A multi-objective mathematical programming problem with fuzzy relation constraints

This study discusses the problem of multi-objective mathematical programming with constraints defined by ‘max-min’ composite fuzzy relation equations. Since the feasible region is normally non-convex, the properties of the efficient points of a non-convex feasible region under multi-objectives are investigated and illustrated by examples. The necessary and sufficient conditions are proposed and proved. To facilitate decisions, a procedure that transforms these efficient points of an interval-valued decision space into a constant-valued decision space is proposed when the level of confidence is given by a decision maker. Then the transformed problem becomes a multi-attribute decision problem that can be evaluated by Yager’s method to find the optimal alternative.