DIBR–DOMBI–FUZZY MAIRCA Model for Strategy Selection in the System of Defense

Strategic management has applications in many areas of social life. One of the basic steps in the process of strategic management is formulating a strategy by choosing the optimal strategy. Improving the process of selecting the optimal strategy with MCDM methods and theories that treat uncertainty well in this process, as well as the application of other and diferent selection criteria, is the basic idea and goal of this research. Te improvement of the process of the aforementioned selection in the defense system was carried out by applying a hybrid model of multicriteria decision-making based on methods defning interrelationships between ranked criteria (DIBR) and multiattributive ideal-real comparative analysis (MAIRCA) modifed by triangular fuzzy num-bers–“DIBR–DOMBI–Fuzzy MAIRCA model.” Te DIBR method was used to determine the weight coefcients of the criteria, while the selection of the optimal strategy, from the set of ofered methods, was carried out by the MAIRCA method. Tis was done in a fuzzy environment with the aim of better treatment of imprecise information and better translation of quantitative data into qualitative data. In the research, an analysis of the model’s sensitivity to changes in weight coefcients was performed. Additionally, a comparison of the obtained results with the results obtained using other multicriteria decision-making methods was conducted, which validated the model and confrmed stable results. In the end, it was concluded that the proposed MCDM methodology can be used for choosing a strategy in the defense system, that the results of the MCDM model are stable and valid, and that the process has been improved by making the choice easier for decision makers and by defning new and more comprehensive criteria for selection.


Introduction
Te basic prerequisite or the "key" for the good business of any organization is quality management. Tere are diferent defnitions of management, depending on the approach, among them that management is "efective knowledge, which is applied in a continuous process: planning, organizing, leading, and controlling business activities to achieve the organizational purpose and goals, so that an organization can be efective and efcient" [1]. It is also defned as the process of performing certain functions, to provide, distribute and efciently using human and other resources, to achieve a previously established goal [2]. Considering today's dynamic environment, the organization must ensure vitality; that is, the management must react promptly and infuence new changes with its actions, inducing strategic thinking about the goals of the organization, as well as about the ways of their realization. For the organization to successfully respond to environmental challenges and changes, various methods, concepts, tools, and techniques must be used in the process of strategic management, such as portfolio concept, scenario method, cost-beneft analysis, gap analysis, SWOT or TOWS matrices, and diferent software tools. [3]. Also, the mentioned changes require a strategic vision of organizational development, which leads to a new scientifc discipline called strategic management.
Strategic management represents "a management discipline that considers the process of formulating and implementing a strategy to achieve the long-term goals of the organization" [4]. Te goal of strategic management is to afrm the company's proactive attitude towards the environment with a strong emphasis on the need for timely recognition and management of changes. Strategic management represents a way to reduce or completely eliminate resistance to changes that do not allow creating a diference between the organization's capabilities and the needs of the environment [5].
Strategic management is an iterative process, and it consists of several steps: (a) strategic assessment, (b) strategic direction, (c) strategy formulation, (d) strategy implementation, and (e) strategic control [6,7]. In this paper, the focus is on the third step, which is the formulation of the strategy. To develop a quality strategy, the optimal one must be selected from the set ofered by the accepted methodology: development of multiple strategy variants, evaluation of strategies, and selection of the optimal strategy. Te process of choosing the optimal strategy until now was realized through expert opinions, with the use of a small number of criteria that did not fully consider all the essential characteristics of the optimal strategy and that it did not include the more serious application of MCDM methods. In order to improve the mentioned methodology, the need for this research was created through the implementation of multicriteria decisionmaking methods in this process and the implementation of more comprehensive criteria for selection.
Te objectives of the paper are as follows: (i) Improvement of the existing process of strategic management in the part related to the selection of the optimal strategy in the defense system, through the introduction of new selection criteria (ii) Improvement of the aforementioned process through the introduction of the MCDM model based on the DIBR and MAIRCA methods (iii) Validation of the proposed MCDM model and confrmation of its possible use in the strategic management process for strategy evaluation and optimal selection In this research, the MCDM hybrid model was developed to choose the optimal defense strategy in the Republic of Serbia (RS), as a "basic document for the projection of development and the functioning of the defense system" [8]. Until now, this choice was usually made based on suitability, feasibility, and acceptability criteria in the seventh phase of strategy development, i.e., in the phase of strategy verifcation (evaluation) [8], without application or more signifcant application of MCDM methods. Presented model used the method defning interrelationships between ranked criteria (DIBR) and fuzzifcation method multiattributive ideal-real comparative analysis (MAIRCA), with the use of the Dombi aggregation operator for aggregating the opinions of experts and new criteria for selection.
Te followings are the practical and scientifc key contributions of this research: (i) Systematization of the criteria that infuence the choice of optimal strategies in the defense system of the Republic of Serbia was carried out (ii) Te weight of the defned criteria was carried out (iii) A mathematical model for decision-making support was created, which quantifes the uncertainties accompanying this process (iv) MCDM methods in group decision-making were used to create the mathematical model Te paper consists of six parts. After the introduction, a brief analysis of the literature related to the research problem and the methods used was performed. Te used methods and criteria are described in the third part. In the fourth part, the presentation of the case study is carried out with the defnition of the alternatives, the calculation of the weight coefcients, and the selection of the best alternative. In the sixth part, the robustness of the presented model was checked, and at the end of the paper, concluding considerations are given.

A Brief Literature Review
Te mathematical decision-making models have found application in a large number of diferent areas of human activity [9][10][11][12][13][14][15][16]. Te authors of the presented research used diferent MCDM methods, in their basic or modifed form, both for determining weighted coefcients of the criteria and for choosing the optimal alternative from the set of proposed ones.
Te modern development of multicriteria decisionmaking (MCDM) methods has led not a small number of researchers to study the selection of strategies using various mathematical models. Te problem of strategy selection using the MCDM method has been discussed in quite a few works. A part of those works is shown in Table 1.
As can be seen from Table 1 and other researches in the feld of strategy selection, for the selection of diferent strategies from diferent areas, diferent MCDM methods were used, among which the TOPSIS method stands out as the most frequent, with diferent modifcations, that is, theories that treat uncertainty well. Also, diferent criteria were used for this selection. None of these studies use the criteria, neither methods nor methodology presented in this paper. Also, the DIBR-MAIRCA model has not yet been used in any MCDM model. Te aforementioned represents a novelty for this article compared to existing studies.
Considering that it is DIBR method a relatively new method for defning the weight coefcients of the criteria, there is not a large number of studies in which this method has been applied. Te analysis of the literature considering this method is given in Table 2.
Based on the analysis of the papers listed in Table 2, which include all published papers in which the DIBR method was used, it can be concluded that the DIBR method has not yet been used to determine the weight coefcients of the strategy selection criteria, in any area, and that it has not yet been applied in the model with the MAIRCA method.
Te usage of the MAIRCA method is given in Table 3.

Research Methodology
To solve the problem of optimal strategy selection from the set proposed in the defense system, the MCDM model was created, which is presented in Figure 1. Te model has three phases, within which two steps were implemented. Te initial phase includes the defnition of the criteria based on which the evaluation of alternatives (strategies) was performed and defning their weight coefcients to quantitatively determine their impact on the fnal ranking. In the specifc case, to calculate the weight coefcients of the criteria, the DIBR method was used. Tis method, its mathematical apparatus, uses comparisons of criteria by importance, obtained by the opinions of experts in the subject area.
After the implementation of the previous phase, the second phase was performed to select the optimal alternative (strategy). Te aforementioned choice is made using the Fuzzy MAIRCA method, where the values of the alternatives for each criterion are fuzzifed.
Given that errors can occur in any decision-making process, a sensitivity analysis of the model was performed by changing the weight coefcients of the criteria and comparing the ranking results with the results of other MCDM methods.
Te problem of choosing an optimal strategy required the application of methods that take uncertainties seriously. Considering the simplicity of the mathematical apparatus and the purpose of the methods, the DIBR-Fuzzy MAIRCA model was applied in this study. First of all, it is necessary to defne the criteria that condition the subject choice, which is described in the next part of the paper.

