Knowledge Dependency Relationships in Incomplete Information System Based on Tolerance Relations

In this paper we define the concepts of knowledge dependency, partial knowledge dependency and dependency degree in rough set models based on tolerance relations for incomplete information system. These concepts, not properly defined and studied in previous research study for incomplete information system, but are very important from data mining and rough set theory community. We consider two kinds of dependency relationships: one is related to the conditional attribute subset and the decision, and the other is related to two different conditional attribute subsets. We then propose several theorems based on our revised knowledge dependency relationships. We give formal proofs of the theorems and verify their correctness with some examples.