The Approaches Of Attribute Reductions Of Three-way Concept Lattices

Formal Concept Analysis(FCA)is an efficient tool of data analysis and knowledge processing.It is formulated based on the notion of a formal context specifying which objects posses what properties or attributes.A formal concept is defined as a pair of a set of objects and a set of properties connected by two set-theoretic operators.Recently,more and more attentions have been paid to the three-way decision(3WD),it has been widely used in many fields,such as computer science,information science,social science,etc.Because of the extensive usages of 3WD and FCA,three-way formal concept analysis will become a very useful tool for knowledge discovery and data analysis.The attribute reduction of formal context is an important topic in formal concept analysis.Based on Wille’s concept lattice and three-way concept lattice,several attribute reduction criteria and attribute reduction approaches have been presented.In this paper,we conduct a further study on the way of the attribute reduction of three-way concept lattices and three-way approximate concept lattices.The major achievements are as follows:1.Based on OE concept lattice,a new approach for granular reduction is proposed by using discernibility attributes of the objects.It simplify the existing granular reduction approach.It is proved that objects-induced three-way concept lattice based granular reduction and rough set based classification reduction are equivalent.2.Based on AE concept lattice,a new approach for reduction is proposed by using equivalence class of the objects.3.Based on OE approximate concept lattice,we propose an approach for granular reduction by characterizing discernibility attributes of the objects.