Defnition of Criteria.
Starting from the fact that a good strategy should balance goals, ways, and means; take care of the strategic environment; properly assess risk; minimize reliance on assumptions; be clear and feasible; and be creative and capable of change. Miller [45] defnes six criteria for the selection (evaluation) of proposed strategies, as opposed to established evaluation criteria (suitability, feasibility, acceptability): Criterion 1 (C1)-Balance: Does the strategy balance ends with ways and means?-It implies answers to the following questions: Does the strategy clearly articulate its goals, which must be measurable? Does the strategy suggest appropriate ways to achieve the goal? Does the strategy have the means to support achieving the goals, i.e., is it feasible? Does the strategy have internal consistency, that is, the alignment with the strategic goals of the organization or the state? Criterion 2 (C2)-Awareness: Does the strategy include an understanding of the strategic environment?-Tis criterion provides answers to the following questions: Does the strategy properly evaluate the state's place in the international system? Does the strategy include the interests and potential strategies of other actors? Does the strategy assess trends in the strategic environment? Criterion 3 (C3)-Honesty: Does the strategy properly assess risk?-It refers to the risks that come from the environment and gives an answer to the following questions: Does the strategy identify the risk and provide options for solving it? Does the strategy identify the risk of doing nothing? Does the strategy count on dramatic success, that is, does it include options for dealing with greater-than-expected success? Criterion 4 (C4)-Parsimony: Does the strategy minimize its reliance on assumptions?-to get an answer to
Application and reference Methods Solving the problems of the circular economy concept [29] DIBR, fuzzy Dombi CoCoSo Choosing the optimal location for the installation of a heavy launch bridge [30] DIBR, Fuzzy MARCOS Selection of antitank missile system [31] Rough DIBR, rough MABAC To prioritize sustainable mobility sharing systems in order to promote sustainability and nurture the concept of shared mobility [32] Fuzzy DIBR, fuzzy-rough EDAS For the selection of alternative priorities for zero-emission zone logistics [33] DIBR, CoCoSo, type-2 neutrosophic numbers Discrete Dynamics in Nature and Society Application and reference Methods Optimal selection of supplier [34] BWM, MAIRCA Optimal choosing of landing operations point [35] IVFRN MAIRCA To improve the risk process in failure mode and efect analysis [36] FAHP, FMAIRCA Coronavirus vaccine selection in the age of COVID-19 [37] IF-MAIRCA For the analysis of the real sector from the economic and fnancial aspect in Turkey [38] CRITIC, MAIRCA Optimal selection of automobile engine oil [39] BWM, FUCOM, MABAC, MAIRCA MCDM approach when using powder-mixed electrical discharge machining of cylindrically shaped parts in 90CrSi tool steel [40] MARCOS, TOPSIS, MAIRCA For the fnancial performance measurements of companies in the BIST electricity index [41] MAIRCA For selecting an appropriate energy storage technology for India [42] Linear diophantine hesitant fuzzy sets (LDHFS), SOWIA, MAIRCA To prioritize the critical success factors of the use of blockchain technology for the agri-food sector [43] ANP, MAIRCA To prioritize industrial fltration technologies [44] q-Rung orthopair fuzzy sets, MAIRCA

Phase 1 Defining the criteria and their weight coefficients
Phase 2 Selection of the optimal alternative (strategy)

