A Possibilistic Optimization over an Integer Efficient Set Within a Fuzzy Environment

Optimizing a linear function over the efficient set of a Multiple Objective Integer Linear Programming (MOILP) problem is known as a difficult problem to deal with, since a discrete efficient set is generally not convex and not explicitly known. Such problem becomes more and more difficult when parameters are defined with uncertainty. In this work, we deal with problems of this type for which parameters are imprecise and are assumed to be trapezoidal fuzzy numbers. The method is based on possibility and necessity measures introduced in the literature by D. Dubois and H. Prade.