Definition of fuzzy Pareto-optimality by using possibility theory

Pareto-optimality conditions are crucial when dealing with classic multi-objective optimization problems because we need to find out a set of optimal solutions rather than only one optimal solution to optimization problem with a single objective. Extensions of these conditions to the fuzzy domain have been discussed and addressed in recent literature. This work presents a novel approach based on the use of possibility theory as a comparison index to define a fuzzily ordered set with a view to generating the necessary conditions for the Pareto-optimality of candidate solutions in the fuzzy domain. Making use of the conditions generated, one can characterize fuzzy efficient solutions by means of carefully chosen single-objective problems. The uncertainties are inserted into the formulation of the studied fuzzy multi-objective optimization problem by means of fuzzy coefficients in the objective function. Some numerical examples are analytically solved to illustrate the efficiency of the proposed approach.