Linear optimization with bipolar max–min constraints

A generalization of the linear optimization problem with fuzzy relational (in)equality constraints by allowing for bipolar max-min constraints, i.e. constraints in which not only the independent variables but also their negations occur.

Abstract

We consider a generalization of the linear optimization problem with fuzzy relational (in)equality constraints by allowing for bipolar max–min constraints, i.e. constraints in which not only the independent variables but also their negations occur. A necessary condition to have a non-empty feasible domain is given. The feasible domain, if not empty, is algebraically characterized. A simple procedure is described to generate all maximizers of the linear optimization problem considered and is applied to various illustrative example problems.