The theory of the concept lattice is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. This pa...The theory of the concept lattice is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. This paper proposes the theory of attribute reduction in the concept lattice, which extends the theory of the concept lattice. In this paper, the judgment theorems of consistent sets are examined, and the discernibility matrix of a formal context is introduced, by which we present an approach to attribute reduction in the concept lattice. The characteristics of three types of attributes are analyzed.展开更多
Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on ...Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.展开更多
The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on t...The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.展开更多
基金This work was supported by the National 973 Program of China(Grant No．2002CB3 1 2200)the National Natural Science Foundation of China(Grant No．60373038) the Natural Scientific Research Project ofthe Education Department ofShaanxi Province in China(Grant No．04JK131)．
文摘The theory of the concept lattice is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. This paper proposes the theory of attribute reduction in the concept lattice, which extends the theory of the concept lattice. In this paper, the judgment theorems of consistent sets are examined, and the discernibility matrix of a formal context is introduced, by which we present an approach to attribute reduction in the concept lattice. The characteristics of three types of attributes are analyzed.
文摘Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.
基金the National 973 Program of China (Grant No.2002CB312200)the National Natural Science Foundation of China (Grant Nos.60703117, 60433010 and 60673096)the Doctor Research Fund of Northwest University in China
文摘The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.
