that may arise, regardless of the people's economic power and will. Thereby, all members of society benefit from general health insurance. However, no matter how the scope of the basic coverage package is determined, it is natural that there is a difference between the health services provided within the scope of the state's social security and the optimal conditions in systems based on public finance. As of 2018, the share of private health insurance in Turkey's insurance sector is 10.9%, which corresponds to 3.8% of the population [5] . Nowadays, increasing average life expectancy, developing technology, and changes in the structure of diseases have increased private health insurance. Recently, many epidemics such as Middle East respiratory syndrome coronavirus (MERS) [7] , severe acute respiratory syndrome (SARS) [8] , bird flu [9] , swine flu [10] , etc. have emerged. Since late 2019, The COVID-19 outbreak caused by the virus named SARS-CoV-2 has been spreading at an increasing rate and threatening the whole world. As of 16th January 2021, as per Johns Hopkins University report [11] , 94,078,427 individuals were infected, and 2,014,436 people died due to this pandemic worldwide. In Turkey, the first COVID-19 case has been officially confirmed on 11th March 2020. Moreover, based upon Turkey's health ministry, the total number of tests administered was 27,223,445, of which 2,380,665 returned positive, with 23,832 passing away, whereas the total number of 2,254,052 patients are recovered [12] . As a result, The COVID-19 epidemic, which directly affects the lifestyle of billions of people, has begun to transform the insurance industry and many other industries in the world. In this challenging period in Turkey, full treatment costs for COVID-19 illness were covered under private health insurers' policy. Thus, analyzing the performance of insurance companies in such a challenging process is a quite significant issue. As a result, this paper aims to propose an effective and reliable decision-tool named intuitionistic fuzzy Measurement of Alternatives and Ranking according to Compromise Solution (IF-MARCOS) for measuring the performance of insurance companies in Turkey in terms of health services during the COVID-19 outbreak. The alternatives' utility functions are stated according to the relationships defined in the MARCOS method, which is a simple and efficient multicriteria technique and based on determining the relationship between ideal and anti-ideal alternatives. A consensus ranking is then realized concerning ideal and non-ideal solutions. Although the MARCOS method is relatively new, many papers have been performed about it [13] [14] [15] [16] [17] . Intuitionistic fuzzy sets (IFSs) have also been performed successfully in real-world problems to employ inconsistent, vague, ambiguous, and incomplete information. It has attracted more and more attention since its introduction and researchers achieved satisfactory results. For example, Li et al. [18] integrated QFD and TOPSIS for selecting a knowledge management system under IFSs. Xue et al. [19] developed a novel approach for solving IFSs-based MCDM problems with incomplete weight information. Büyüközkan and Göçer [20] studied the MCDM problem through AHP and axiomatic design approach for IFSs. Schitea et al. [21] employed WASPAS, COPRAS, and EDAS multi-criteria methods to solve site selection problems under IFSs. Recently, Kumari and Mishra [22] studied a green supplier selection problem based on parametric measures of IFSs. Rouyendegh et al. [23] discussed an IF-based TOPSIS technique for evaluating green suppliers. Though MARCOS is a robust tool, it cannot express DMs' vagueness, ambiguity, and incomplete information. Thanks for extending the MARCOS method to IFSs; therefore, the introduced IF-MARCOS methodology can handle imprecise, indeterminate, vague, and incomplete information successfully in real situations. Evaluation of health insurance companies, especially regarding customer-oriented factors, has become a vital research area of plenty of insurance research centers during the COVID-19 pandemic. This is mainly due to the undeniable importance of health insurance on the capital market and the critical role of service quality in customer satisfaction. This issue has remained one of the major topics associated with the insurance industry, which has not been sufficiently studied in the literature. In summary, this study is structured around the following main objectives: • To assess ten insurance companies operating in Turkey regarding health services during the COVID-19 pandemic and determine which one is the best. • While making this assessment, it is the first time in the literature to handle a novel approach called MARCOS method under an intuitionistic fuzzy environment. • To determine the importance of the evaluation criteria used in evaluating insurance companies. The contributions of this work can be pointed out as follows: • Although the MARCOS technique is a powerful decisionmaking tool, it cannot express fuzziness and ambiguity information. • Combined with the intuitionistic fuzzy sets, we posit the IF-MARCOS model, which can better describe