Matrix games with dense fuzzy payoffs

Seikh, Mijanur Rahaman; Karmakar, Shuvasree; Nayak, Prasun Kumar

doi:10.1002/int.22360

Cited by 21 publications

(5 citation statements)

References 37 publications

(56 reference statements)

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“…Then S * 1 and S * 2 are called the projectile's gain floor and aircraft target's loss ceiling. For the two players, S * 1 and S * 2 are the Nash equilibrium solution of the hybrid strategy on the projectile and the aircraft target, which satisfies Formula (12) [34,35].…”

Section: Calculation Of the Nash Equilibrium Solution Of The Damage G...mentioning

confidence: 99%

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

Zhang

Chen

2022

Mathematics

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The efficiency of target damage is to measure the effect of projectile attacks. Because there is antagonism at the intersection of projectiles and targets, it is very difficult to establish scientific damage assessment strategy model and a numerical calculation method. To scientifically evaluate the target damage effect when the projectile attacks the aircraft target, this paper introduces a game confrontation mechanism and proposes a numerical calculation method of aircraft target damage game strategy under the intersection confrontation. According to the theory of two-person non-cooperative games, the projectile is regarded as one of the players in the confrontation damage game, and the aircraft target is regarded as the other player. The damage gain model and gain function of the intersection confrontation of both sides are established. The effective expectation function and the minimum and maximum theorem are used to obtain the optimal Nash equilibrium solution of the game matrix strategy, and the Nash equilibrium point of the strategy space set is derived. Through calculation and comparative analysis, the results show that the optimal gain degree composed of the damage strategy selected by both the projectile and aircraft target under the Nash equilibrium solution brings the greatest gain. The proposed hybrid game strategy of damage assessment can be an effective reference for air combat decision making in the state of intersection confrontation.

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Section: Calculation Of the Nash Equilibrium Solution Of The Damage G...mentioning

confidence: 99%

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

Zhang

Chen

2022

Mathematics

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“…Yang 27 described the solution procedure of the matrix game where the payoffs are represented by triangular dual hesitant fuzzy numbers. Very recently, Seikh et al 28 presented a solution approach for matrix games with dense fuzzy payoffs.…”

Section: Literature Reviewmentioning

confidence: 99%

Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Seikh

Dutta

2021

Int J Intell Syst

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Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual-layer information. In real-life problems, there are many situations where players of a matrix game cannot assess their pay-offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay-offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.

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“…In the recent past, Jana and Roy [23] explored the linguistic Pythagorean hesitant fuzzy matrix game and applied it to multicriteria decision making. Utilizing the lexicographic approach, Seikh et al [24] designed the solution methodology of a matrix game with hesitant fuzzy payoffs. Yang and Song [25] rendered the solution procedure for matrix games with triangular dual hesitant fuzzy payoffs.…”

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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Matrix games with dense fuzzy payoffs

Cited by 21 publications

References 37 publications

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

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

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