Abstract
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.
Highlights
Granular computing can be viewed as a world outlook and methodology for observing and recognizing objective things, it is a computing paradigm unifying under the ‘‘information granules umbrella’’ different methodologies and techniques used for processing complex structure data
We introduce the notion of and the semantic of attribute logic formula based on a formal context
We prove a general granule description theorem that each granule in a concept can be expressed as the semantic of an attribute logic formula
Summary
Granular computing (in short, GrC) can be viewed as a world outlook and methodology for observing and recognizing objective things, it is a computing paradigm unifying under the ‘‘information granules umbrella’’ different methodologies and techniques used for processing complex structure data. X. Wu et al.: Attribute Logic Formula Description of Granule and Its Application to Build Concept Lattice according to a given partition criteria, and approximate describing the concepts or the subsets of the domain that cannot be described by the primitive classification criterion. Zhi studied the granule description from the perspective of necessary attribute analysis based on object-oriented concept lattice [28]. This paper is a continuation of our previous work on attribute logic formulas and granule description based concept analysis [30]. Based on basic granule description theorems, we give some methods that use attribute logic formulas and their semantic to represent 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.
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