Solving Constrained Matrix Games With Fuzzy Random Linear Constraints

  • Sabiha Djebara Laboratoire de Recherche Opérationnelle et de Mathématiques de la Décision, Faculté des Sciences, Université Mouloud Mammeri de Tizi Ouzou, 15000 Tizi-Ouzou, Algeria
  • Farida Achemine Laboratoire de Mathématiques Pures et Appliquées, Faculté des Sciences, Université Mouloud Mammeri de Tizi Ouzou, 15000 Tizi-Ouzou, Algeria http://orcid.org/0009-0007-1798-333X
  • Moussa Larbani Ecole Nationale Supérieure de Statistique et d’Economie Appliquée (ENSSEA), Koléa, Algeria

Abstract

In real-world games, players may face an uncertain environment where fuzziness and randomness coexist. The main difficulty in dealing with games involving fuzziness and randomness arises when comparing the payoffs. The purpose of this paper is to introduce a new approach to deal with constrained matrix games where the entries of the constraint matrices are LR-fuzzy random variables. Our methodology is based on constructing a new matrix game using the chance constraint method adapted to the probability-possibility measures. First, a specific type of saddle point is defined as an equilibrium solution. Then, conditions for the existence of the proposed solution are established. Further, a technique based on second-order programming for computing the saddle point is presented. Finally, a numerical illustration of the approach is provided.

Published
2024-04-25
How to Cite
DJEBARA, Sabiha; ACHEMINE, Farida; LARBANI, Moussa. Solving Constrained Matrix Games With Fuzzy Random Linear Constraints. Yugoslav Journal of Operations Research, [S.l.], apr. 2024. ISSN 2334-6043. Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1268>. Date accessed: 14 dec. 2024. doi: https://doi.org/10.2298/YJOR231122013D.
Section
Research Articles

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