Algebraic approaches to granular computing

Abstract

We study the granular structures in granular computing from algebraic views. We model a granular structure based on an algebra that consists of a universe and a closure operator. Based on this formulation, we define the basic granules in a granular structure through the notion of subalgebras. Using formal concept analysis and rough set analysis as two examples, we demonstrate that the proposed formulation can unify a number of current studies on the related areas of granular computing. Moreover, by modelling the granular structures in rough sets with algebraic approaches, we generalize the notion of approximations in rough sets into a general granular structure. The algebraic approaches provide a mathematical formulation of granular structures, which may assist us in the construction and interpretation of granules and granular structures.