Concept granular computing based on lattice theoretic setting

Abstract

Based on the theory of concept lattice and fuzzy concept lattice, a mathematical model of a concept granular computing system is established, and relationships of the system and concept lattices, various variable threshold concept lattices and fuzzy concept lattices are then investigated. For this system, concept granules, sufficiency information granules and necessity information granules which are used to express different relations between a set of objects and a set of attributes are proposed. Approaches to construct sufficiency and necessity information granules are also shown. Some iterative algorithms to form concept granules are proposed. It is proved that the concept granules obtained by the iterative algorithms are the sub-concept granules or sup-concept granules under some conditions for this system. Finally, we give rough approximations based on fuzzy concept lattice in formal concept analysis. © 2009 Springer-Verlag Berlin Heidelberg.