Fuzzy Logic

Abstract

This chapter introduces fuzzy logic as the basic for a collection of techniques for representing knowledge in terms of natural language like sentences and as a means of manipulating these sentences in order to perform inference using reasoning strategies that are aproximate rather than exact. It was first introduced in the early 1970s by Zadeh in order to provide a better rapport with reality [Klir and Yuan 1995; Zadeh 1973]. Fuzzy logic can be viewed as a means of formally performing approximate reasoning about the value of a system variable given vague information about the values of other variables, and knowledge about the dependence relations between them (that is typically represented as IF-THEN rules expressed as fuzzy relations). For example, if knowledge is expressed in terms of IF-THEN rules, such as IF X is A THEN Y is B, and if the fact X is A’ is known, then the deductive process needs to derive Y is B as a logical consequences. In an approximate reasoning setting, in contrast to a classical logic setting, where inference is performed by manipulating symbols, inference is performed at a semantic level by numeric manipulation of membership functions that characterise the symbols.

“Classical logic is like a person who comes to a party dressed in black suit, white starched shirt, a black tie, shiny shoes, and so forth. And fuzzy logic is a little bit like a person dressed informally, in jeans, tee shirt and sneakers” [Zadeh 1987]