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 , , , , ,  and .
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
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
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.