decision-makers' evaluation information. • We extend assessments of decision-makers to the intuitionistic fuzzy sets to extract criteria weights and rank the alternatives. • IF-MARCOS approach is suggested to apply to multiple criteria group decision making (MCGDM) problems. • A real-world problem of insurance companies' assessment is given for the extended MARCOS methodology to MCGDM problems. To achieve the mentioned objectives, the rest of this work is organized as follows. A literature review is performed in Section 2. In the third section of the study, IF-MARCOS is presented in detail. Application and sensitivity analysis is carried out in Section 4. The fifth section of the paper is about managerial implications. Finally, the concluding observations with directions for future works and limitations are presented in Section 6. In this paper, the literature section is divided into two subsections. The first is the studies that applied the MARCOS method, while the second is the insurance studies conducted multiple criteria decision making (MCDM) techniques. MARCOS represents a new multi-criteria technique developed by Stević et al. [24] . They showed that the advantages of the MARCOS methodology with traditional multi-criteria techniques: Multi-Attributive Border Approximation area Comparison (MABAC) [25] , Additive Ratio Assessment (ARAS) [26] , Weighted Aggregated Sum Product ASsessment (WASPAS) [27] and technique for order of preference by similarity to ideal solution (TOP-SIS) [28] . The advantages of the MARCOS methodology were confirmed through a case study in which the evaluation of sustainable supplier selection in healthcare industries was performed. After the initial study, in just a few months, several studies have appeared in the literature that exploit the advantages of the MARCOS methodology [13, 14, 16, 17, 29, 30] . The MARCOS method has undergone several extensions using fuzzy theories, gray theories, and D numbers [13, 14, 16] . An extension of the MARCOS methodology in a fuzzy environment was presented by Stankovic et al. [14] and Ilieva et al. [13] . In their study, Stankovic et al. [14] used fuzzy triangular numbers to represent the uncertainties that exist when analyzing road traffic risks. Ilieva et al. [13] also used fuzzy triangular numbers to represent uncertainty in the MARCOS model and demonstrated the application of the fuzzy MARCOS methodology for cloud service selection. Chakraborty et al. [16] extended the MARCOS method using D numbers for supplier selection in an iron and steel industry. D numbers were used to represent the uncertainties in the expert evaluation of the decision matrix criteria. In addition to extending the MARCOS method using fuzzy and D numbers, Badi and Pamucar [17] extended the MARCOS method using gray numbers and demonstrated the possibilities of applying the MARCOS-G methodology for supplier selection for a steelmaking company. In addition to application in an uncertain environment, Puška et al. [29] developed a multi-criteria framework for project management software evaluation. In the study [29] , the MARCOS methodology was used to assess alternatives, while the weighting coefficients of the criteria were defined based on subjective assessments of experts. Since the importance of insurance is evident for each country, various studies have been carried out in this area. Doumpos et al. [31] argued that the papers related to the financial performance of insurance companies could be generally classified into the following four groups: (i) papers that consider individual financial ratios, (ii) papers that examine the credit ratings of firms, (iii) failure prediction works, and (iv) studies on the efficiency of insurers [32] [33] [34] [35] . In recent years, however, studies using MCDM methods to select, evaluate, and rank insurance companies have been increasing exponentially [3, [36] [37] [38] [39] [40] [41] . Table 1 demonstrates some recent MCDM works in the field of insurance. As shown in Table 1 , these works have applied various methods like AHP, TOPSIS, DEA, Gray relational analysis (GRA), PROMETHEE, etc. Each one of these methods has its advantages as well as disadvantages. However, it is a fact that there is a need for reliable and robust models to better cope with ambiguity and vagueness for evaluating private health insurers in the age of COVID-19. Accordingly, unlike the others, this work posits an extension to MARCOS under the intuitionistic fuzzy environment (IF-MARCOS) methodology for the first time in the literature. The fuzzy set proposed by Zadeh [58] employs uncertainty in a mathematical format. Nonetheless, it can merely concentrate on the membership degree of ambiguous situations [59, 60] . It does not succeed in dealing with the non-membership degree of vague conditions. To fill this gap, Atanassov [61] introduced Intuitionistic Fuzzy Sets (IFS) as an effective way of coping with vagueness and imprecision due to the degree of hesitation in the system. To understand the following section, IFS is explained below [21, 62, 63] . Let a set X be a fixed universe of discourse and its subset which corresponds to the degree of hesitancy. It is evident that 0 ≤ π A (x) ≤ 