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Is There a Need for Fuzzy Logic?*
Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720 -1776
Director, Berkeley Initiative in Soft Computing (BISC)
zadeh@eecs.berkeley.edu
the roles of the precisiend and precisiand, respectively.
ABSTACT
Cointension is a qualitative measure of the proximity of
"Is there a need for fuzzy logic?" is an issue which is meanings of the precisiend and precisiand. A precisiand is
associated with a long history of spirited discussions and cointensive if its meaning is close to the meaning of the
debates. There are many misconceptions about fuzzy logic. precisiend.
Fuzzy logic is not fuzzy. Basically, fuzzy logic is a precise A concept which plays a key role in the nontraditional
logic of imprecision and approximate reasoning. More view of fuzzy logic is that of a generalized constraint. If X is a
specifically, fuzzy logic may be viewed as an attempt at variable then a generalized constraint on X, GC(X), is
formalization/mechanization of two remarkable human expressed as X isr R, where R is the constraining relation
capabilities. First, the capability to converse, reason and make and r is an indexical variable which defines the modality of
rational decisions in an environment of imprecision, the constraint, that is, its semantics. The primary constraints
uncertainty, incompleteness of information, conflicting are: possibilistic, (r =blank), probabilistic (r=p) and veristic
information, partiality of truth and partiality of possibility—in (r=v). The standard constraints are: bivalent possibilistic,
short, in an environment of imperfect information. And probabilistic and bivalent veristic. In large measure, science is
second, the capability to perform a wide variety of physical based on standard constraints.
and mental tasks without any measurements and any Generalized constraints may be combined, qualified,
computations (Zadeh 1999, 2001). In fact, one of the principal propagated and counterpropagated. The set of all generalized
contributions of fuzzy logic—a contribution which is widely constraints, together with the rules which govern generation of
unrecognized—is its high power of precisiation. generalized constraints, is referred to as the Generalized
Fuzzy logic is much more than a logical system. It has many Constraint Language, GCL. The Standard Constraint
facets. The principal facets are: logical, fuzzy-set-theoretic, Language, SCL, is a subset of GCL.
epistemic and relational. Most of the practical applications of In fuzzy logic, propositions, predicates and other
fuzzy logic are associated with its relational facet. semantic entities are precisiated through translation into GCL.
In this paper, fuzzy logic is viewed in a nonstandard Equivalently, a semantic entity, p, may be precisiated by
perspective. In this perspective, the cornerstones of fuzzy representing its meaning as a generalized constraint.
logic—and its principal distinguishing features—are: By construction, fuzzy logic has a much higher level of
graduation, granulation, precisiation and the concept of a generality than bivalent logic. It is the generality of fuzzy
generalized constraint. logic that underlies much of what fuzzy logic has to
A concept which has a position of centrality in the offer. Among the important contributions of fuzzy logic are
nontraditional view of fuzzy logic is that of precisiation. the following.
Informally, precisiation is an operation which transforms an 1. FL-generalization. Any bivalent-logic-based theory,
object, p, into an object, p*, which in some specified sense is T, may be FL-generalized, and hence upgraded,
defined more precisely than p. The object of precisiation and through addition to T of concepts and techniques
the result of precisiation are referred to as precisiend and drawn from fuzzy logic. Examples: fuzzy control,
precisiand, respectively. In fuzzy logic, a differentiation is
fuzzy linear programming, fuzzy probability theory,
made between two meanings of precision—precision of value,
v-precision, and precision of meaning, m-precision. fuzzy topology, etc.
Furthermore, in the case of m-precisiation a differentiation is
made between mh-precisiation, which is human-oriented 2. Linguistic variables and fuzzy if-then rules. The
(nonmathematical), and mm-precisiation, which is machine formalism of linguistic variables and fuzzy if-then
oriented (mathematical). A dictionary definition is a form of rules is, in effect, a powerful modeling language
mh-precisiation, with the definiens and definiendum playing which is widely used in applications of fuzzy logic.
*
Research supported in part by ONR N00014-02-1-0294, BT Grant CT1080028046, Omron Grant, Tekes Grant and the BISC Program of UC Berkeley.
Basically, the formalism serves as a means of developed computational theory of perceptions and precisiated
summarization and information compression through natural language.
the use of granulation.
