Two Formal Systems of Set Theory

Application of Rough Set Theory in Data Mining for Decision Support Systems (DSSs)

Decision support systems (DSSs) are prevalent information systems for decision making in many competitive business environments. In a DSS, decision making process is intimately related to some factors which determine the quality of information systems and their related products. Traditional approaches to data analysis usually cannot be implemented in sophisticated Companies, where managers ne...

Two-Part Set Systems

The two part Sperner theorem of Katona and Kleitman states that if X is an n-element set with partition X1 ∪X2, and F is a family of subsets of X such that no two sets A,B ∈ F satisfy A ⊂ B (or B ⊂ A) and A ∩ Xi = B ∩ Xi for some i, then |F| ≤ ( n ⌊n/2⌋ ) . We consider variations of this problem by replacing the Sperner property with the intersection property and considering families that satis...

Formal Theory of Differential-algebraic Systems

1994 Abstract. We propose a new approach to diierential-algebraic systems based on the formal theory of partial diierential systems. This results in a new deenition of the index of the system, which is similar to but more general than the one proposed recently by Rabier and Rheinboldt. This index, however, is not related to the numerical diiculty of solving the system, but to the amount of symb...

Set theory and dynamical systems

We give an introduction to a recent direction of research in set theory, developed primarily over the last 15–20 years, and discuss its connections with aspects of dynamical systems and in particular rigidity phenomena in the context of ergodic theory.

Set-serializability: a Formal Theory for Partitioned Data (extended Abstract)