AbstractIn this study we discuss 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