An alumnus of the University of Tehran, MIT, and
3. Cointensive precisiation. Fuzzy logic has a high Columbia University, Dr. Zadeh is a fellow of the IEEE,
AAAS, ACM, AAAI and IFSA, and a member of the National
power of cointensive precisiation. This power is
Academy of Engineering. He held NSF Senior Postdoctoral
needed for a formulation of cointensive definitions of Fellowships in 1956-57 and 1962-63, and was a Guggenheim
scientific concepts and cointensive formalization of Foundation Fellow in 1968. Dr. Zadeh was the recipient of the
human-centric fields such as economics, linguistics, IEEE Education Medal in 1973 and a recipient of the IEEE
law, conflict resolution, psychology and medicine. Centennial Medal in 1984. In 1989, Dr. Zadeh was awarded
the Honda Prize by the Honda Foundation, and in 1991
4. NL-Computation (Computing with Words). Fuzzy received the Berkeley Citation, University of California.
logic serves as a basis for NL-Computation, that
is, computation with information described in natural In 1992, Dr. Zadeh was awarded the IEEE Richard W.
Hamming Medal "For seminal contributions to information
language. NL-Computation is of direct relevance to
science and systems, including the conceptualization of fuzzy
mechanization of natural language understanding and sets." He became a Foreign Member of the Russian Academy
to computation with imprecise probabilities. More of Natural Sciences (Computer Sciences and Cybernetics
generally, NL-Computation is needed for dealing Section) in 1992, and received the Certificate of
with second-order uncertainty, that is, uncertainty Commendation for AI Special Contributions Award from the
about uncertainty, or uncertainty2 for short. International Foundation for Artificial Intelligence. Also in
1992, he was awarded the Kampe de Feriet Prize and became
In summary, progression from bivalent logic to fuzzy an Honorary Member of the Austrian Society of Cybernetic
logic is a significant positive step in the evolution of Studies.
science. In large measure, the real world is a fuzzy world. To
deal with fuzzy reality what is needed is fuzzy logic. In In 1993, Dr. Zadeh received the Rufus Oldenburger
coming years, fuzzy logic is likely to grow in visibility, Medal from the American Society of Mechanical Engineers
importance and acceptance. "For seminal contributions in system theory, decision analysis,
and theory of fuzzy sets and its applications to AI, linguistics,
logic, expert systems and neural networks." He was also
LOTFI A. ZADEH awarded the Grigore Moisil Prize for Fundamental
Lotfi A. Zadeh joined the Department of Electrical Researches, and the Premier Best Paper Award by the Second
Engineering at the University of California, Berkeley, in 1959, International Conference on Fuzzy Theory and Technology.
and served as its chairman from 1963 to 1968. Earlier, he was In 1995, Dr. Zadeh was awarded the IEEE Medal of Honor
a member of the electrical engineering faculty at Columbia "For pioneering development of fuzzy logic and its many
University. In 1956, he was a visiting member of the Institute diverse applications." In 1996, Dr. Zadeh was awarded the
for Advanced Study in Princeton, New Jersey. In addition, he Okawa Prize "For outstanding contribution to information
held a number of other visiting appointments, among them a science through the development of fuzzy logic and its
visiting professorship in Electrical Engineering at MIT in applications."
1962 and 1968; a visiting scientist appointment at IBM
Research Laboratory, San Jose, CA, in 1968, 1973, and 1977; In 1997, Dr. Zadeh was awarded the B. Bolzano Medal by
and visiting scholar appointments at the AI Center, SRI the Academy of Sciences of the Czech Republic "For
International, in 1981, and at the Center for the Study of outstanding achievements in fuzzy mathematics." He also
Language and Information, Stanford University, in 1987- received the J.P. Wohl Career Achievement Award of the
1988. Currently he is a Professor in the Graduate School, and IEEE Systems, Science and Cybernetics Society. He served as
is serving as the Director of BISC (Berkeley Initiative in Soft a Lee Kuan Yew Distinguished Visitor, lecturing at the
Computing). National University of Singapore and the Nanyang
Technological University in Singapore, and as the Gulbenkian
Until 1965, Dr. Zadeh's work had been centered on Foundation Visiting Professor at the New University of
system theory and decision analysis. Since then, his research Lisbon in Portugal. In 1998, Dr. Zadeh was awarded the
interests have shifted to the theory of fuzzy sets and its Edward Feigenbaum Medal by the International Society for
applications to artificial intelligence, linguistics, logic, Intelligent Systems, and the Richard E. Bellman Control
decision analysis, control theory, expert systems and neural Heritage Award by the American Council on Automatic
networks. Currently, his research is focused on fuzzy logic, Control. In addition, he received the Information Science
soft computing, computing with words, and the newly Award from the Association for Intelligent Machinery and the
SOFT Scientific Contribution Memorial Award from the University of Saskatchewan, Saskatoon, Canada and the
Society for Fuzzy Theory in Japan. In 1999, he was elected to Polytechnic University of Madrid, Madrid, Spain.
