Object(Attribute)-Oriented Concept Reduction Preserving Binary Relations

Concept lattice is a powerful tool for knowledge representation and data mining.However,the construction of concept lattices is essentially an NP-hard problem,which is rather time-consuming,especially for a large volume of data.Therefore,it is very important to investigate the reduction of a concept lattice while preserving some of its specific properties.This paper studies object-oriented and attribute-oriented concept reduction preserving binary relations in formal concept analysis and extends to fuzzy concept reduction.The main contributions of this paper are described as follows:(1)The definition of factorization based on object-oriented and attribute-oriented concepts,and object-oriented and attribute-oriented concept reduction were proposed.Then,the existence and judgment method of object-oriented and attribute-oriented concept reduction were discussed.And then,the approaches for object-oriented and attribute-oriented concept reduction were proposed.(2)The incremental updating algorithms for object-oriented and attribute-oriented concept reduction were proposed.Then,according to the different roles of object-oriented and attribute-oriented concepts in the process of reduction,they were divided into core,relative necessary,and unnecessary object-oriented and attribute-oriented concepts,and the characteristics of these three types of object-oriented and attribute-oriented concepts were respectively discussed.(3)The definition of factorization based on fuzzy concepts,and fuzzy concept reduction were proposed.Then,the existence and judgment method of fuzzy concept reduction were discussed.And then,an approach for fuzzy concept reduction was proposed.According to the different roles of fuzzy concepts in the process of reduction,they were divided into core,relative necessary,and unnecessary fuzzy concepts,and the characteristics of these three types of fuzzy concepts were respectively discussed.Furthermore,fuzzy concept reduction was extended to multi-value fuzzy concept reduction.(4)By experiments to explore the influence of attribute granulation on attribute-oriented concept reduction and quantitative relationships between attribute-oriented concept reduction,3-value,and 5-value fuzzy concept reduction.Research manifested that for a classical or fuzzy formal context,there exists at least one object-oriented and attribute-oriented concept reduction or fuzzy concept reduction,which can be obtained by factorizing or feature recognizing.In this paper,there are a total of 13 figures,24 tables,and 86 references.