Soft robust solutions to possibilistic optimization problems

This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy inter-vals. 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 repre-sentation 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. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper discusses a class of uncertain optimization problems, where unknown parameters are modeled by fuzzy intervals. Known concepts of robustness and light robustness for traditional interval uncertainty representation can be generalized to optimize solutions against plausible parameter realizations under this possibilistic setting. Solutions can be efficiently computed for linear programming problems with fuzzy parameters, making them not much computationally harder than their deterministic counterparts.