Phase 3 Sensitivity Analysis and Comparative Study
Step 1.1 Defining criteria Step 1.2 Application of the DIBR method and the Dombi operator to calculate of the weight coefficients of the criteria Step 2.2 Application of the Fuzzy MAIRCA method and the Dombi operator to select the optimal alternative (strategy) Step 3.1 Defining 15 different scenarios and analyzing the sensitivity of the model to the change in the weight coefficients of the criteria Step 2.1 Identification of alternatives (strategies) Step 3.2 Comparison with other methods check whether the strategy is economical from the following questions: Does the strategy identify its assumptions? Does the strategy have to make assumptions about these six evaluation criteria? Does the strategy make the right assumptions? Criterion 5 (C5)-Elegance: Is the strategy clear and feasible?-Te previous four criteria require the expert to be a critical thinker-to analyze the strategy and its constituent parts, while this and the following require the expert to be a more creative thinker, i.e., to answer to the following questions: Does the strategy ofer clear choices to decision makers? Does the strategy give clear direction to those who will implement it? Does the strategy require secrecy? Criterion 6 (C6)-Creativity: Is the strategy innovative and capable of change?-It implies answers to the following questions: Is the strategy creative? (a creative strategy, defned as one that is unexpected, will have a greater chance of success than one that is uncreative); Is the strategy adaptable? Is the strategy fexible? Adaptability refers to incorporating alternative options into the strategy, while fexibility means that the strategy can be adjusted when faced with unexpected change.
Te criteria are listed according to their signifcance, from the most signifcant to the least signifcant, based on the agreed opinion of experts. All criteria are qualitative and beneft type of criteria, and the ranking and determination of the signifcance of the criteria was performed by fve subjectmatter experts. Qualitative descriptions of the criteria were converted into quantitative data using a three-or four-level scale, depending on the number of questions that need to be answered, as well as the degree of conviction of the decision maker in the statements made. For example, for criterion C4 (Parsimony) to be fully satisfed, the strategy must provide answers to four questions (Does the strategy identify its assumptions? Does the strategy have to make assumptions about these six evaluation criteria? Does the strategy make the right assumptions?). If the proposed strategy answers three questions, the value of the alternative is 3, and if it gives an answer to two questions, the value is 2. Te evaluation of alternatives (strategies) according to each of the defned criteria by the experts is shown as, for example, (3 : 70), where 3 represents the previously described evaluations of alternatives, and 70 represents the level of expert confdence in the given evaluation in percentages. Te DIBR method was used to defne the weight coefcients of the mentioned criteria.

