More often than not, the classes of objects encountered in the real physical world do not have precisely defined criteria of membership. For example, the class of animals clearly includes dogs, horses, birds, etc. as its members, and clearly excludes such objects as rocks, fluids, plants, etc. However, such objects as starfish, bacteria, etc. have an ambiguous status with respect to the class of animals. The same kind of ambiguity arises in the case of a number such as 10 in relation to the “class” of all real numbers which are much greater than 1.
American electrical engineer and computer scientist (1921–2017)
Lotfali Askar Zadeh (February 4, 1921 – September 6, 2017) was an Azerbaijani-born Iranian American mathematician, electrical engineer, computer scientist, artificial intelligence researcher, and professor emeritus of computer science at the University of California, Berkeley, known for the development of .
From: Wikiquote (CC BY-SA 4.0)
Native Name:
Lütfəli Rəhim oğlu Əsgərzadə
Alternative Names:
Lotfi Zadeh
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Lotfi Asker Zadeh
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Lotfi Aliaskerzadeha
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Lotfali Askar-Zadeh
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Lotfali Askar Zadeh
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Lofti Zadeh
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Lofti A. Zadeh
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Lofti Askar Zadeh
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Lotfi A Zadeh
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Lofti A Zadeh
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Zadeh
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Lotfi Aliasker Zadeh
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Lütfi Zadə
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Lütfizadə
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Zadeh, Lotfi Asker
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Заде, Лотфи
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Заде Л. А.
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Заде Лютфи Аскер
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Заде, Лютфи Аскер
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Заде, Лютфи
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Заде, Лотфи А.
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Заде Лотфи Аскер
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Заде, Лотфи Аскер
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Заде Л.
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Заде
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Аскерзаде, Лютфали
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Аскер Заде, Лотфи
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Аскер Заде, Лютфи
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Лотфи Аскер Заде
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Лотфи А. Заде
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Лотфи Заде
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Л. Заде
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Лютфи Аскер Заде
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Лютфи А. Заде
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Лютфи Заде
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Л. А. Заде
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Лотфи Задех
From Wikidata (CC0)
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.
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