Attribute Reduction of Concept Lattice Based on Irreducible Elements

Attribute reduction of formal context is a crucial reseach issue in formal concept analysis. In this paper, based on the meet-irreducible elements and join-irreducible elements of concept lattice, two kinds of attribute reductions of formal context are proposed, which are called MI-attribute reduction and JI-attribute reduction. Subsequently, we discuss the relationships among them and two existing attribute reductions of formal context, lattice-based attribute reduction and granular reduction. Consequently, we find that the MI-attribute reduction and lattice-based attribute reduction are identical. For JI-attribute reduction, the judgement theorems of JI-consistent attribute sets are obtained. Finally, by using the discernibility attribute sets, a method of computing all JI-attribute reducts of a formal context is presented.

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

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

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

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

[5]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

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

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

[8]  Wen-Xiu Zhang,et al.  Attribute reduction theory of concept lattice based on decision formal contexts , 2008, Science in China Series F: Information Sciences.

[9]  Hong Wang,et al.  Approaches to knowledge reduction in generalized consistent decision formal context , 2008, Math. Comput. Model..

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

[11]  Xuelong Li,et al.  A Wavelet-Based Image Quality Assessment Method , 2008, Int. J. Wavelets Multiresolution Inf. Process..

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

[13]  Mohammad Fazle Azeem,et al.  Wavelet Neuro-Fuzzy Model with Hybrid Learning Algorithm of Gradient Descent and Genetic Algorithm , 2011, Int. J. Wavelets Multiresolution Inf. Process..

[14]  Jinhai Li,et al.  Knowledge reduction in decision formal contexts , 2011, Knowl. Based Syst..

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

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

[17]  Claudio Carpineto,et al.  Exploiting the Potential of Concept Lattices for Information Retrieval with CREDO , 2004, J. Univers. Comput. Sci..

[18]  Tong-Jun Li.  A type of attribute reduction of formal contexts , 2012, 2012 International Conference on Machine Learning and Cybernetics.

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

[20]  Zongben Xu,et al.  Generalization Bounds of Regularization Algorithms Derived Simultaneously through Hypothesis Space Complexity, Algorithmic Stability and Data Quality , 2011, Int. J. Wavelets Multiresolution Inf. Process..

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

[22]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.

[23]  Shuqun Yang,et al.  An algorithm of constructing concept lattices for CAT with cognitive diagnosis , 2008, Knowl. Based Syst..

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

[25]  Wei-Zhi Wu,et al.  Attribute Reduction in Formal Contexts: A Covering Rough Set Approach , 2011, Fundam. Informaticae.

[26]  Gerd Stumme,et al.  Document retrieval for e-mail search and discovery using formal concept analysis , 2003, Appl. Artif. Intell..