Lotfi A. Zadeh: Setting

“A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.”

Lotfi A. Zadeh

Source: 1960s, Fuzzy sets (1965), p. 338

“A frequent source of misunderstanding has to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLw is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLw</sub”

Lotfi A. Zadeh

Zadeh (1995) in Foreword of George J. Klir Fuzzy sets and fuzzy logic: theory and applications.
1990s

Problem , Sense

“Essentially, a fuzzy algorithm is an ordered sequence of instructions (like a computer program) in which some of the instructions may contain labels or fuzzy sets, e. g.:
Reduce x slightly if y is very large
Increase x very slightly if y is not very large and not very small
If x is small then stop; otherwise increase x by 2.”

Lotfi A. Zadeh

Source: 1970s, Outline of a new approach to the analysis of complex systems and decision processes (1973), p. 30

“It was a biologist — Ludwig von Bertalanffy — who long ago perceived the essential unity of system concepts and techniques in the various fields of science and who in writings and lectures sought to attain recognition for “general systems theory” as a distinct scientific discipline. It is pertinent to note, however, that the work of Bertalannfy and his school, being motivated primarily by problems arising in the study of biological systems, is much more empirical and qualitative in spirit than the work of those system theorists who received their training in exact sciences.
In fact, there is a fairly wide gap between what might be regarded as “animate” system theorists and “inanimate” system theorists at the present time, and it is not at all certain that this gap will be narrowed, much less closed, in the near future.
There are some who feel this gap reflects the fundamental inadequacy of the conventional mathematics—the mathematics of precisely defined points, functions, sets, probability measures, etc.—for coping with the analysis of biological systems, and that to deal effectively with such systems, we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions. Indeed the need for such mathematics is becoming increasingly apparent even in the realms of inanimate systems”

Lotfi A. Zadeh

Zadeh (1962) "From circuit theory to system theory", Proceedings I.R.E., 1962, 50, 856-865. cited in: Brian R. Gaines (1979) " General systems research: quo vadis? http://pages.cpsc.ucalgary.ca/~gaines/reports/SYS/GS79/GS79.pdf", General Systems, Vol. 24 (1979), p. 12
1960s

School , Feeling , Mathematics , Motivation

“A frequent source of misunderstanding has to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw is almost synonymous with the theory of fuzzy sets.”

Lotfi A. Zadeh

In this context, what is important to recognize is that: (a) FLw is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLw
Zadeh (1995) in Foreword of George J. Klir Fuzzy sets and fuzzy logic: theory and applications.
1990s

Sense , Problem