DIBR Method.
Te DIBR method was frst presented by Pamučar et al. [29]. Te implementation of the DIBR method is presented as follows [29]: Step 1. Ranking of Defned Criteria. If n indicates the number of defned criteria, then the set of defned criteria can be displayed as a set C � C 1 , C 2 , ..., C n .
For the sake of easier presentation of the method, the following signifcance of the criteria is assumed where the criterion has the greatest importance; that is, the criterion C n has the lowest importance.
Step 2. Comparison of Defned Criteria. Te comparison values defned by the decision maker or expert e (where 1 ≤ e ≤ ε) can be marked as ϑ e i−1,i , where i ∈ (1, 2, 3, ..., n). In each comparison of criteria, the total value of 100% signifcance is distributed to the two criteria that are the subject of comparison. For example, if the relationship between the criteria C 2 and C 3 is equal to 0.4, that is, ϑ e 2,3 � 0.4, this implies that the importance of the criterion C 2 equals 60%, while the criterion C 3 equals 40%. Tis relationship between the criteria is also shown mathematically by the following: , ...
where equation (4) represents the control relation of the relationship of the other criteria.
Step 3. Defning Relations. Using equation (1), the value of the weight coefcient of the criteria C 2 can be defned, which equals By applying equations (1) and (2), the weight coefcient of the criteria C 3 can be defned, as follows: In the end, by applying equations (1) to (4), the value of the criterion C n is found.
Step 4. Calculation of the Weight Coefcient of the Most Signifcant Criterion. If it is assumed that the sum of the weight coefcients is equal to one, then according to equations (5)- (7), that relation can be presented as follows: Discrete Dynamics in Nature and Society Equation (8) has one unknown, namely w 1 , which is calculated as follows: After calculating the weight coefcient of the most signifcant criterion, the conditions were met to defne the weight coefcients of the other criteria using equations (5)-(7).
Step 5. Control of Decision Makers' Preferences. Based on equation (4), the ratio of the most signifcant and the least important criterion (ϑ 1,n ′ ) can be calculated, which is calculated as follows: If the values of the calculated ratio (ϑ ′ 1,n ) and the relationship assigned by the decision maker (ϑ 1,n ) are roughly the same, then there is consistency in the opinions of decision makers in the process of evaluating the importance of the criteria. If the value deviation of ϑ 1,n and ϑ ′ 1,n is greater than 10%, it can be concluded that the evaluations of the criteria ratio are not consistent. Ten, the redefning of the value ϑ 1,n is applied or alternatively, and a re-evaluation of the signifcance of the criteria is carried out.
For this research, the comparison and defnition of the relationship between the criteria were done by experts, and the aggregation of their opinions was conducted using the Dombi weighted geometric averaging (DWGA) operator, applying the following expression [29]: where is ρ > 0 and describes stabilization parameter of the Dombi function, while f(w ij ) represents the normalized values of the obtained weight coefcients for each of the experts. Te Fuzzy MAIRCA method was used to select the optimal strategy from the set of proposed ones, and the method steps are described as follows.
3.3. Fuzzy MAIRCA Method. Imprecisely defned membership of an element to a set, i.e., membership of an element to a set more or less, represents the main diference between Fuzzy sets and classical sets. Tis feature of fuzzy logic is closer to human understanding of reality than classical logic [46][47][48]. Lotf Zadeh introduced and presented the frst principles of fuzzy logic [49]. Fuzzy set L is defned as follows: where Z is the set on which the fuzzy set is defned L; 0 ≤ μ L (z) ≤ 1 is the function of element; z (z ∈ Z) belongs to the set L. Triangular fuzzy numbers, which have the shape L � (l 1 ,l 2 ,l 3 ), are most often used (l 1 -the left distribution, l 2 -the place where μ L � 1, l 3 -the right distribution of the confdence interval of the fuzzy number L). Tere are different approaches to fuzzifcation, and one of them is presented by Bobar et al. [50]: A fuzzy number L � (l 1 , l 2 , l 3 ) � (zc, z, (2 − c)z), z ∈ [1, ∞] is defned by the following expressions: Defuzzifcation of fuzzy number L: where λ represents an index of optimism λ ∈ [0, 1], that is, the expert's belief in risk when deciding, and it can be pessimistic, moderate, and optimistic [51]. Te MAIRCA method was published at the RAILCON international scientifc conference [52].
Formation of the initial decision matrix represents the initial step of applying the Fuzzy MAIRCA method: 6 Discrete Dynamics in Nature and Society (17) where m is the total number of alternatives, and n represents the total number of criteria. Te initial decision-making matrix is obtained by aggregating the opinions of experts, using equation (11). Te steps of the Fuzzy MAIRCA method are shown as follows [52]: Step 1. Defning the probability of choosing alternatives P Ai , by expression (18): Mostly, the probability (P Ai ) is the identical for all alternatives: Step 2. Derivation of the matrix of theoretical weights and its elements: where w n -weight coefcients of the criteria.
Step 3. Derivation of the matrix of real weights T r : Using the expressions: where x + i represents the maximum value of the right distribution, x − i is the minimum value of the left distribution, and x ij , x + i ix − i represent the elements of the matrix X.
Step 4. Derivation of the gap matrix G: Step 5. Obtaining the values of criterion functions (Q), expression (25): Te obtained criterion functions of the alternatives are defuzzifed by applying the expressions (15) or (16), and then, they are ranked (the lowest value represents the frst ranked).
Step 6. Determination of the dominance index (A D,1−j ), using the expression (26): where Q 1 is the frst-ranked alternative criterion function, Q j is the criterion function of the alternative which one is compared, Q n is the last ranked alternative criterion function, and j is the rank of the alternative. After obtaining the dominance index, the determination of the dominance threshold is calculated, using the following expression (27): In case, if it is A D,1−j ≥ I D , then the initial rank is retained, and otherwise, the ranks should be corrected and denoted by (1″).

Defnition of Alternatives (Strategies).
Alternatives represent opportunities for solving the problem and achieving the set goal, where during the structuring of the problem, a set of alternatives is generated to bridge the diferences between the desired and the current state. In the specifc case, the alternatives represent diferently formulated strategies from a specifc area in the defense system. Strategy formulation is the third step in the strategic management process.
Te Law on the Planning System of the Republic of Serbia [53] defnes "strategy" as "a basic document of public policy, which comprehensively determines the strategic direction of action and public policy in the specifc area of planning and implementation of public policies established by Government regulation." It defnes the period of adoption of the strategy from fve to seven years which should be accompanied by an action plan for the implementation of the strategy. Te law [53] divides the strategies into sectoral and intersectoral, while according to the spatial coverage, it divides into national and subnational. It also defnes the method of preparation, taking into account the results of exante and ex-post analyses in the observed area.
For this research and presentation of the model of selection of one of the proposed defense strategies, fve formulated alternatives (strategies) were used, as shown in Table 4. Te listed strategies represent diferent defense strategy proposals, which have not been adopted but are currently being elaborated in the process of developing the strategy.

