Properties of Membership Functions, Fuzzification, and Defuzzification

This chapter introduces various popular forms of converting fuzzy sets to crisp sets or to single scalar values. It discusses the various features and forms of a membership function and the idea of fuzzyifying scalar quantities to make them fuzzy sets. The primary focus of the chapter, however, has been to explain the process of converting from fuzzy membership functions to crisp formats - a process called defuzzification. Since all information contained in a fuzzy set is described by its membership function, it is useful to develop a lexicon of terms to describe various special features of this function. There may be situations where the output of a fuzzy process needs to be a single scalar quantity as opposed to a fuzzy set. Defuzzification is the conversion of a fuzzy quantity to a precise quantity, just as fuzzification is the conversion of a precise quantity to a fuzzy quantity. Controlled Vocabulary Terms fuzzy control; fuzzy set theory