1. In this paper, we are utilized to MCDM method to obtain the weight of each criterion with respect to the intuitionistic fuzzy method and intuitionistic fuzzy weighted averaging (IFWA) operator introduced by Xu [64] , and the linguistic variables are converted into intuitionistic fuzzy numbers (IFNs). The MARCOS technique introduced by Stevic et al. [65] is based on the measurement of choices and their ranking as a compromise solution. Although the MARCOS method is a powerful decision-making tool, it cannot express fuzziness and uncertainty information. It is, therefore, necessary to make the technique more capable with a fuzzy extension. The description IF-MARCOS method is defined as follows. Step 1 The linguistic assessments for the criteria and DMs are realized using Table 2 . We, therefore, obtain the weights of DMs as 0.285, 0.430, and 0.285, respectively. Let D = [P me ] n * f (e = 1, 2, . . . , f ; m = 1, 2, . . . , n) be the IF decision matrix of decision-makers. Here, P me indicates the assessment of dth about DM the jth criteria. P me is utilized by IFN, and it could be expressed that π Pme is the hesitation degree of π me is calculated as follows: . For example, suppose that DMs rate the first criterion (C1) as I, M, M, respectively. Then, aggregated µ, ϑ, and π of C1 are computed as follows: The linguistic evaluations for the alternatives are carried out utilizing Table 3 . Membership functions of the linguistic variables presented in Table 3 are illustrated in Fig. 2 . The IF has positive (IFPIS), which is τ + = (1, 0, 0) and negative ideal solution (IFNIS), which is τ − = (0, 1, 0). While IFNIS and IFPIS are defined by max and min operators, it is stated that there is no significant difference in their results [21] . Step 4. Calculate the distance measures A fuzzy normalized Euclidean distance equation is used for determining the distance measure [66] . δ + m and δ − m are utilized in these equations below to demonstrate positive and negative distance measures, respectively. For instance, δ + 1 , δ − 1 and CC 1 for C1 is calculated as follows: Step 5. Determine the closeness coefficient (CC) values CW m is the CC of the mth criterion, and it is defined utilizing IFPIS δ + m and IFNIS δ − m as follows: CC value of C1 can be calculated as follows: Step 6. Calculate the weights of criteria and alternatives The importance of each criterion is obtained from the CC values. It is noted that the total weights should be equal to 1, and normalization is applied to compute the finalized weights. After Steps 5 and 6, we get a decision matrix ⌣ D. Let CW values of benefit-type evaluation criteria be 0.616, 0.735, and 0.824, respectively. We use normalization to gain the relative weight of C1 as follows: Step The ⌣ AAI is the worst alternative, whereas the ⌣ AI is an alternative with the most acceptable performance. They are computed by applying Eqs. (7) and (8), respectively. It is noted that B consists of benefit-type criteria, while C consists of cost-type criteria. For example, let C1 be a benefit criterion, and CW values of three alternatives be 0.635, 0.216, and 0.756, respectively. Then we get: The normalized value ⌣ ζ ij of alternatives are obtained as follows. For example, the normalized value of C1 in relation to A1 is obtained as follows: Similarly, the normalized values of other alternatives are found to be 0.286 and 1.000, respectively. The weighted values for each alternative are calculated as follows. In Eq. (10), ⌣ w j represents the relative importance of jth criterion. For example, the weighted value of A1 as per C1 is computed as follows: Step 10. Create the For example, should the weighted decision matrix values of alternative A1 according to three criteria are 0.238, 0.107, and 0.143, respectively, ⌣ S 1 is obtained by some of these values, i.e. ⌣ S 1 = 0.238 + 0.107 + 0.143 = 0.488 Step 11. Determine the utility degrees of alternatives The utility degrees of alternatives are determined through Eqs. (12) and (13) . Let the sum of AI and AAI values be 1.000 and 0.438, respectively. Afterward, the utility degree of A1 is computed as follows: Step 12. Identify the utility function of alternatives By using Eq. (14), the utility functions of alternatives are computed. In Eq. (14), f represents the utility function of the ideal solution, whereas f represents the utility function as per the are calculated using Eqs. (15) and (16). For example, the ideal and anti-ideal solutions of A1 are calculated as follows, respectively: Finally, the utility function of A1 can be determined as follows: The utility functions of the remaining alternatives are calculated similarly. Step 13. Rank the alternatives Ranking the alternatives is realized in the last step based on the final values of utility functions. That is to say, and the most preferred alternative is the one with the highest utility value. Due to its contribution to economic stability and the environment of trust it emerged, the insurance industry has become an essential part of the financial sector in recent years. Additionally, the health insurance market, which is the subject of this study, is a large market and economic resource. About the literature review