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This study demonstrates how to find equilibrium in bi-matrix games with fuzzy rough payoffs, suggesting new optimization methods for decision-making under uncertainty.
This study proposes a novel methodology for solving constrained bi-matrix games with payoffs represented by fuzzy rough numbers, addressing uncertainties common in real-world decision-making. By integrating fuzzy rough set theory with α-cut techniques, the method establishes the existence of an fuzzy rough equilibrium value. Five linear programming models are developed to compute the mean equilibrium and its lower-lower, lower-upper, upper-lower, and upper-upper bounds, based on 0-cut and 1-cut representations. For any confidence level α, corresponding equilibrium bounds are determined through α-cut-based optimization. The methodology is validated through a case study on corporate environmental behavior, demonstrating its effectiveness and practical relevance.
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M. G. Brikaa (2025) studied this question.
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