Granule description based on positive and negative attributes

Abstract

Granule description is a fundamental problem in granular computing. The existing studies are mainly based on Wille’s concept lattice, and attribute reduction techniques, e.g., minimal generators of granules, are often adopted to compute the most concise description of a given granule. However, on one hand, as the construction of concept lattice has a relatively high time complexity especially for large formal contexts, it may bring difficulties in real applications. On the other hand, how to use positive and negative attributes for granule description is still an open problem. In this paper, to improve the description efficiency, we first consider attribute-induced atomic granules as the building blocks of more complicated granules. And then, we discuss granule description based on positive and negative attributes, respectively. Finally, granule description is also investigated by combining positive and negative attributes. The main contribution of this study is to find the most concise descriptions of definable granules from the perspectives of positive and negative attributes.