A type of attribute reduction of formal contexts

Formal concept analysis is an important mathematical tool for knowledge representation and knowledge discovery. Attribute reduction is a crucial research issue attracting many attention of researchers on formal concept analysis. This paper proposes one type of attribute reduction of formal context, in which all join-irreducible elements of a concept lattice are preserved. The join-irreducible elements of a formal context and their properties are first discussed. Then, the concept of join-irreducible-attribute reduction of formal context is then introduced. Finally, an equivalence condition of join-irreducible-consistent attribute set is given.

[1]  Qinghua Hu,et al.  An efficient gene selection technique for cancer recognition based on neighborhood mutual information , 2010, Int. J. Mach. Learn. Cybern..

[2]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[3]  Claudio Carpineto,et al.  A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval , 1996, Machine Learning.

[4]  Wei-Zhi Wu,et al.  Approaches to knowledge reduction based on variable precision rough set model , 2004, Inf. Sci..

[5]  Congxin Wu,et al.  Separating theorem of samples in Banach space for support vector machine learning , 2011, Int. J. Mach. Learn. Cybern..

[6]  Wen-Xiu Zhang,et al.  Attribute reduction theory and approach to concept lattice , 2007, Science in China Series F: Information Sciences.

[7]  Ming-Wen Shao,et al.  Reduction method for concept lattices based on rough set theory and its application , 2007, Comput. Math. Appl..

[8]  Ling Wei,et al.  Relation between concept lattice reduction and rough set reduction , 2010, Knowl. Based Syst..

[9]  Wei-Zhi Wu,et al.  Attribute reduction based on evidence theory in incomplete decision systems , 2008, Inf. Sci..

[10]  Zhang Wen-xiu,et al.  Attribute reduction theory and approach to concept lattice , 2005 .

[11]  Yee Leung,et al.  Approaches to attribute reduction in concept lattices induced by axialities , 2010, Knowl. Based Syst..

[12]  Jitender S. Deogun,et al.  Sequential Association Rule Mining with Time Lags , 2004, Journal of Intelligent Information Systems.

[13]  Xia Wang,et al.  Relations of attribute reduction between object and property oriented concept lattices , 2008, Knowl. Based Syst..

[14]  S. Pal,et al.  Rough-Fuzzy C-Medoids Algorithm and Selection of Bio-Basis for Amino Acid Sequence Analysis , 2007, IEEE Transactions on Knowledge and Data Engineering.

[15]  W. Marsden.  I and J , 2012 .

[16]  Yee Leung,et al.  Granular Computing and Knowledge Reduction in Formal Contexts , 2009, IEEE Transactions on Knowledge and Data Engineering.

[17]  Claudio Carpineto,et al.  A lattice conceptual clustering system and its application to browsing retrieval , 2004, Machine Learning.