of Acharya et al. [67] , Adebayo et al. [68] , Alhassan et al. [69] , Habib et al. [70] , Choi et al. [71] , and Erlangga et al. [72] , the number of research on health insurance has remarkably increased recently, which emphasize the significance of this issue. Therefore, in this paper, we propose an IF MARCOS framework for selecting the best private health insurance company among those having the largest market share in Turkey. The flowchart of the proposed method is illustrated in Fig. 3 . Although health insurance covers illness, private health, health for foreigners, emergency health, supplementary health, and travel health products, this study is restricted to merely private health insurance. In this sense, ten private health insurance companies are examined for the present work. Based on the extensive literature review summarized in Table 1 , as well as the opinions and experience of five experts in the health care insurance sector, the most relevant criteria are specified as follows: The experts were: a health insurance director, a market development manager, a business development manager, a technical coordinator, and a marketing communication expert. As of 2019, the top 10 insurance companies in Turkey in terms of total premium production were included in the alternatives set and analyzed. In 2019, these companies carried out 94% of the total premium production in Turkey. The names of these insurance companies were kept confidential; thus, they were named A1, A2,. . . , A10. By the end of June 2020, in the field of health and sickness, they have had a market share of 4.11%, 1.83%, 7.91%, 5.24%, 34.32%, 2.16%, 0.54%, 22.44%, 0.78%, and 9.56%, respectively [73] . The solution steps using the proposed methodology are explained in detail below. Step 1 and 2. The survey questionnaire used to evaluate the criteria and alternatives is presented in the appendix (Table A. 1). The seven criteria' linguistic assessments are realized by the decisionmakers (DMs) using rating scales in Table 2 , which assess the Table 4 Linguistic assessments for the rating of the evaluation criteria. DM2 DM3 DM4 DM5 C1 M I M M I C2 I I I M M C3 VI I VI I I C4 I I I I M C5 M I I VI I C6 VI VI VI VI VI C7 VI VI VI I VI *M: Medium, I: Important, VI: Very important. Linguistic assessments for the rating of the alternatives. Evaluation criteria ten insurer alternatives as per the seven criteria using the rating scale in Table 3 . The linguistic evaluations for the criteria and alternatives are presented in Tables 4 and 5 . Step 3. The ratings for the DMs are defined by the committee utilizing Table 4 . Then Eq. (1) is applied to extract the weight of each DM. These weights are given in Table 6 . For example, the importance of the first DM is calculated in Box I. Step 4. The aggregated IF decision matrix demonstrated in Table 7 is obtained using Eq. (2). For example, aggregated µ, ϑ, and π of the first criterion are computed as follows: Step 5. By using Table 7 Table 8 . For example, while the IFPIS and IFNIS are τ + = (1, 0, 0) and 0.916 + 0.505 = 0.645 Step 6. As in Step 4, utilizing Table 5 , firstly, the values µ, ϑ, and π are found in this step. These values are given in Table 9 . Second, by using Table 9 and Eqs. (3)-(5), Table 10 is obtained. Step 7. With the help of Eqs. (7) and (8) and using CW values from Table 10 , we construct an extended decision matrix as presented in Table 11 . For example, since C1 is a benefit-type criterion, AI and AAI values for it are calculated as follows: Table 9 Aggregated µ, ϑ, and π values of alternatives as per each criterion. Aggregated IF decision matrix for alternatives. For C6, as a cost-type criterion, AI and AAI values are determined as follows: Step 8. Using Eq. (9), the normalized values for each criterion are computed. The normalized IF decision matrix is demonstrated in Table 12 . For example, the normalized value of C1 as per the A1 alternative is obtained as follows: Step 9. With the help of Eq. (10), the weighted values for each alternative are computed. Also, Tables 8 and 12 are considered to obtain these weighted values. The weighted IF decision matrix is shown in Table 13 . For example, the weighted value fro position A1-C1 is computed as follows: Step 10. In this step, Table 14 . Step 11. Via Eqs. (12) and (13), the utility degree of alternatives are computed. For example, the utility degree of A1 is obtained Utility degrees and utility functions of alternatives. Thus, the utility degrees of alternatives are given in the second and third columns of Table 14 . Step 12. In order to get the utility functions of alternatives, one should first compute the utility functions as per ideal and antiideal solutions through Eqs. (15) and (16) . For example, the ideal and anti-ideal solutions of A1 are calculated as follows, respectively: Afterward, the utility functions of each alternative are calculated with the help of Eq. (14) . The utility function of A1, for example, can be determined as follows: As a result, Table 14 presents an ideal solution, an anti-ideal solution, and the utility functions of alternatives evaluated. Step 12. Lastly, alternatives are ranked in descending order according to their