Fuzzy Sets and Fuzzy Logic: Discovery and Controversy
Lotfi A. Zadeh
Professor in the Graduate School and
Director, Berkeley Initiative in Soft Computing (BISC),
Computer Science Division and the Electronics Research Laboratory,
Department of EECS,
University of California, Berkeley, CA
E-Mail: zadeh@cs.berkeley.edu
Noon: Wednesday, October 27th, 1999
Gabelle Room, Townsend Center, Stephens Hall
University of California, Berkeley
Abstract
To view the evolution of fuzzy logic in a proper perspective it is
necessary to start with a clarification -- a clarification of the meaning of
"fuzzy logic."
A source of common misunderstanding is that the term "fuzzy logic" has
two distinct meanings. In a narrow sense, fuzzy logic is a logical system
which underlies modes of reasoning which are approximate rather than exact.
But in a wide sense -- which in dominant use today -- fuzzy logic is much
more than a logical system; it is, in effect, coextensive with fuzzy set
theory.
More specifically, fuzzy logic in its wide sense, FL, has four principal
facets which overlap and have unsharp boundaries.
The first facet, FL/L, is the logical facet -- a facet which is
coextensive with fuzzy logic in its narrow sense. The second facet, the
set-theoretic facet, FL/S, is the part of FL which is concerned with classes
which have unsharp boundaries. My 1965 paper on fuzzy sets dealt with this
facet. Today, most of the papers in the mathematical literature on fuzzy sets
relate to the set-theoretic facet.
The third facet, the relational facet, FL/R, is concerned with
representation and analysis of imprecise dependencies. Most applications of
fuzzy logic, especially in the realms of consumer electronics, industrial
systems and control fall within the province of this facet.
The fourth facet, the epistemic facet, FL/E, is concerned with
knowledge, meaning and information. Possibility theory is a part of this
facet, as is possibilistic logic, which is shared with the logical facet.
The core of FL is centered on two basic concepts: fuzzification and
granulation, along with their conjunction, fuzzy granulation. Fuzzification,
or f-generalization, is a mode of generalization in which a set is replaced
by a fuzzy set. Fuzzy granulation, or f.g-generalization, is a mode of
generalization in which a fuzzy set is partitioned into fuzzy granules, with
a granule being a clump of points (objects) which are drawn together by
indistinguishability, similarity, proximity or functionality. For example,
the fuzzy granules of a face are the nose, chin, cheeks, lips, etc. Fuzzy
granulation plays a pivotal role in fuzzy logic and its applications; it
underlies the two most important concepts in FL, namely, the concepts of a
linguistic variable and fuzzy if-then rule sets. These concepts were
introduced in my 1973 paper, "Outline of a New Approach to the Analysis of
Complex Systems and Decision Processes," and marked a new direction in fuzzy
logic and its applications. Reflecting the deep-seated tradition of respect
for numbers and derision for words, the initial reaction to these concepts
was a mixture of hostility and warm embrace.
A new and important direction in fuzzy logic is related to what may be
called the computational theory of perceptions (CTP). This theory, which is
based on fuzzy logic, provides a machinery for processing of information which
is perception-based, e.g., "it is likely to rain later in the evening," "most
Swedes are blond," etc. Existing scientific theories do not have this
capability.
By providing a machinery for computation with perceptions, CTP opens
the door to a major enlargement of the role of natural languages in scientific
theories, especially in probability theory, decision analysis and control. A
countertraditional move in this direction has the potential for leading to a
significant paradigm shift in both basic and applied sciences.
*********************************************************************
Please direct questions on the talk to the speaker
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Frank Hoffmann UC Berkeley
Computer Science Division Department of EECS
Email: fhoffman@cs.berkeley.edu phone: 1-510-642-8282
URL: http://http.cs.berkeley.edu/~fhoffman fax: 1-510-642-5775
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