Fuzzy Modeling Fundamentals
Patricia Melín, Oscar Castillo · Wiley Encyclopedia of Computer Science and Engineering · 2008
Abstract This article introduces the basic concepts, notation, and basic operations for fuzzy sets that are needed in fuzzy modeling. Because research on fuzzy set theory has been underway for over 30 years now, it is practically impossible to cover all aspects of current developments in this area. Therefore, the main goal of this article is to provide an introduction to and a summary of the basic concepts and operations that are relevant to the study of fuzzy sets. We introduce in this article the definition of linguistic variables and linguistic values and explain how to use them in fuzzy rules, which are an efficient tool for quantitative modeling of words or sentences in a natural or artificial language. By interpreting fuzzy rules as fuzzy relations, we describe different schemes of fuzzy reasoning, in which inference procedures based on the concept of the compositional rule of inference are used to derive conclusions from a set of fuzzy rules and known facts. Fuzzy rules and fuzzy reasoning are the basic components of fuzzy inference systems, which are the most important modeling tool, based on fuzzy set theory.