Approaches Of Attribute Reductions For Dual Interval-set Concept Lattices And Object/Attribute-oriented Concept Lattices

The theory of formal concept analysis is first proposed by Wille and Ganter in 1982.It is a powerful tool of data analysis to formalize and conceptualize information in databases.The extension and intension of any concept are determined each other by the Galois connection.Relationships between any two concepts can be connected according to a partial binary relation.Then a partial hierarchical structure,called a concept lattice,is generated.In recent years,concept lattices have been widely used in cognitive computing,ontology research,medical hygiene,software engineering,mineral mining,machine learning and so on.The combination of formal concept analysis and other theories is also a hot issue to study.The object/attribute-oriented concept lattice is an extension model of concept lattices proposed by combining rough sets and concept lattices.Due to the uncertainty and incompleteness of information,it is difficult to represent the extension or intension of a concept with an accurate set.Since the interval set can be used to describe the range of the intension and extension of an inaccurate concept,the interval-set concept lattice gives a method to describe the inaccurate concepts.This paper defines the dual interval-set concept lattice by introducing the interval set into the dual concept lattice.The construction approach and attribute reductions of dual interval-set concept lattices are also discussed.The essence of attribute reductions is to preprocess the formal context,and remove redundant attributes based on attribute importance to simplify the formal context.Another main study in this paper is to investigate the attribute reductions of various concept lattices by using of the relation matrix.The paper mainly study the following contents:For the first part,we combine the interval set with the dual concept lattice,and propose the dual interval-set concept lattices.Its properties is discussed.Applying the relationships between the dual concepts and the dual interval-set concepts,the construction method of the dual interval-set concept lattices is studied.By introducing a partial binary relation on the dual interval-set concept lattice,an interval-set consistent set is defined,and the judgment theorems of the corresponding interval-set reductions are depicted.For the second part,we introduces the notion of the relation matrix into the object/attribute-oriented concept lattice,and discuss the approaches to obtain all object-oriented concepts and attribute-oriented concepts.The attribute characterizations of the object-oriented concept are discussed by using the relation matrix,and the matrix-based judgment approaches of the attribute consistent set are then studied.For an attribute-oriented concept lattice,an object granule matrix is first introduced,which is used to describe the object characterization.The matrix-based judgment approaches of object-oriented consistent sets are also depicted.Lastly,approaches to obtain object/attribute-oriented concept lattices are discussed according to the relation matrix and interval-set vectors.