Rule induction for tolerance relation-based rough sets

Tolerance relation, derived partition, quotient set and named quotient space are very important concepts based on tolerance relations. In this paper, we review them at first. Then we present the construction of three spaces, namely, granular, quotient and knowledge spaces. We define the concepts of knowledge dependency in rough set models based on tolerance relations, such as weak dependency, strong dependency and central dependency, as well as the relationships among them. We present the process how to obtain the tolerance information table from knowledge base. An example is given to illustrate extracting rules from tolerance information table.