In traditional game theory numerous approaches are available to convert a non-linear constrained optimization problem, splitting Primal-Dual problem for the original objective function is one of them. My question is , using fuzzy system ( taking the variables/ some of the parameters are fuzzy numbers) how can I replace this problem into game problem/ game matrix where the participation of game Players are clearly viewed?
Suppose , the given objective function is a function of x and y; where x represents the variable for player1, and the variable y stands for player 2. Take the strategies of x as ( x1,x2,x3,.....) and that of y as (y1,y2,y3,...). Now view these strategies as fuzzy sets of x and y respectively. If you wish to take 3X3 matrix game then take the fuzzy sets as triangular, for 4X4 matrix , it is trapezoidal and so on. The constraints will follow the same fuzzy sets accordingly.
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