BISC The 



Fuzzy Set: 1965 … Fuzzy Logic: 1973 …
BISC: 1990 … HumanMachine Perception: 2000  … BISC
Principal Achievements Lotfi A. Zadeh A Personal Statement
(19652014) List of principal contributions
Principal
contributions prior to 1965
A
new direction—development of fuzzy set theory and fuzzy logic Publication
of my first paper on fuzzy sets in 1965 marked the beginning of a new phase
of my scientific career. From 1965 on, almost all of my publications
have been focused on development of fuzzy set theory, fuzzy logic and their
applications. It should be noted that most of my papers published prior to
1977, and all papers published since then, are singleauthored. My
publications list contains 247 papers and books. My publications are
associated with 125,653 Google Scholar citations. My first paper entitled “Fuzzy
sets,” got a mixed reaction. My strongest supporter was the late
Professor Richard Bellman, an eminent mathematician and a leading contributor
to systems analysis and control. For the most part, I encountered
skepticism, derision and sometimes outright hostility. There were two
principal reasons: The word “fuzzy” is usually used in a pejorative sense;
and, more importantly, my abandonment of the classical, Aristotelian,
bivalent logic was a radical departure from deepseated scientific
traditions. What changed the situation was the enthusiastic acceptance of my
ideas in Japan. Starting in the early seventies, Japanese universities and
industrial research laboratories began to play an active role in the
development of fuzzy logic and its applications. Much has happened since that
period. A summary of the current status of fuzzy logic and its applications
appears in the attached Report on the Impact of Fuzzy Logic. What is
worthy of note is that as of 2/26/14, my 1965 paper on fuzzy sets drew 53,172
Google Scholar citations. It is the highest cited paper in the literature of
Computer Science (Web of Science); it is the seventh highest cited paper in
the literature of Science (Web of Science). The first five highest cited
papers in Science are in biomedicine, and the sixth highest ranking paper is
in Chemistry. The
concept of a linguistic variable. Decisionmaking in a fuzzy environment. During
the past fortynine years, I played an active and visible role in the
development of fuzzy logic and its applications. My 1973 paper entitled
“Outline of a new approach to the analysis of complex systems and decision
processes,” was a pathbreaking work in which the concept of a linguistic
variable was introduced, and a calculus of fuzzy ifthen rules was
developed. Today, almost all applications of fuzzy logic employ the concept
of a linguistic variable, and there is a huge literature centering on
fuzzyrulebased calculi. A related paper entitled, “The concept of a
linguistic variable and its application to approximate reasoning,” published
in 1975, is the highest cited paper in Information Sciences. Another
important paper was my 1970 paper entitled, “Decisionmaking in a
fuzzy environment,” coauthored with R.E. Bellman. This paper is widely
viewed as a seminal contribution to application of fuzzy logic to decision
analysis. Development of
possibility theory My 1978 paper, “Fuzzy sets as a
basis for a theory of possibility,” laid the foundation for what I called
“possibility theory.” Greeted with skepticism at first, possibility theory
has become a widely used tool for dealing with uncertainty, with the
understanding that possibility theory and probability theory are
complementary rather than competitive. My 1978 paper on possibility theory is
the highest cited paper in Fuzzy Sets and Systems. Development of a
theory of approximate reasoning My 1979 paper entitled, “A
theory of approximate reasoning,” initiated a new direction in the
development of fuzzy logic as the logic of approximate reasoning. The
basic ideas introduced in this paper underlie most of the techniques
which are in use today for purposes of inference and deduction from
information which is approximate rather than exact. Soft computing In
1991, I introduced the concept of soft computing—a consortium of
methodologies which collectively provide a foundation for the conception,
design and utilization of intelligent systems. One of the principal
components of soft computing is fuzzy logic. Today, the concept of soft
computing is growing rapidly in visibility and importance. In 2005, a
European Center for Soft Computing was established in Spain. Many of
my papers written in the eighties and early nineties were concerned, for the
most part, with applications of fuzzy logic to knowledge representation and
commonsense reasoning. Computing with
words (CWW) In 1996, a major idea occurred
to me—an idea which underlies most of my current research activities. This
idea was described in two seminal papers entitled, “Fuzzy logic=Computing
with words” and “From computing with numbers to computing with words—from
manipulation of measurements to manipulation of perceptions.” My 1999 paper
initiated a new direction in computation which I called, Computing with Words
(CWW). CW opened the door to computation with information described in
natural language—a system of computation which is of intrinsic importance
because much of human knowledge is described in a natural language.
