Fuzzy multi-criteria optimization based on fuzzy relations

Fuzzy multi-criteria optimization problems (FMO) form a subclass of decision - making problems where preferences between alternatives are described by means of criteria functions defined on the set of alternatives. The formulation a FMO problem associated with the classical mathematical programming problem (MP) is presented. Then the concept of a feasible solution and compromise solution of FMO problem are presented. These concepts are based on generalized equality and inequality fuzzy relations. Among others we show that the class of all MP problems with crisp parameters can be naturally embedded into the class of FMO problems with fuzzy parameters. We also show that the feasible and compromise solutions being fuzzy sets are convex under some mild assumptions.