utility functions. Put another way, the alternative having the most significant utility function is the best. As a result, alternative A5 is the best alternative, i.e., the most preferred insurance company. It is followed by A2, A4, A8, A10, A3, A1, A7, A6, and A9 . After obtaining the initial results in the MCMD model, the question arises of how subjectively defined input parameters affect the model results and what results are obtained by applying other multi-criteria models [74] . Therefore, an indispensable step in multi-criteria decision-making is to check the results' robustness and analyze the sensitivity of the obtained results to changes in the input parameters of the MCDM model [75] . Keeping in mind the literature's recommendations [76] [77] [78] [79] [80] [81] , in the following part, the sensitivity analysis and validation of the results were performed through three sections. In the first section, the influence of the change of weight coefficients of the decision-maker was performed. In the second section, the analysis of the impact of the change of the most important criterion on the ranking results was performed, and in the third section, the robustness of the obtained solution was checked by comparison with other MCMD techniques. The decision-makers' weighting coefficients were defined based on subjective assessments and were used for the fusion of the weighting coefficients of the criteria. Since the decisionmakers' (DMs) weights directly influence the determination of the criteria weight's values, it is necessary to perform an analysis of the impact of changes in their values on the final ranking results. In the following part, an experiment is presented. The changes in the value of the weight coefficients of the DM that have the greatest influence on decision making, i.e., those with the highest values of weight coefficients, are simulated. The , where w * The results show that the first three alternatives (A5, A2, and A4) have a good advantage over the remaining alternatives through all 50 scenarios, i.e., they represent a set of dominant alternatives. The worst alternative from the group (A9) remained the last ranked through all 50 scenarios. Alternatives A8 and A10 retained their ranks through scenarios S1-S24, re- Based on the presented analysis, we can generally conclude that the change in the decision-makers' weight coefficients' value may affect the final ranking results in the multi-criteria models. In this experiment, changes in the weight of the decision maker's criteria lead to minor changes in the alternative ranks, which shows that the obtained solution is stable and that there is a good advantage of a set of dominant alternatives over other alternatives. The influence of the change of weight coefficients on the ranking results was analyzed through an experiment in which 50 scenarios were formed. Through each of the scenarios, the value of the criteria weight of the most influential criterion (C6) was reduced by 2%, thus simulating the weighting factor's change in the interval w 6 ∈ [0.0016, 0.1626]. The values of the remaining criteria in the scenarios were proportionally adjusted to meet the condition ∑ n j=1 w j = 1. Therefore, new vectors of weight coefficients of the criteria were obtained (Fig. 6) , and their influence on the change of utility functions was analyzed in Fig. 7 . Based on the presented analysis (Fig. 7) , it can be noticed that the changes in the value of the weight coefficient of criterion C6 mostly affect the change in the rank of alternative A2, which is the second-ranked alternative in terms of initial rank. Changes in the value of the most influential criterion's weighting factor did not affect the difference in the remaining alternatives' ranks. Based on the presented analysis, we can conclude that the first-ranked alternative (A5) remained dominant through all 50 scenarios. It represents the best solution regardless of the changes in the weighting coefficients of the evaluation criteria. The A4 alternative retained its position in dominant options, as it ranked second-ranked or third-ranked through 50 scenarios. Simultaneously, it was confirmed that alternatives A6, A7, and A9 represent the worst solutions through all 50 scenarios. We can conclude that the alternative's initial rank is confirmed and credible despite the changes in some alternatives' positions. This statement is confirmed by Spearman's rank correlation coefficient, which shows a significant statistical correlation between the initial set of ranks and the ranks obtained through the scenarios. Spearman's correlation coefficient's average value through scenarios is 0.940, which shows a high correlation and confirms the initial solution's stability. Since intuitionistic fuzzy sets were used in this paper to deal with uncertainty and inaccuracy, three IF multi-criteria techniques were chosen to compare the results: intuitionistic fuzzy COPRAS (COmplex PRoportional ASsessment) technique [22] , intuitionistic fuzzy MABAC (Multi-Attributive Border Approximation area Comparison) technique [19] , intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) technique [23] . A comparative overview of the application