Computation with information described in natural language cannot be dealt
with through the use of the machinery of natural language processing (NLP).
The problem is semantic imprecision of natural languages. More specifically,
a natural language is basically a system for describing perceptions.
Perceptions are intrinsically imprecise, reflecting the bounded ability of
sensory organs, and ultimately the brain, to resolve detail and store
information. Semantic imprecision of natural languages is a concomitant of
imprecision of perceptions. My book entitled, “Computing with Words—Principal
Concepts and Ideas,” was published by Springer in 2012. Development of a
computational theory of perceptions (CTP) Measurements of one kind or another have a
position of centrality in science. In large measure, science is based on
measurements but what is striking is that humans have a remarkable capability
to perform a wide variety of mental and physical tasks without any measurements
and any computations. Driving a car in heavy city traffic is an example. In a
paper published in 1999, “From computing
with numbers to computing with words—from manipulation of measurements to
manipulation of perceptions,”
and in other papers which followed, I described an unconventional
approach—computational theory of perceptions (CTP)—to mechanized reasoning
and computation with perceptions rather than measurements. The key idea in
CTP is that of describing perceptions in natural language employing the
machinery of computing with words to act on perceptionbased information.
This simple idea has a potential for wideranging applications in robotics,
control and related fields. A particularly important area is robotics.
Another important application area is what is referred to as “perceptual
computing.” Development of a
theory of precisiation of meaning. The concept of a
restriction. Raw natural language does not
lend itself to computation. A prerequisite to computation is precisiation of meaning. What I consider to be one of my
major contributions is the development of a theory of precisiation
of meaning, starting with my 1978 paper, “PRUF—a meaningrepresentation
language for natural languages” and continuing to present. My theory of precisiation of meaning is a radical departure from
traditional approaches to semantics of natural languages, especially
possibleworld and truthconditional semantics. The centerpiece of my theory
is the concept of a restriction (generalized constraint)—a concept which was
introduced in my 1975 paper, “Calculus of
fuzzy restrictions,”
and extended in my 1986 paper, “Outline of a
computational approach to meaning and knowledge representation based on the
concept of a generalized assignment statement.” The key idea involves representing the meaning
of a proposition, p, drawn from a natural language as a restriction. A
restriction is an expression of the form X isr R,
where X is the restricted (constrained) variable, R is the restricting
(constraining) relation and r is an indexical variable which defines the way
in which R restricts X. Generally, X, R and r are implicit in p. At this
juncture, restrictionbased semantics of natural languages is the only system
of precisiation of meaning which makes it possible
to solve problems which are described in a natural language. The importance
of my theory of precisiation of meaning has not as
yet been widely recognized because it breaks away from traditional theories
of natural language. I believe that eventually my theory will gain acceptance
and wide use. Development of a
generalized theory of uncertainty (GTU) In a seminal paper published in
2002, “Toward a perceptionbased theory of probabilistic reasoning with
imprecise probabilities” I initiated a significant generalization of
probability theory. The ideas
introduced in my 2002 paper were further developed in my 2005 paper, “Toward
a generalized theory of uncertainty (GTU)—an outline” and in my 2006 paper,
“Generalized theory of uncertainty (GTU)—principal concepts and ideas.” The
Generalized Theory of Uncertainty (GTU) which is described in these papers
adds to standard probability theory an essential capability which standard
probability does not have—the capability to compute with probabilities,
events, quantifiers and relations which are described in a natural language.
As we move further into the age of machine intelligence and automated
everyday reasoning, this capability is certain to play an increasingly
important role in decision analysis, planning, risk assessment and economics.
