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.
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.