# Fuzzy Logic

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## Fuzzy Logic

A system which mathematically models complex relationships which are usually handled in a vague manner by language. Under the title of "Fuzzy Logic" falls formal fuzzy logic (a multi-valued form of logic), and fuzzy sets. Fuzzy sets measure the similarity between an object and a group of objects. A member of a fuzzy set can belong to both the set, and its complement. Fuzzy sets can more closely approximate human reasoning than traditional "crisp" sets. See: Crisp sets.

## Fuzzy Logic

A form of logic programmed into some computers to allow them to use probability. That is, fuzzy logic allows computers to deal with uncertainty and to make decisions based on the information available. Unlike pure logic, which requires certainty, fuzzy logic helps computers make decisions the way humans do, only faster. This can be important in some investment strategies, such as arbitrage, that require decisions to be made very quickly.
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Since the very inception of Soft set theory proposed by Molodtsov [3] it met with high appreciation.
Fuzzy set theory was first introduced by Polish mathematician Pawlak in 1982, and it offers unique advantages in the handling of incomplete and low-accuracy data.
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As there exists an established practice of physics, so there exists an established practice of set theory--and as physics is to be considered as being (roughly) on the right track, so are set theory and mathematics.
Before we pass from the first order logic to the other kinds of logic, respectively to one useful for us, namely Cermelo-Fraenkel set theory, I wish to make an important remark in order to prevent possible misunderstandings: mathematics can be treated syntactically as a theory with its extensions and as a structure with its expansions.
True, they had decided to use the context of Axiomatic Set Theory, ZF, as developed by Zermelo and Fraenkel for their work.
It is feasible that a symbiosis of the proposed theory and Vdovin set theory [1, 2] will permit to formulate a (presumably) non-contradictory axiomatic set theory which will represent the core of Cantor set theory in a maximally full manner as to the essence and the contents.
Comparison of fuzzy set theory and stochastic method in application to the analysis of the load-carrying capacity of steel members under tension, in Proc.
By stating the non-Aristotelian premises in the set theory notation that we used (a Bourbaki algebraic dialect), we showed these premises as acceptable, as judged by the logical standards of set theory.

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