Discrete Dynamics in Nature and Society
Based on the established model (Figure 1), frst the weight coefcients of the defned criteria are calculated.
By applying the other steps of the method, the following weight coefcients are reached (Table 6): Te values of the weight coefcients for all experts, obtained in the previously described manner, are given in Table 7.
By applying the expression (11), expert's opinions were aggregated, and the fnal values of the weight coefcients of the criteria are calculated (Table 8).
Based on the weight coefcients of the criteria obtained, it can be concluded that the initial importance of the criteria was fully respected, as well as that criterion C1 will have the greatest impact on the fnal decision; that is, criterion C6 will have the least impact.

Ranking of Alternatives and Selection of Strategy.
After the values of the weight coefcients of the criteria were obtained, the optimal alternative was chosen by applying the Fuzzy MAIRCA method.
First of all, applying the MAIRCA method is to form the initial decision matrix (Table 9), which in this case included values for fve proposed alternatives (strategies), based on the aggregated opinions of fve experts, using expression (11).
Te element of the initial decision matrix (3 : 70.19) indicates that the decision maker evaluated the strategy A 1 with a score of 3 with 70.19% confdence in the given statement. After the fuzzifcation of experts' claims, the fuzzy values of the initial decision matrix (Table 10) were calculated by applying expressions (13) and (14).
In Step 1, by applying expressions (18) and (19), the following value of P Ai was found: Te calculation of the elements of the matrix of theoretical weights, in Step 2 (Table 11), was done using the expression (20).
In Step 3, the matrix of real weights (Table 12) was calculated by applying expressions (22) or (23), depending on whether the criterion is beneft or cost type.
Te matrix of the gap G between theoretical and actual weights, in Step 4 (Table 13), was found by applying the expression (24).
Further application of the Fuzzy MAIRCA method led to the following values of the expected solution (Q i ), its defuzzifed values using expressions (15) and (16), and for λ, the value is 0.5, and after that, the initial rank of alternatives (strategies) is obtained and shown in Table 14: Upon obtaining the index and the dominance threshold, by applying expressions (26) to (27), which represent the specifcs of this MCDM method, which is 0.16, the fnal ranking of alternatives is reached (Table 15).
By applying the established model, the fnal ranking of alternatives (strategies) A1, A2, A3, and A5, which represent the best, from the set of ofers, was determined. Considering the initial ranking, strategy A1 represents the best-ranked alternative, but the decision maker can decide to choose between alternatives A2, A3, and A5 if they believe that the frst-ranked alternative has certain weaknesses, because MCDM methods represent tools for decision support, while  8 Discrete Dynamics in Nature and Society     Table 9: Te initial decision matrix.   Table 11: Te matrix of theoretical weights.   Table 13: Te matrix of the gap between theoretical and actual weights. a human is the one who makes the fnal decision. Also, alternative A4 cannot in any case be chosen as optimal, by the evaluation criteria.

