A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs
محل انتشار: مجله مدلسازی ریاضی، دوره: 11، شماره: 3
سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 31
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شناسه ملی سند علمی:
JR_JMMO-11-3_001
تاریخ نمایه سازی: 19 خرداد 1403
چکیده مقاله:
The main purpose of this study is to construct a new approach for solving a constrained matrix game where the payoffs and the constraints are LR-fuzzy numbers. The method that we propose here is based on chance constraints and on the concept of a comparison of fuzzy numbers. First, we formulate the fuzzy constraints of each player as chance constraints with respect to the possibility measure. According to a ranking function \mathcal{R}, a crisp constrained matrix game is obtained. Then, we introduce the concept of \mathcal{R}-saddle point equilibrium. Using results on ordering fuzzy numbers, sufficient existence conditions of this concept are provided. The problem of computing this solution is reduced to a pair of primal-dual linear programs. To illustrate the proposed method, an example of the market competition game is given.
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نویسندگان
Sabiha Djebara
Laboratoire de Recherche Operationnelle et de Mathematiques de la Decision, Faculte des sciences,Universite Mouloud Mammeri de Tizi Ouzou, ۱۵۰۰۰ Tizi-Ouzou, Algeria
Farida Achemine
Laboratoire de Mathematiques Pures et Appliquees, Faculte des sciences, Universite Mouloud Mammeri de Tizi Ouzou, ۱۵۰۰۰ Tizi-Ouzou, Algeria
Ouiza Zerdani
Laboratoire de Recherche Operationnelle et de Mathematiques de la Decision, Faculte des sciences,Universite Mouloud Mammeri de Tizi Ouzou, ۱۵۰۰۰ Tizi-Ouzou, Algeria