Granular entropy based hybrid knowledge reduction using uniform rough approximations

Knowledge reduction is usually a key pre-processing step before some other action such as induction of rules is performed. Rough set theory is a powerful tool to deal with knowledge reduction. The values of attributes in real world may often be both symbolic and real-valued, that is, hybrid. In order to deal with the reduction of the hybrid knowledge, we analyze Pawlak\´s rough approximations and its different kinds of extensive versions and then obtain a uniform form of knowledge granules and rough approximations under crisp and fuzzy relations. Aimed at hybrid knowledge reduction using the uniform rough approximations, we give a new interpretation to Yager\´s entropy from "knowledge granules" and present the concept and definitions of "granular entropy". Based on the granular entropy, we propose an approach to hybrid knowledge reduction. The utility of this approach is demonstrated with an application example, in the wine recognition dataset from the UCI machine learning data repository.