Granular Transformation and Irreducible Element Judgment Theory Based on Pictorial Diagrams

As an important tool for data analysis and knowledge processing, formal concept analysis has been applied to many fields. Currently, granular computing (GrC) provides a novel approach for data analysis. In this paper, pictorial diagrams of a formal context are first defined based on equivalence relations. And then, from the viewpoint of GrC, the transformation between equivalence classes and three kinds of concepts (formal concept, property oriented concept, and object oriented concept) in formal contexts are studied. Further, using the relationships between arrow relations proposed by Wille and Ganter and irreducible elements of a concept lattice, the new judgment theorems for join(meet)-irreducible elements of a concept lattice, join-irreducible elements of a property oriented concept lattice and an object oriented concept lattice are achieved.