Soft robust solutions to possibilistic optimization problems

Abstract

This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the uncertain parameters. It is shown how the known concepts of robustness and light robustness, for the traditional interval uncertainty representation of the parameters, can be generalized to choose solutions that optimize against plausible parameter realizations under the assumed model of uncertainty in the possibilistic setting. Furthermore, these solutions can be computed efficiently for a wide class of problems, in particular for linear programming problems with fuzzy parameters in constraints and objective function. Thus the problems under consideration are not much computationally harder than their deterministic counterparts. In this paper a theoretical framework is presented and results of some computational tests are shown.