Sensitivity Analysis and Comparative Study
For any MCDM-related analysis, it is important to check the stability of the outcome as it is susceptible to changes in the given conditions [54,55]. Te paper analyzed the sensitivity of the Fuzzy MAIRCA method to changes in weight coefcients as one of the approaches to analyzing the sensitivity of results of the MCDM methods [56][57][58][59][60], through 15 scenarios (Figure 2). Te correlations of the obtained ranks by applying the proposed methodology on the mentioned scenarios were calculated using Spearman's rank correlation coefcient (S rcc ), which is calculated according to the following expression [61]: where D i represents the diferences between the ranks [61], and m is number of alternatives. By applying expression (32), the following values of the Spearman's coefcient (S rcc ) were obtained ( Figure 3).
From the previous fgure, it is concluded that the correlation coefcients in 15 scenarios generally tend towards an ideal positive correlation and that the defned MCDM model is mostly stable about the change in the weight coefcients. However, this should be taken into account when defning them by experts, because favoritism of one criterion directly afects the fnal choice of alternatives, which is also certifed by the value of the Spearman's coefcient in scenario number six. High values of the Spearman's coefcient (0.9-1) indicate a high level of rank correlation. Te ranks of alternatives A2 and A5 in scenario S1 underwent a slight change; that is, there was a change in the order of alternatives in the 3rd and 4th place. In scenarios S6-S15, there is a change in the place of the frst-ranked and second-ranked alternative in relation to the initial ranking. In all scenarios, alternative A5 is ranked last; that is, its ranking does not change compared to the initial one, which indicates the fact that this alternative must not be chosen as optimal in any case.  S8 S9 S10 S11 S12 S13 S14 S15 Scenarios of changing the weight coefficients of the criteria C1 C2 C3 C4 C5 C6 Furthermore, a comparison of the obtained results with the results obtained using other 12 methods was performed, which is shown in Figure 4.
From the previous picture, it can be concluded that the results of the Fuzzy MAIRCA method do not difer much from the results of other methods. Tey are mostly identical to the results of the presented methodology, and there are no big diferences in the results obtained. In most cases, alternative A1 is ranked frst, while in all cases, A4 is the last ranked alternative. Also, it can be concluded that the changes in the ranking of the alternatives in relation to the ranking obtained by the Fuzzy MAIRCA method occur in the case of alternatives A2 and A5 as the third ranked and fourth ranked in the MAIRCA and MABAC methods. Te reasons for the diferences between the Fuzzy MAIRCA method and the crisp MAIRCA method are precisely the improvement of the mentioned methodology, through the implementation of Fuzzy theory, which achieves compliance with the results of most other methods. Also, there are diferences in the ranks of the frst-ranked and secondranked alternatives in the CODAS and TOPSIS methods, while in all other cases, the ranking of the alternatives is identical to the rank obtained by the Fuzzy MAIRCA method.
Te scientifc implications of this research are refected in the fact that the proposed MCDM model provides stable results and enables the selection of an optimal strategy, which improves the current way of evaluating strategies in the defense system, which constitutes a practical implication of the paper, and enables further upgrading of the same, through the introduction of new areas that treat uncertainties well, as well as other methods for determining weighting coefcients of criteria and choosing the optimal alternative in future research.

Conclusions
As a powerful tool for long-term sustainable survival, organizations facing a complex and changing environment embrace strategic management. Te concept of strategic management is based on a clearly defned vision, mission, and goals, which have resulted from a detailed analysis of expected changes in the environment.
Strategic management represents a process that includes all the functions of the scientifc feld of management, adapted to strategy as an output product and its specifcities. Te defense system recognized the importance of applying strategic management as a basic instrument for change management. Te process of strategic management, in its third step, includes the formulation of a strategy. Tis is focused on the generation of diferent strategies from one area, their evaluation, and the selection of an optimal strategy from a set of proposed ones.
Te aim of this research was to establish a model that would represent the improvement of the decision-making process when selecting an optimal strategy. Tis was done by implementing the MCDM method in the process of strategic management, with the application of other and new criteria for selection. Guided by the existing methods in the process of formulating the strategy, this study applied the model created according to the following methodology. First, the literature dealing with this area was analyzed, and the criteria and their importance were determined. After that, the weight coefcients of the criteria were obtained using the DIBR method, and the selection of the optimal alternative applying the Fuzzy MAIRCA method, using the level of experts' confdence in the claims when evaluating the alternatives (strategies). By applying the degree of confdence, imprecise qualitative information was transformed into precise quantitative information, using fuzzy theory and fuzzy numbers.
By analyzing the sensitivity of this model, it was confrmed that the Fuzzy MAIRCA method shows good stability of output results and that the model is viable and applicable in practice. Special attention must be paid to the defnition of weight coefcients by experts because the defned model is sensitive to changes in them. Also, the results obtained by comparing the results of the Fuzzy MAIRCA method with the results of 12 other methods indicate the fact that the presented methodology provides valid results.
Te main limitation of this research is related to the insufcient treatment of uncertainty in the DIBR method, which will be worked on in the future through the S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 The values of the Spearman coefficient  Discrete Dynamics in Nature and Society implementation of Fuzzy, gray, rough, or other similar theories. Also in future research, the proposed model will be improved by further elaboration of the criteria and the application of other MCDM methods for choosing the optimal alternative from the set of proposed ones, as well as the application of other theories that treat imprecision and uncertainty well. Te application of the mentioned MCDM model is possible in all areas of human life, such as for the selection of public policies in diferent areas, optimal machines for carrying out construction works, suppliers, drones for diferent purposes, boat sailing directions, diferent locations, and diferent means of transport.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author on reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.