A key idea in GTU is that of equating information to restriction. The
principal modes of restriction are possibilistic,
probabilistic and veristic. Development of
extended fuzzy logic In a short but important paper
published in 2009, I outlined an extension of fuzzy logic which opens the
door to mechanization of reasoning with unprecisiated
concepts. A model of extended fuzzy logic is fgeometry. In Euclidian
fgeometry, figures are drawn by hand with a spray pen. There is no ruler and
no compass. There are flines, ftriangles and fcircles. There are
fdefinitions, faxioms and fproofs. At this stage, extended fuzzy logic is
in its early stages of development, but it has a potential for important
applications in the future. Introduction of
the concept of a Znumber In a
2011 paper entitled, “A note on Znumbers,” a new concept—the concept of a
Znumber is introduced. Basically, a Znumber is an ordered pair of two fuzzy
numbers. The first fuzzy number is a restriction on the values which a
realvalued variable can take. The second fuzzy number is a restriction on
the probability of the first fuzzy number. Typically, the two fuzzy numbers
are described in a natural language. The concept of a Znumber is intended to
associate a measure of reliability with the value of a variable. The concept
of a Znumber has a potential for important applications in economics,
planning, risk assessment and decision analysis. A new
direction which is being explored is aimed at enhancing Web IQ (WIQ) through
addition of deduction capability to search engines. Existing search engines
have this capability to a very limited degree. The principal obstacle is the
nature of world knowledge. In large measure, world knowledge is
perceptionbased, e.g., “it is hard to find parking near the campus before
late afternoon.” Such knowledge cannot be dealt with through the use of
methods based on classical, bivalent logic. In the approach that is being
explored, world knowledge is dealt with through the use of PNL, in
association with an epistemic lexicon and a modular, multiagent
deduction database. A new approach to
truth and meaning The concepts of truth and
meaning have a position of centrality in logic and theories of natural
language. In 2013, in a short but important paper entitled, “Toward a
restrictioncentered theory of truth and meaning (RCT)” I described a new
approach to truth and meaning based on the concept of a restriction. In this
paper, a proposition, p, drawn from a natural language is associated not just
with one truth value—as in traditional theories, but with two truth
values—internal truth value and external truth value. In representation of
meaning, the concept of explanatory database, ED, plays a pivotal role. RCT
is the only system which offers a capability to represent the meaning of
fuzzy propositions, that is, propositions which contain words which are
labels of fuzzy sets, e.g., tall, fast, most, etc. Propositions drawn from a
natural language are predominantly fuzzy propositions. Existing approaches to
semantics of natural languages, principally possibleworld semantics and
truthconditional semantics, do not have this capability. Similaritybased
definitions of possibility and probability The concept of probability has been around for more
than two centuries. Probability theory is one of the most important and
widely used theories in science. Probability theory is a deep and rigorous
theory. But in realworld settings, there are many simple questions which
relate to probability theory to which answers are hard to come up with. The
problem is rooted in the fact that probability theory is based on the
classical, Aristotelian, bivalent logic. Bivalent logic is intolerant of
imprecision and partiality of truth. In the new approach which is outlined,
fuzzy logic is employed to construct a similaritybased definition of
probability which lend itself to the use of machine learning techniques. The
similaritybased definition of probability opens the door to a wide range of
applications in which very large databases are involved, particularly in the
realms of medical diagnostics and recognition technology. From
its inception, fuzzy logic has been an object of controversy, skepticism and
sometimes outright hostility. Eventually, the wideranging applications of
fuzzy logic within science and technology have acquired visibility and
acceptance. It is my belief that in coming years, fuzzy logic will continue
to grow in importance and visibility. With the passage of time, it’s likely
that the impact of fuzzy logic will be felt increasingly in many fields of
science and technology. Strangely as it may seem, fuzzy logic may have a
profound impact on both pure and applied mathematics. There is a reason, the
concept of a set is one of the most fundamental concepts in mathematics.
Progression from the concept of a set to the concept of a fuzzy set may
eventually lead to a generalization of many theories and formalisms within
mathematics which are based on the classical, Aristotelian, bivalent logic. Citations
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Short Curriculum Vitae



Fuzzy Set: 1965 …
Fuzzy Logic: 1973 … BISC: 1990 … HumanMachine Perception: 2000  … 