An Overview of Flexible and Generalized Uncertainty Optimization

Abstract

This chapter, some of whose ideas we have taken from [82], [78], and [150], develops flexible and generalized uncertainty optimization where the salient feature of the problem is decision making under gradual set belonging. As we have mentioned in Chapter , optimization problems are normative processes that embody the idea of order since we must measure how one outcome is “ better” than another. This requires an order. That is, “best” is a normative criterion for optimization that requires an order that measures “ best”. The real number system contains within itself a complete order or we might say that the real number system is what we mean by a complete order. We use the real numbers, $\mathbb {R}$, onto which the normative criteria “best” of flexible and generalized uncertainty optimization is mapped.