Generalized Uncertainty Theory: A Language for Information Deficiency

Abstract

This chapter focuses on the various theories of generalized uncertainty that occur in the data associated with optimization models under generalized uncertainty. Fuzzy set theory as it is applied to optimization is quite well-developed and a distinct study with many textbooks [3, 64] as well as an associated journal, Fuzzy Optimization and Decision Making. Therefore, fuzzy set theory is not emphasized in our development in this chapter. Since the way we will use generalized uncertainty to generate upper and lower bounding functions is perhaps less well-known, we concentrate on generalized uncertainty. In Chapter 3 we do develop the methods to translate fuzzy set and generalized uncertainty data into the input we use in flexible optimization problems.