Multicriteria Decision Analysis of Health Insurance for Foreigners in the Czech Republic

Multicriteria decision making (MCDM) is the superclass of model in most readily understandable branch of basic leadership. It is a branch of a general class of operations research (OR) models which manages choice issues under the nearness of various choice criteria. MCDM techniques have advanced to oblige different sorts of utilizations. Many techniques have been produced, with even small varieties to existing strategies bringing about the production of new branches of examination. The aim of this chapter is to present selected MCDM methods and application in case of health insurance decision problems.


Introduction
Multicriteria decision making (MCDM) has seen a staggering measure of utilization. Its part in various application territories has expanded fundamentally, particularly as new techniques are created and as old strategies make strides. This chapter breaks down a few basic MCDM strategies and decides their relevance by assessing their relative points of interest and burdens. A survey of the utilization of these strategies and an examination of the development of their utilization after some time is then performed. The objective of this chapter is through setting up a situation as case study which uses the MCDM methods (WSA, MAPPAC, TOPSIS, and ELECTRE) to choose the best and most appropriate health insurance (UNIQA, SLAVIA, MAXIMA, and VZP) for international policyholder visiting the Czech Republic.

Applications of MCDM approaches in decision problems
MCDM is a branch of a general class of operations research (OR) models which deals with decision problems under the presence of a number of decision criteria. In light of the distinctive purposes and diverse information sorts, MCDM is isolated into multiobjective decision making (MODM) and multiattribute decision making (MADM). Within the field of OR, the development of MCDM is based on the simple finding in terms of environment: criteria, goals, attributes, objectives, and decision matrix.
The MCDM field is given to the advancement of suitable procedures that can be utilized in circumstances where different clashing choice elements must be considered all the while.
Customary enhancement, measurable, and econometric investigation approaches utilized inside the money-related building connections regularly taking into account the presumption that the considered issue is all around postured, very much defined with respect to the truth included, and they as a rule consider the presence of a solitary target, assessment standard, or perspective that underlies the led examination. In such a case, the arrangement of monetary issues is anything but difficult to acquire. In any case, in reality, the demonstrating of monetary issues depends on an alternate sort of rationale mulling over the accompanying components: • The presence of various criteria • The clashing circumstance between the criteria • The mind boggling, subjective, and not well-organized nature of the assessment process • The presentation of money-related chiefs in the assessment process Financial related and operation specialists have as of late embraced this creative, thorough, and reasonable point of view, with results. On the premise of the diverse creators' view that it is conceivable to recognize primary reasons which have persuaded a change of perspective in the displaying of the money-related issues: • Formulating the issue as far as looking for the ideal, objective get included in an exceptionally limit dangerous, regularly unessential to the genuine choice issue.
• The diverse monetary choices are taken by the people and not by the models; the leaders get increasingly profoundly included in the basic leadership process. With a specific end goal to take care of issues, it gets to be important to think about their inclinations, their encounters, and learning.
• For monetary choice issues, for example, the decision of venture undertakings, the portfolio choice, and the assessment of business disappointment hazard.
MCDM methodologies are appropriate for the investigation of a few money-related basic leadership issues. The broadened way of the components that influence monetary choices, the many-sided quality of the money related, business and financial situations, the subjective way of numerous budgetary choices are just a percentage of the elements of money-related choices which are as per the MCDM demonstrating system.

Case study: MCDM of health insurance products in the Czech Republic
Everybody who visits the Czech Republic needs sufficient proof of health insurance. If you are a nonEU national and do not work for a Czech employer, you need to get travel health insurance before coming to the Czech Republic. Based on this background, the subject of the case study is an international tourist who wants to visit the Czech Republic and hence needs to make a decision for health insurance.

Health insurance for foreigners in the Czech Republic
Foreign nationals in the Czech Republic are required to have valid health insurance. There are two types of health insurance that are described below:

Public health insurance
The following people have a legal right to public health insurance: • Anyone with permanent residency status in the Czech Republic • Employees whose employer is based in the Czech Republic

Commercial (private) health insurance
There are two varieties of commercial health insurance: • Comprehensive medical insurance: it is suitable for foreigners who intend to stay for 90 days or longer and require long-term visa or long-term stay, or request an extension of a visa or residence permit. This health insurance is similar to public health insurance.
• Basic medical insurance: it covers necessary treatment and hospitalization which cannot be postponed at all health care facilities. This insurance is recommended for individuals who do not fall under the public health system and plan only short-term stay. The insurance covers costs incurred as a result of an accident or sudden illness during the stay, including any costs related to repatriation to the country that issued the travel document or to the country where the foreigner has legal residence. Minimal coverage must be EUR 60,000 excluding any financial contribution to the aforesaid costs on the part of the insured person. See euraxess.cz.