of these intuitionistic fuzzy MCMD methodologies is shown in Fig. 8 . Based on the obtained results, it was confirmed that alternative A5 represents the best solution according to all MCDM methodologies. The results showed that the application of IF MARCOS and IF COPRAS multi-criteria techniques gives the same rank. Small differences in rank occurred with IF MABAC, and IF TOPSIS methods. However, these changes are not drastic, which is confirmed by Spearman's rank correlation coefficient, which is 0.976 for IF TOPSIS, and 0.988 for IF MABAC. The presented analysis proves the validity of the methodology proposed in this paper and that the proposed choice of alternative A3 is credible. This paper posits a multiple-criteria group decision-making methodology called IF-MARCOS, which aims to select the most acceptable insurance company in terms of health services among diverse alternatives considering several conflicting criteria. The proposed framework allows decision-makers to express their opinions and assessments with linguistic variables and enables various people to join by a robust technique to come to a final decision. Since MARCOS provides a compromise solution as per ideal and non-ideal solutions, satisfactory performance is achieved in a fuzzy environment. The main contributions of the work are summarized below: • The proposed approach ensures the selected insurance company meets the requirements of decision-makers. • The study suggested a novel MCGDM framework for modeling and analyzing evaluation information with a high degree of ambiguity. • Due to its intuitionistic fuzzy sets basis, the proposed model can better capture the inconsistency, deficiency, and uncertainty of human judgment. • Some approaches based on intuitionistic fuzzy sets could be seen from relevant literature; however, as far as the authors' knowledge, applying these methodologies within the context of insurance company evaluation and selection has not been conducted. • The salient characteristic of the proposed approach is that it considers the importance of each decision-maker. In most decision support tools, the decision-makers' importance is ignored, i.e., their knowledge, opinions, and experience are equally important. • In this work, criteria weights were assigned by the decisionmakers through linguistic variables. Then, linguistic criteria weights were transformed into suitable intuitionistic fuzzy numbers. Via the IFWA operator, each decision-maker judgment was merged to calculate the aggregated criteria weight. Finally, these weights were directly used in IF-MARCOS along with the aggregated IF rating of criteria. • The IF-MARCOS framework is based on experts' opinions in which evaluation information is exceptionally crucial. Therefore, it can be used in problems where experts have enough information on the issue. Although this study contributes to the literature, it also has some limitations. The limitations of this work are emphasized below: • The difficulty accessing the information and data needed to implement this approach could be one of the limitations. • In this paper, the ranking order of insurance companies has been validated by some MCDM methods under only IF environments. The lack of comparison with other fuzzy set extensions (hesitant, spherical, neutrosophic, picture, etc.) may be limited. • The ranking results obtained in this study are based on the opinions and assessments of five experts. Different ranking results may arise in the analysis to be conducted according to various experts' considerations. It is evident that decision-making tools that enable the processing of uncertain group information require complex mathematical formulations, which, to some extent, makes them challenging to understand. This group of tools includes the multi-criteria model presented in this paper. The development of such models goes through two phases. In the first phase, after the mathematical formulation of the model, the model is tested through the conceptual version of the software and implementation to solve complex real-world problems. This study represents the first phase of model development. The software was developed within the Microsoft Excel program, while Matlab 2018 was used to visualize the sensitivity analysis results. The Excel program was used as a database in which expert assessments of alternatives were processed. Visual Basic (VB) code for validation of results and sensitivity analysis of multi-criteria Methodology implemented within the Excel program. Visual Basic code for analyzing the impact of changes in weight coefficients on ranking results is presented in Appendix B. In addition to the proposed VB code, a unique VB code was developed to analyze the impact of experts' weight coefficients on ranking results. As this is the first phase of development that involves testing and implementing a decision support system, the authors have not yet developed a user-oriented interface. The development of a user-oriented interface is planned for the second phase of model development. Within that stage, the full implementation of the multi-criteria framework in the decision-making system will be achieved. It is planned to develop