Linear fractional programming problem with bipolar max-product fuzzy relation equation constraints

In this paper, the linear fractional programming problem subject to a system of bipolar fuzzy relation equations with max-product composition operator is studied. The structure of its feasible domain is investigated. Some sufficient conditions are then given that under them, one of the optimal solutions of the problem can be determined directly. Also, under other sufficient conditions, some components of an optimal solution can be characterized without solving the problem. Then the problem is transformed into a linear programming problem by reformulating the system of bipolar fuzzy relation equations as a system of 0-1 mixed integer inequalities and using the Charnes and Cooper’s method. Finally, an algorithm is suggested to solve the problem based on the above reductions.

کلیدواژه ها:

Linear fractional programming problem ، Bipolar fuzzy relation equations ، Max-product composition ، Fuzzy optimization