Abstract
In reality, occasionally, the players of a bi-matrix game problem are forced to bring little changes in their game strategies to manage the situation. As a result, this phenomenon could lead to a change in the pay-offs of a game problem. This paper aims to model such kind of bi-matrix games with pay-offs as dense fuzzy lock sets. A novel defuzzification function of this new set, viz., \(Val_{D}(.)\) function is defined here. An auxiliary quadratic dense fuzzy programming problem (QDFPP) is established to solve the bi-matrix game. Later this QDFPP is transformed into an equivalent crisp programming problem by employing the induced defuzzification function and its linearity property. A notable facet of this approach is that players’ profits increase with increased trials. The efficacy and applicability of the proposed methodology are explained by reflecting a tourism planning strategy problem.
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Karmakar, S., Rahaman Seikh, M. (2022). A Novel Ranking-Based Non-linear Programming Approach to Solve Bi-matrix Games in Dense Fuzzy Environment. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_56
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