The Construction of Flexible and Generalized Uncertainty Optimization Input Data

Abstract

Chapter 1 introduced the topics of interest to this monograph. Chapter 2 briefly looked at the underlying theory behind the data input types—flexible/fuzzy entities and generalized uncertainty entities: intervals, fuzzy intervals, possibility pairs, interval-valued probabilities, cumulative probability bounds (P-Boxes), clouds, Kolmogorov–Smirnov bounds, belief/plausibility pairs, probability intervals, and random sets. Since cumulative probability bounds, probability intervals, and clouds can directly be translated into probability based possibilities and enclosed by a pair of distributions in general, we will consider these types as being derived by probability based possibility. Moreover, nested belief/plausibility and some random sets (see [1,2,3]) can be translated into interval-valued distribution pairs. However, these three uncertainty types (belief/plausibility, probability intervals, random sets), in general, require stronger hypotheses to translate them into upper/lower distributions enclosing or approximating the unknown distributions which underlie partial information.