General vague rough approximation: an extended method of fuzzy knowledge representation

Abstract

The classical rough set theory has been extended to fuzzy data environments by many authors, resulting in the development of the fuzzy rough set. Recently, vague set is treated as an extension of fuzzy set, but the existing theories and approaches of fuzzy rough set could not be applied directly to data set represented by vague set. In this article, we attempt to establish a theoretical model for vague data by combing both rough set and vague set. We first introduced the basic notions of vague t-norms and t-conorms. Next, we developed a general vague rough approximation set for generalizing to fuzzy rough set. Then, to overcome the inconvenience of dealing vague data, we also introduced a model for transforming a vague set into a fuzzy set to take the place of an interval vague set. Moreover, we also give some perspectives for future research.