Input data interpretationweight calculation criteria (SAATY method)
Usually, before selecting the best and most appropriate health insurance, policyholder needs to consider the items of premium, claims, and minimum coverage maturity as criteria. Also, there are four insurance companies who provide health insurance for foreigner as alternatives, which are Pojišťovna VZP, a.s., UNIQA pojišťovna, a.s., MAXIMA pojišťovna, a.s., and SLAIA pojišťovna (see Table 2).
In the process of making multiattribute decision, it should set weight for different criteria by using direct and indirect method, and in this case study will use the SAATY pairwise comparison method (Thomas, 2004(Thomas, , 2006(Thomas, , 2008,which is a kind of indirect method created by Thomas L. Saaty. Table 3 presents a typical criteria matrix C. Table 3 presents the preference on criteria i to criteria j. Which is also called the ratio w i =w j , and the preference can be judged from 1 to 9 in fundamental scale of absolute number which will be shown in Table 4, C i, j ∈½ 1 9 , 9 and C i, j Á C j, i ¼ 1. Hence, if preferred i to j, then C i, j > 1; if preferred j to i , then C i, j < 1; if preferred the same preference on criteria i to j, then C i, j ¼ 1.  Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation 1.1-1.9 When activities are very close a decimal is added to 1 to show their difference as appropriate A better alternative way to assigning the small decimals is to compare two close activities with other widely contrasting ones, favoring the larger one a little over the smaller one when using the 1-9 values

Reciprocals of above
If activity i has one of the above nonzero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i A logical assumption

Measurements from ratio scales
When it is desired to use such numbers in physical applications. Alternatively, often one estimates the ratios of such magnitudes by using judgment

WSA method
Weighted sum analysis method is based on the linear utility function construction at the scale 0-1. The worst variant based on the given criteria will have utility 0; the best variant will have utility 1 and other variants will have utility between both extreme values. WSA derives from the principle of utility maximization; however, the method presumes only linear function. For the maximization case, the best alternative is the one that yields the maximum total performance value.
First, the normalized criteria matrix will be created R ¼ ðr ij Þ, whose elements are derived from criteria matrix Y ¼ ðy ij Þ, based on where r ij is variant's utility of X i when evaluated based on criteria Y j , r ij represents corresponding values from initial criteria matrix, D j is the lowest criteria value of Y j , and H j is the highest criteria value of Y j . This matrix represents matrix of utility values from ith variant based on jth criteria. Criteria values are linearly transformed that r ij ∈〈0, 1〉. D j corresponds to minimal criteria value of column j and H j corresponds to maximum criteria value in column j.
In case of minimization criteria normalization of column in matrix can be executed as If it is necessary that all criteria in the matrix must be maximized then before executing standardization/normalization of matrix, it is necessary to recount elements in the column as follows Meaning, deduct from the current highest element maximum H j−min in the given column progressively with all other elements and by this the column with minimization criteria will be transformed to maximization. When using additive multicriterial utility function the variance utility a i is then equal to Variant that reaches the maximum utility value is selected as the best, alternatively it is possible to rank the variants based on descending utility values, see Iveta and Jana (2015). The calculation of WSA method is done by the following procedures.
Obtaining the utilities and the preferred order of alternatives can be expressed as: A1 > A2 > A3 > A4. Hence, on the basis of the results above, the optimal choice is: UNIQA > SLAVIA > MAXIMA > VZP.

MAPPAC method
Multicriterion analysis of preferences by means of pairwise actions and criterion comparisons (MAPPAC) method, first introduced by Matarazzo (1986), is based on the comparison of pairs of feasible actions taking into account all possible pairs of criteria. The proposed method, known as MAPPAC, is based on a pairwise comparison of alternatives relative to each pair of criteria, defining the two relations P (preference) and I (indifference), which constitute a complete preorder. Moreover, by aggregating these preferences, it is possible to obtain a variety of relations on a set of feasible actions (Paruccini and Matarazzo, 1994). See Salt (2011).
The MAPPAC method has three assumptions (Matarazzo, 1990): • For each K i a quantitative, V ij can be assigned to each alternative, a j representing the performance of a j with respect to K i ; • A quantitative value V ij c; • An be assigned to each alternative, a j on the basis of each criterion K i ; • The value VðV ij Þ of each V ij can be quantified on the interval [0,1]; and • The criteria are mutually difference and independent.
For each K i a value V ij is assigned to each a j representing the performance of a j on the basis of K i . A numerical weight w i is assigned to each K i representing the importance of K i with ∑ n n¼1 w i ¼ 1. For each K i representing the importance of vðv ij Þ to each V ij with 0≤vðv ij Þ≤1. see Hassan (2013). The calculation of MAPPAC method is done by the following procedures. The process of modified input data is the same in Table 6.
Obtaining the utilities and the preferred order of alternatives can be expressed as: A2 > A1 > A3 > A4. Hence, on the basis of the results above, the optimal choice is: SLAVIA > UNIQA > MAXIMA > VZP (Tables 7-9

