Flexible Optimization

Abstract

This chapter focuses on flexible optimization. Given that we are able to construct fuzzy relations from target values, fuzzy goals, and from fuzzy relation membership functions, we then have a fuzzy constraint set. The next step in the process is to translate a fuzzy constraint set into a real vector constraint set and to redefine the objective function as a maximization of set belonging. If there are crisp relations and constraints, these remain as part of the real-valued constraint set and augment the translated fuzzy constraint set. If all or part of the original (non-fuzzy goal) objective function is real-valued, then the maximization of set belonging is added to the real-valued objective just as one would do when one adds a new variable to the objective function and constraint for real-valued mathematical programming problems.