## What Is Fuzzy Logic and What Are Its Applications?

Fuzzy logic has been—and to some extent still is—an object of controversy. Some are turned-off by its name. But, more importantly, fuzzy logic is tolerant of imprecision and partial truth. It is this tolerance that is in conflict with the deep-seated Cartesian tradition of aiming at truth which is bivalent, with no shades of gray allowed.

There are many misconceptions about fuzzy logic. In large measure, the misconceptions reflect the fact that the term “fuzzy logic” has two distinct interpretations. More specifically, in a narrow sense, fuzzy logic is the logic of approximate reasoning. But in a wider sense—which is in dominant use today—fuzzy logic, denoted as FL, is coextensive with the theory of fuzzy sets, and contains fuzzy logic in its narrow sense as one of its branches. In fact, most applications of FL involve modes of analysis which are computational rather than logical in nature.

Fuzzy logic, FL, has four principal facets. First, the logical facet, FL , which is fuzzy logic in its narrow sense. Second, the set-theoretic facet, FLs, which is concerned with classes having unsharp boundaries, that is, with fuzzy sets. Third, the relational facet, FLr, which is concerned with linguistic variables, fuzzy if-then rules and fuzzy relations. It is this facet that underlies almost all applications of fuzzy logic in control, decision analysis, industrial systems, and consumer products. And fourth, the epistemic facet, FLe, which is concerned with knowledge, meaning, and linguistics. One of the important branches of FLe is possibility theory.

A concept which has a position of centrality in FL is that of fuzzy granularity or, simply, f-granularity. F-granularity reflects the bounded ability of human sensory organs and, ultimately, the brain, to resolve detail and store information. In particular, human perceptions are, for the most part, f-granular in the sense that (a) the boundaries of perceived classes are fuzzy, and (b) the perceived attributes are granulated, with a granule being a clump of values drawn together by indistinguishability, similarity, proximity or functionality. In this perspective, the colors red, blue, green, etc., may be viewed as labels of granules of perception of color.

Precision carries a cost. This is the main reason why in most of its applications, the machinery of fuzzy logic is employed to exploit the tolerance for imprecision for achieving tractability, robustness and low solution cost. In fact, it is the tolerance for imprecision that underlies the remarkable human capability to perform a wide variety of physical and mental tasks, e.g., drive in city traffic, based solely on perceptions, without any measurements and any computations. It is this capability that motivated the development of fuzzy-logic-based computational theory of perceptions (CTP). Existing theories and, in particular, probability theory, do not have the capability to operate on perception-based information.

The computational theory of perceptions is a branch of the fuzzy-logic-based methodology of computing with words (CW). Development of the methodology of computing with words is an important event in the evolution of fuzzy logic. Eventually, it may lead to a radical enlargement of the role of natural languages in information processing, decision, and control.

* Professor in the Graduate School and Director, Berkeley initiative in Soft Computing (BISC), Computer Science Division and the Electronics Resear ch Laboratory, Department of EECS, University of California, Berkeley, CA 94720- 1776; Telephone: 510-642-4959; Fax: 510-642-1712; E-Mail: zadeh@cs.berkeley.edu.