The Relationships Among Several Attribute Reduction Methods Of Formal Context

Formal Concept Analysis is an powerful tool of data analysis and knowledge expression,which is based on formal context.A formal context consists of objects,attributes and binary relations between objects and 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.As an important tool of knowledge processing,the attribute reduction of formal context has been applied in many fields.Based on Wille's concept lattice,many attribute reduction criteria and attribute reduction methods have been proposed.This paper mainly discusses the relationship between some attribute reduction of concept lattices and the problem of decision rules based on property oriented and object oriented concept lattices.The major achievements are as follows:1.The notions of granular consistent set and granular reduction in the formal context with respect to attribute oriented concept lattice are proposed in this paper.The judgment theorem for granular consistent set is provided and the granular reduction method is presented by using discernible attributes between objects.Furthermore,the relationships among granular reduction,attribute oriened granular reduction and classification reduction are investigated.It is shown that the attribute oriented granular consistent sets are granular consistent sets.2.Based on decision formal context,we propose the decision rules based on object and property oriented concept lattices.The semantic interpretation of decision rules is provided.Furthermore,the relationships between decision rules based on property oriented concept lattices and decision rules based on Wille's concept lattices are described.A method for determining the consistent of attribute sets is given.