Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

Brikaa, M. G.; Zheng, Zhoushun; Ammar, E. E.

doi:10.3390/math8030305

Cited by 18 publications

(4 citation statements)

References 44 publications

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“…). By solving the above mathematical programming models, we obtain the following tabulated optimal solutions, given in Tables [13][14][15][16][17][18]. From the results shown in Tables 1-18, the optimal strategies obtained by different ranking approaches are the same as those of the proposed approach.…”

Section: Comparison Analysismentioning

confidence: 99%

“…Bhaumik et al [15] introduced multiobjective linguistic-neutrosophic matrix game with applications to tourism management. Brikaa et al [16] applied resolving indeterminacy technique to find optimal solutions of multicriteria matrix games with IF goals. So far, as the authors are aware, there are only four articles that studied constraint bimatrix games.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Gaber

Alharbi

Dagestani

et al. 2021

Journal of Mathematics

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Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.

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Section: Comparison Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Gaber

Alharbi

Dagestani

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Xia [8] implemented Archimedean triangular norms and triangular conorms for solving matrix games with payoffs of interval-valued I-fuzzy numbers. Brikaa et al [9] explored an indeterminacy approach for solving zero-sum matrix games having intuitionistic fuzzy goals. Verma and Kumar [10] developed the Ambika method to deal with matrix games in an intuitionistic fuzzy scenario.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Programming Approach to Solving Interval-Valued Intuitionistic Hesitant Noncooperative Fuzzy Matrix Games

Karmakar,

Seikh

2024

Symmetry

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Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models.

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“…26 Utilizing the concept of robust ranking method, Bhaumik et al 27 made a solution methodology of intuitionistic fuzzy matrix games. Brikaa et al 28 rendered a solution approach of multicriteria matrix game with payoffs of IFSs. Verma and Kumar 29 resolved matrix games with intuitionistic fuzzy payoffs using the Ambika method.…”

Section: Introductionmentioning

confidence: 99%

Matrix games with dense fuzzy payoffs

2021

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A novel notion of dense fuzzy lock set was introduced as an extension of fuzzy sets. Learning experiences have a vital role in this fuzzy lock set instigation. The novel fuzzy lock set reduces the fuzziness of the situation. Occasionally, the players are bound to make little changes in their game strategies to reach their goal for some matrix game problems. It may lead to some changes in payoffs. In this scenario, a matrix game's payoffs are chosen as dense fuzzy lock sets to make the problem more realistic. This paper's prime intent is to develop a mathematical model of a matrix game that represents payoffs by triangular dense fuzzy lock sets. Initially, a new defuzzification function MagD(.) is defined to find a ranking order relation of the dense fuzzy lock sets. Then a pair of auxiliary dense fuzzy programming problems is established for two players. These two problems are transformed into two equivalent crisp linear programming problems applying the proposed defuzzification function and its linearity property. The reduced problems are solved using LINGO 17.0 software to determine each player's optimal strategies and the game values. One surprising fact of this approach is that the value of the game increases with the increment of the player's learning experience. The validity, applicability, and superiority of this proposed methodology are illustrated by considering a real-life media share problem.

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Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

Cited by 18 publications

References 44 publications

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

A Nonlinear Programming Approach to Solving Interval-Valued Intuitionistic Hesitant Noncooperative Fuzzy Matrix Games

Matrix games with dense fuzzy payoffs

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