an online decision-making system that will be easy to use without requiring detailed knowledge of the model's mathematical formulations. That will make this tool acceptable for use by a large number of users. The model's adaptability is planned in terms of the number of experts who can participate in the research. Also, adaptability can be updated in terms of the number of criteria and alternatives for evaluation. One of the significant limitations of the proposed multi-criteria model is the impossibility of online learning of the IF MARCOS algorithm. One possibility to improve this model's adaptability is to adapt the IF membership functions of the linguistic variables used to represent expert preferences. This improvement would allow a more objective presentation of individual expert preferences depending on the problem's knowable level. Therefore, it is necessary to focus future research on increasing the adaptability of linguistic variables' membership functions depending on the changing of experts' weight coefficients. Future research should also focus on developing artificial intelligence (AI) based algorithm trained by the IF MARCOS algorithm. Such an AI-based algorithm would have the ability to generalize future decisions efficiently. Increasing health needs and health expenses with the aging population, the increase in average life expectancy, and patient expectations in parallel with technology development increase the pressure on financing health expenses. In the age of COVID-19, the importance of private health insurance has been better understood. From this perspective, analyzing insurance companies' performance in this process is an essential issue for customers, managers of insurance companies, and politicians. In this respect, this study aims to provide a decision support tool. Combined the intuitionistic fuzzy sets with the MARCOS method, a useful, efficient, easy to use, flexible, and robust decision tool is developed to measure insurance companies' performance in health services. In this paper, ten insurance companies in Turkey are evaluated by five experts from the insurance sector as per seven criteria determined by the extensive literature review and expert opinions through the IF-MARCOS approach. The findings execute that the payback period (0.163), premium price (0.160), and network (0.156) are the most significant factors for the insurance sector to select the most acceptable insurance company. In this research, a sensitivity analysis is performed as well. The sensitivity analysis indicates the validity of the introduced IF-MARCOS model. As per this analysis, the proposed methodology is also well-consistent with existing ones (IF-COPRAS, IF-MABAC, and IF-TOPSIS). Further, the ease of calculation and increase of the approach's steadiness is the proposed framework's superiorities over the other methods. The sensitivity analysis also states and identifies the effect of various weights of criteria and decision-makers on the insurance company evaluation. Likewise, its outcomes also prove the stability and validity of the introduced framework. Thus, it has been gathered that the IF-MARCOS methodology is relatively successful in assessing evaluation criteria and alternatives in real-world problems and reflecting human judgments in the best way. Finally, the introduced approach can be a reliable decision technique for other compelling issues faced by managers, politicians, and shareholders. Managerial implications are also offered to carry out the suggested methodology better. Through the above analysis as well as sensitivity and validation tests, we can indicate that the proposed IF-MARCOS methodology has the following advantages: (1) It not only takes the imprecise information into account but also deals with different importance of decision-makers; (2) With different criteria weights, we can obtain various ranking outcomes and the most acceptable alternative; and (3) Because the criteria weights are determined as per the opinions of experts, firms can improve their evaluation process through the proposed IF-MARCOS approach. MARCOS technique with intuitionistic fuzzy set information has a considerable chance of success for MCDM problems. Future research may be applied to various decision-making problems such as supplier selection, renewable energy sources' evaluation, project selection, sustainability assessments, etc., in engineering, finance, management science, and other scientific applications. It could be recommended to consider different criteria for evaluating insurance companies. The proposed model could be attempted to operate under interval-valued IFS. In the future, interval-valued IFNs or trapezoidal IFNs could be employed by researchers. Moreover, D numbers, Z numbers, spherical fuzzy sets, hesitant fuzzy sets, and picture fuzzy sets can be applied for future works. The introduced framework can be implemented under uncertainty sets such as gray numbers, rough numbers, D numbers, Z numbers, and other extensions of fuzzy sets (spherical, hesitant, neutrosophic, picture, etc.). All participants were asked to sign an online informed consent. 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