University of California, Berkeley
PATTERNS OF SCIENTIFIC DISCOVERY
A series sponsored by the Doreen B. Townsend Center for the Humanities, the
School of Public Health and the Office for the History of Science and
Technology
-----Session 35-----
Fuzzy Sets and Fuzzy Logic:
Discovery and Controversy
Lofti A Zadeh
Professor Emeritus Electrical Engineering and Computer Science
Director, Berkeley Initiative in Soft Computing (BISC)
NOON Wednesday, October 27 , 1999
Gabelle Room, Townsend Center, Stephens Hall
UNIVERSITY OF CALIFORNIA, BERKELEY
[Professor Zadeh originated "fuzzy logic" and " fuzzy sets". Hostility to
these notions arose since he first proposed them and persists in some
quarters, probably to a large extent for semantic reasons. But others have
embraced and applied them fruitfully in many important contemporary "real
world" applications. He will discuss both the discovery and evolution of
these concepts as well as aspects of the controversy that has swirled about
them since he first proposed them.]
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 the 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 in 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.
___________________________________________________________________________
[For information concerning this seminar or the series contact the Office
of History of Science and Technology (Susan Alexander at 510 -642 4581 or
alexcand@uclink4.berekely.edu) or Professor Ernest B. Hook, School of
Public Health (510 642 4490 or ebhook@socrates.berkeley.edu) at UC,
Berkeley.]
---------------------------------------------------------------------------
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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