Chapter 0 - Foundation

Abstract

This book synthesizes summarizes the research carried out over the last twenty years on the structure identification of “expressions” in combination of concepts as a base for computing with words (CWW). The chapter also illustrates the derivation of the fuzzy set and logic. The application of these formulas in approximate reasoning schemas is also demonstrated. In this context, the chapter discusses the implicit and explicit statements of linguistic expressions, which are essential in CWW, to identify “descriptive” and “veristic” frameworks. Several critical thinkers of the classical theory have argued that it restricts or reduces reality to be “objective”; and that classical theory leads inadvertently to many paradoxes in which the theory becomes over-structured, over-selective, and sometimes even overshadows the real life data. In these pioneering works, investigations on membership functions, fuzzy relations, fuzzy logic and inference, classification and similarity measures, expert systems, medical diagnosis, psychological measurements and human behavior, fuzzy clustering algorithms, individual and group decision-making in fuzzy environments, fuzzy mathematical programming, multi-criteria decision-making, and decision support systems have been observed.