Attribute Logic Formula Description of Granule and Its Application to Build Concept Lattice

This paper focus on the granule description based on formal concept analysis. First, we introduce the notion of attribute logic formula in a formal context, and then prove a general granule description theorem by using attribute logic formulas. Second, we prove some basic granule description theorems based on concept, property-oriented concept and object-oriented concept respectively. Third, we propose some methods that use attribute logic formulas to describe concept, property-oriented concept and object-oriented concept respectively, and prove that a property-oriented concept lattice and an object-oriented concept lattice are anti-isomorphic. Finally, we apply granule description methods to build concept lattice, property-oriented concept lattice and object-oriented concept lattice, propose some algorithms for building concept lattice, property-oriented concept lattice and object-oriented concept lattice, and give some examples and experiments to show the utility of algorithms.