Granular Reduction of Property-Oriented Concept Lattices

Konwledge reduction on concept lattices is an important research topic in formal concept analysis, and there are some different meanings and methods. This paper mainly studies the granular reduction of property-oriented concept lattices which can preserve the property-oriented concepts, which is called granules in this paper. Firstly, the granules of a property-oriented concept lattice is presented, and it is proven that each extension of property-oriented concepts can be constructed by the granules. Then, the granular reduction of a property-oriented concept lattice is proposed, and the granular discernibility attribute matrix and the granular discernibility attribute function are respectively employed to determine granular consistent sets and calculate granular reducts. Finally, the relation between a granular consistent set and a lattice consistent set of a property-oriented concept lattice is discussed.

[1]  Ivo Düntsch,et al.  Approximation Operators in Qualitative Data Analysis , 2003, Theory and Applications of Relational Structures as Knowledge Instruments.

[2]  William Zhu,et al.  Relationship between generalized rough sets based on binary relation and covering , 2009, Inf. Sci..

[3]  Rokia Missaoui,et al.  INCREMENTAL CONCEPT FORMATION ALGORITHMS BASED ON GALOIS (CONCEPT) LATTICES , 1995, Comput. Intell..

[4]  Yiyu Yao,et al.  A multiview approach for intelligent data analysis based on data operators , 2008, Inf. Sci..

[5]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[6]  Wen-Xiu Zhang,et al.  Attribute Reduction in Concept Lattice Based on Discernibility Matrix , 2005, RSFDGrC.

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

[8]  Robert E. Kent,et al.  Digital Libraries, Conceptual Knowledge Systems, and the Nebula Interface , 2011, ArXiv.

[9]  Yiyu Yao,et al.  A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis , 2004, Rough Sets and Current Trends in Computing.

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

[11]  Lhouari Nourine,et al.  Representing lattices using many-valued relations , 2009, Inf. Sci..

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

[13]  Andrew M. Sutton,et al.  Recovering UML class models from C++: A detailed explanation , 2007, Inf. Softw. Technol..

[14]  Xia Wang,et al.  A Novel Approach to Attribute Reduction in Concept Lattices , 2006, RSKT.

[15]  Ivo Düntsch,et al.  Modal-style operators in qualitative data analysis , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[16]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[17]  Yiyu Yao,et al.  Concept lattices in rough set theory , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

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

[19]  Wei Zhao,et al.  The Reduction Theory of Object Oriented Concept Lattices and Property Oriented Concept Lattices , 2009, RSKT.