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Fuzzy Set Theory

2018
This chapter reviews concepts from fuzzy set theory indispensable for the fuzzy extension of th e multi-criteria decision making methods based on pairwise comparison matrices. Trapezoidal and triangular fuzzy numbers and intervals, which are most often used for the fuzzy extension of pairwise comparison methods, are introduced here, and normalization ...
Ali Ebrahimnejad, José Luis Verdegay
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Fuzzy Set Theory

Operations-Research-Spektrum, 1992
The term “fuzzy” was proposed by Zadeh in 1962 [273]. In 1965, Zadeh formally published the famous paper “Fuzzy Sets”[274]. The fuzzy set theory is developed to improve the oversimplified model, thereby developing a more robust and flexible model in order to solve real-world complex systems involving human aspects.
Young-Jou Lai, Ching-Lai Hwang
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Fuzzy set theory

2000
The theory of fuzzy sets was introduced in 1965 by Lotfi A. Zadeh as a generalization of the classical Cantorian set theory whose logical basis is the two-valued Boolean logic (compare also [Klaua 1965, 1967]). It was suggested in [Zadeh 1965] to use the minimum T M, the maximum S M, and the standard negation N S in order to model the intersection, the
Erich Peter Klement   +2 more
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Fuzzy Set Theory

2011
Fuzzy set theory has been developed to solve problems where the descriptions of activities and observations are imprecise, vague, or uncertain. The term “fuzzy” refers to a situation in where there are no well defined boundaries of the set of activities or observations to which the descriptions apply.
Jiuping Xu, Xiaoyang Zhou
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Fuzzy Set Theory

2017
This entry presents a definition of fuzzy set theory and an overview of some applications to model flexible information retrieval systems. The entry focuses on a description of fuzzy indexing procedures defined to represent the varying significance of terms in synthesizing the documents’ contents, the representation of structured documents so as to ...
Kraft D, Bordogna G, Pasi G
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Fuzzy Set Theory

2008
In this chapter we present the reader with the fundamental concepts of fuzzy set theory. The basic primer on fuzzy set theory remains Zadeh’s1965 seminal work. A number of scholars have since discussed several aspects of fuzzy set theory pertinent to the social sciences. Perhaps the best overview is provided by Smithson and Verkuilen (2006).
Terry D. Clark   +4 more
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Fuzzy Set Theory

1984
An extension of conventional set theory, with the grade of membership for an element in a set taking a value anywhere in the range [0,1], instead of 0 or 1 only. Developed as a means of avoiding the complexity in descriptions of subjective or ill-understood processes. Fuzzy logic extends the simple Boolean operators and can express Implication.
Alan Bundy, Lincoln Wallen
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Fuzzy logic and fuzzy set theory

Archive for Mathematical Logic, 1992
On the semantic side, the authors consider the truth degree set \([0,1]\) with a constant for the degree 0.5, with min, max, Gödel implication, the negation defined by it in the intuitionistic style, but also with Łukasiewicz's (1-..)-negation, bounded sum, and product as connectives, and with sup, inf as quantifiers.
Takeuti, Gaisi, Titani, Satoko
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Fuzzy-Set-Theorie

1999
Da die Fuzzy-Set-Theorie ein Instrument zur Abbildung der in Kapitel zwei dargestellten Imponderabilien und Unsicherheiten ist, werden nachfolgend sowohl die elementaren Grundla-gen als auch die auf ihnen basierenden und ftir die weitere Untersuchung relevanten Fuzzy-Algorithmen vorgestellt.
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Using fuzzy set theory

IEEE Potentials, 1996
Two main trends are mentioned: the fuzzy set theory and the fuzzy logic. Both build upon set theory and logic, respectively. Three features distinguish the approaches: (1) the use of so called linguistic variables, instead of or together with numeric variables; (2) the use of fuzzy conditional statements to represent simple relations between variables;
C. Radu, R. Wilkerson
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