On modeling data mining with granular computing

This paper deals with the formal and mathematical modeling of data mining. A framework is proposed for rule mining based on granular computing. It is developed in the Tarski's style through the notions of a model and satisfiability. The model is a database consisting of a finite set of objects described by a finite set of attributes. Within this framework, a concept is defined as a pair consisting of the intension, an expression in a certain language over the set of attributes, and an extension of the concept, a subset of the universe. An object satisfies the expression of a concept if the object has the properties as specified by the expression, and the object belongs to the extension of the concepts. Rules are used to describe relationships between concepts. A rule is expressed in terms of the intentions of the two concepts and is interpreted in terms of the extensions of the concepts. Two interpretations of rules are examined in detail, one is based on the logical implication and the other on the conditional probability.