# 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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It is generally accepted that the (presumably) non-contradictory Zermelo-Fraenkel set theory ZF with the axiom of choice is the most accurate and complete axiomatic representation of the core of Cantor set theory.
223-232)--in which I compare a version of the Laws of Thought of Aristotle, stated in our set theory language, with the non-Aristotelian postulates of Korzybski, stated in my non-standard notation (discussed below).
Rough Set Theory (RST) has been an excellent mathematical tool for data analysis and it has offered an exciting theoretic base for the solution of many problems within knowledge discovery [4], [5], [6], [7], [8], [9] and [10].
In the other dimension, the formalized language of classical set theory is expanded to the more expressive language of fuzzy set theory, where further distinctions are based on various special types of fuzzy sets.
At first glance the problem appears as a rudimentary set theory problem.
This statement is the basic axiom, or performative, of mathematical set theory. The rest of set theory, as well as the rest of mathematics, can be derived from the acceptance of this simple, existential statement.
Fuzzy Set Theory (FST) has become a branch of mathematics that generalizes the concept of a set (2) to provide better tools for dealing with the sorts of situations described in the previous paragraph.
The authors are probably confused by the fact that in some applications of rough set theory, discretization is used as a preprocessing.
Some computer scientists are so used to thinking in terms of types that they find untyped set theory completely unnatural.
This is the almost universal belief that naive set theory, a theory which had seemed well-nigh self-evident, has been shown to be false by the set-theoretic antinomies.
Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets.
He said the theme of the conference will cover the major areas of mathematical sciences, such as Functional Analysis and its Applications, Fluid Dynamics, Fuzzy logic, Topological Vector Spaces and Nonlinear Operator Theory, Best Approximations Theory, Soft Set Theory, Graph Theory, Algebra and so on.

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