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Fuzzy Math – Beginner level introduction to Fuzzy Logic Fuzziness and exactness – Fuzziness in everyday life, science, religion, ethics, politics, etc. Fuzzylite – A cross-platform, free open-source Fuzzy Logic Control Library written in C++.
Fuzzy mathematics is the branch of mathematics including fuzzy set theory and fuzzy logic that deals with partial inclusion of elements in a set on a spectrum, as opposed to simple binary "yes" or "no" (0 or 1) inclusion. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets. [1]
In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets.In fuzzy logic, it represents the degree of truth as an extension of valuation.
A fuzzy set is a pair (,) where is a set (often required to be non-empty) and : [,] a membership function. The reference set (sometimes denoted by or ) is called universe of discourse, and for each , the value () is called the grade of membership of in (,).
In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic.
A systematic study of particular t-norm fuzzy logics and their classes began with Hájek's (1998) monograph Metamathematics of Fuzzy Logic, which presented the notion of the logic of a continuous t-norm, the logics of the three basic continuous t-norms (Łukasiewicz, Gödel, and product), and the 'basic' fuzzy logic BL of all continuous t-norms ...
A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. [2] Just like fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers.
Fuzzy set operations are a generalization of crisp set operations for fuzzy sets. There is in fact more than one possible generalization. There is in fact more than one possible generalization. The most widely used operations are called standard fuzzy set operations ; they comprise: fuzzy complements , fuzzy intersections , and fuzzy unions .
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