TOPSIS method
The technique for order of preference by similarity to ideal solution (TOPSIS) is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and the longest distance from the negative ideal solution. It is a method of compensatory aggregation that compares a set of alternatives by identifying weights for each criterion, normalizing scores for each criterion and calculating the distance between each alternative and the ideal alternative, which is the best score in each criterion. The TOPSIS method is expressed in a succession of six steps as follows: x 2 ij s i ¼ 1, 2, :::, m and j ¼ 1, 2, :::, n: 2. Calculate the weighted normalized decision matrix v ij ¼ r ij w j i ¼ 1, 2, :::, m and j ¼ 1, 2, :::, n: where w j is the weight of the jth criterion or attribute and ∑ n j¼1 w j ¼ 1.

Determine the ideal (A*) and negative ideal (A -) solutions
4. Calculate the separation measures using the m-dimensional Euclidean distance. The separation measures of each alternative from the positive ideal solution and the negative ideal solution, respectively, are as follows 6. Rank the preference order.
The calculation of TOPSIS method is done by the following procedures (Tables 10 and 11). Obtaining the utilities and the preferred order of alternatives can be expressed as: A1 > A2 > A3 > A4. Hence, on the basis of the results above, the optimal choice is: UNIQA > SLAVIA > MAXIMA > VZP.

ELECTRE III method
The ELECTRE (for elimination and choice translating reality; English translation from the French original) method was first introduced in Benayoun et al. (1966). The basic concept of the ELECTRE method is to deal with "outranking relations" by using pairwise comparisons among alternatives under each one of the criteria separately. The outranking relationship of the two alternatives A i and A j denoted describes that even when the ith alternative does not dominate the jth alternative quantitatively, then the decision maker may still take the risk of regarding A i as almost surely better than A j in Roy (1973). Alternatives are said to be dominated, if there is another alternative which excels them in one or more criteria and equals in the remaining criteria.
The ELECTRE method begins with pairwise comparisons of alternatives under each criterion. Using physical or monetary values, denoted as g i ðA j Þ and g i ðA k Þ of the alternatives A j and A k , respectively, and by introducing threshold levels for the difference g i ðA j Þ−g i ðA k Þ, the decision maker may declare that he/she is indifferent between the alternatives under consideration, that he/she has a weak or a strict preference for one of the two, or that he/she is unable to express any of these preference relations. Therefore, a set of binary relations of alternatives, the socalled outranking relations, may be complete or incomplete. Next, the decision maker is requested to assign weights or importance factors to the criteria in order to express their relative importance.
Through the consecutive assessments of the outranking relations of the alternatives, the ELECTRE method elicits the so-called concordance index, defined as the amount of evidence to support the conclusion that alternative A j outranks, or dominates, alternative A k , as well as the discordance index, the counterpart of the concordance index. Finally, the ELECTRE method yields a system of binary outranking relations between the alternatives (Tables 12  and 13). The calculation of ELECTRE method is done by the following procedures. The first process of modified input data is the same in Table 6.
Obtaining the utilities and the preferred order of alternatives can be expressed as: A1 > A2 > A3 > A4. Hence, on the basis of the results above, the optimal choice is: UNIQA > SLAVIA > MAXIMA > VZP.

Discussion and summary
Using the Borda method to rank the results obtains the most appropriate insurance for policyholder. The Borda method is an election method in which the voters rank options or candidates in order of preference: the highest Borda count wins.

Conclusion
Various MCDM techniques have been developed and used in the course of recent years. As of late, on account of easement cause by driving development, consolidating diverse techniques has ended up ordinary in MCDM. The blend of numerous techniques addresses gaps that might be found in specific strategies. These strategies, alongside the techniques in their unique structures, can be to a great degree fruitful in their applications, just if their qualities and shortcomings are appropriately surveyed. This chapter illustrates the case study of MCDM methods and evaluation for solving the problem which select the optimal choice of health insurance for foreigners who are willing to visit the Czech Republic.