membership in Berkeley Fellows and received the Certificate
of Merit from IFSA (International Fuzzy Systems Dr. Zadeh has single-authored over two hundred papers
Association). In 2000, he received the IEEE Millennium and serves on the editorial boards of over fifty journals. He is
Medal; the IEEE Pioneer Award in Fuzzy Systems; the a member of the Advisory Committee, Center for Education
ASPIH 2000 Lifetime Distinguished Achievement Award; and Research in Fuzzy Systems and Artificial Intelligence,
and the ACIDCA 2000 Award for the paper, "From Iasi, Romania; Senior Advisory Board, International Institute
Computing with Numbers to Computing with Words—From for General Systems Studies; the Board of Governors,
Manipulation of Measurements to Manipulation of International Neural Networks Society; and is the Honorary
Perceptions." In addition, he received the Chaos Award from President of the Biomedical Fuzzy Systems Association of
the Center of Hyperincursion and Anticipation in Ordered Japan and the Spanish Association for Fuzzy Logic and
Systems for his outstanding scientific work on foundations of Technologies. In addition, he is a member of the Advisory
fuzzy logic, soft computing, computing with words and the Board of the National Institute of Informatics, Tokyo; a
computational theory of perceptions. In 2001, Dr. Zadeh member of the Governing Board, Knowledge Systems
received the ACM 2000 Allen Newell Award for seminal Institute, Skokie, IL; and an honorary member of the
contributions to AI through his development of fuzzy logic. In Academic Council of NAISO-IAAC.
addition, he received a Special Award from the Committee for
Automation and Robotics of the Polish Academy of Sciences Professor in the Graduate School and Director, Berkeley
for his significant contributions to systems and information Initiative in Soft Computing (BISC), Computer Science
science, development of fuzzy sets theory, fuzzy logic control, Division, Department of EECS, University of California,
possibility theory, soft computing, computing with words and Berkeley, CA 94720-l776; Telephone: 5l0-642-4959; Fax:
computational theory of perceptions. In 2003, Dr. Zadeh was 5l0-642-l7l2; E-mail: zadeh@eecs.berkeley.edu
elected as a foreign member of the Finnish Academy of
Sciences, and received the Norbert Wiener Award of the IEEE http://www.cs.berkeley.edu/~zadeh/ References
Society of Systems, Man and Cybernetics “For pioneering
contributions to the development of system theory, fuzzy logic
and soft computing.” In 2004, Dr. Zadeh was awarded
Civitate Honoris Causa by Budapest Tech (BT) Polytechnical
Institution, Budapest, Hungary. Also in 2004, he was awarded
the V. Kaufmann Prize by the International Association for
Fuzzy-Set Management and Economy (SIGEF). In 2005, Dr.
Zadeh was elected as a foreign member of Polish Academy of
Sciences, Korea Academy of Science & Technology and
Bulgarian Academy of Sciences. He was also awarded the
Nicolaus Copernicus Medal of the Polish Academy of
Sciences and the J. Keith Brimacombe IPMM Award.
Dr. Zadeh is a recipient of twenty-three honorary
doctorates from: Paul-Sabatier University, Toulouse, France;
State University of New York, Binghamton, NY; University
of Dortmund, Dortmund, Germany; University of Oviedo,
Oviedo, Spain; University of Granada, Granada, Spain;
Lakehead University, Canada; University of Louisville, KY;
Baku State University, Azerbaijan; the Silesian Technical
University, Gliwice, Poland; the University of Toronto,
Toronto, Canada; the University of Ostrava, the Czech
Republic; the University of Central Florida, Orlando, FL; the
University of Hamburg, Hamburg, Germany; the University of
Paris(6), Paris, France; Jahannes Kepler University, Linz,
Austria; University of Waterloo, Canada; the University of
Aurel Vlaicu, Arad, Romania; Lappeenranta University of
Technology, Lappeenranta, Finland; Muroran Institute of
Technology, Muroran, Japan; Hong Kong Baptist University,
Hong Kong, China; Indian Statistical Institute, Kolkata, India;
