On a fully fuzzy framework for minimax mixed integer linear programming

TL;DR

This paper introduces a fuzzy modeling framework for minimax mixed integer linear problems, extending traditional methods to handle fuzzy data and applying it to a fuzzy capacitated center location problem.

Contribution

It develops a novel fuzzy framework for minimax mixed integer problems and demonstrates its application to a fuzzy version of a classic facility location problem.

Findings

Framework effectively models fuzzy minimax problems.

Equivalent formulation as a multi-objective mixed integer program.

Application to a fuzzy capacitated center problem shows practical utility.

Abstract

In this work, we present a modeling framework for minimax mixed 0-1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We establish that the considered problem can be equivalently formulated as a multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem.