Robust Possibilistic Optimization with Copula Function

Abstract

This paper deals with a linear optimization problem with uncertain objective function coefficients modeled by possibility distributions. The fuzzy robust optimization framework is applied to compute a solution. Namely, the necessity degree that the objective value is lower than a given threshold is maximized. The aim of this paper is to take the knowledge on dependencies between the objective coefficients into account by means of a family of copula functions. It is shown that this new approach limits the conservatism of fuzzy robust optimization, better evaluates possibility distributions for the values of the objective function and do not increase the complexity of the problem.