Soft robust solutions to possibilistic optimization problems

TL;DR

This paper introduces a theoretical framework for obtaining soft robust solutions in possibilistic optimization problems with fuzzy parameters, enabling efficient computation for linear programming models under uncertainty.

Contribution

It generalizes robustness concepts to possibilistic settings and provides an efficient method for solving fuzzy parameter linear programming problems.

Findings

Framework for soft robust solutions in possibilistic optimization

Efficient computation methods for fuzzy linear programming

Computational tests demonstrating practical applicability

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 interval uncertainty representation of the parameters, can be generalized to choose solutions 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. In this paper a theoretical framework is presented and results of some computational tests are shown.