Interval and Fuzzy Analysis: A Unified Approach

Abstract

A unified approach to real-valued interval and fuzzy analysis emphasizing common themes is presented in this chapter. Interval analysis and fuzzy analysis are viewed as a bridge between deterministic problem solving and problems with generalized uncertainty. The chapter discusses the basic knowledge of interval analysis and fuzzy set theory. Interval analysis and fuzzy set theory, as active fields of research and application, are relatively new mathematical disciplines receiving the impetus that defined them as separate fields. The connection between interval analysis and possibility theory arose out of fuzzy set theory. The theory of interval analysis models, among other things, the uncertainty arising from numerical computation, which can be considered a source of ambiguity. Fuzzy set theory and possibility theory model, among other things, the uncertainty of vagueness and ambiguity arising from the transitional nature of entities and a lack of information. The chapter also discusses the distinction between fuzzy set theory and possibility theory.