Linear fractional programming problem with fuzzy relation inequality constraints

In this paper, an optimization problem with a linear fractional objective function subject to a system of Fuzzy Relation Inequality (FRI) constraints is studied. We firstly determine the structure of its feasible domain and show its non-convexity. To do this, it is shown that feasible domain of the problem is completely determined by the maximum and quasi-minimal solutions of the feasible domain. We use FRI paths to find the quasi-minimal solutions. Then, the problem is equivalently converted to some traditional linear programming problems and they are solved by linear programming methods. With regard to their solutions, we can determine optimal solution of the original problem.

Keywords:

Linear fractional programming , Fuzzy relation inequality , Max-product composition , Fuzzy relation inequality path , Non-convex programming