Concept Lattices of Subcontexts of a Context

As an effective tool for data analysis and knowledge processing, the theory of concept lattices has been studied extensively and applied to various fields. In order to discover useful knowledge, one often ignores some attributes according to a particular purpose and merely considers the subcontexts of a rather complex context. In this paper, we make a deep investigation on the theory of concept lattices of subcontexts. An approach to construct the concept lattice of a context is first presented by means of the concept lattices of its subcontexts. Then the concept lattices induced by all subcontexts of the context are considered as a set, and an order relation is introduced into the set. It is proved that the set together with the order relation is a complete lattice. Finally, the top element and the bottom element of the complete lattice are also obtained.

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

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

[3]  Jitender S. Deogun,et al.  Formal Rough Concept Analysis , 1999, RSFDGrC.

[4]  Jouni Järvinen,et al.  Knowledge Representation and Rough Sets , 2007 .

[5]  Ju Wang,et al.  Concept Approximation in Concept Lattice , 2001, PAKDD.

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

[7]  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.

[8]  Tu Bao Ho,et al.  An Approach to Concept Formation Based on Formal Concept Analysis , 1995, IEICE Trans. Inf. Syst..

[9]  Peter A. Grigoriev,et al.  Elements of an Agile Discovery Environment , 2003, Discovery Science.

[10]  J. Deogun,et al.  Concept approximations based on rough sets and similarity measures , 2001 .

[11]  Brian A. Davey,et al.  Introduction to Lattices and Order: Preface to the second edition , 2002 .

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

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

[14]  Claudio Carpineto,et al.  GALOIS: An Order-Theoretic Approach to Conceptual Clustering , 1993, ICML.

[15]  Yiyu Yao,et al.  Rough set approximations in formal concept analysis , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

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

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

[18]  Jouni Järvinen,et al.  A Representation of Dependence Spaces and Some Basic Algorithms , 1997, Fundam. Informaticae.

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

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

[21]  Miroslav Novotný,et al.  Dependence Spaces of Information Systems , 1998 .

[22]  Jouni Järvinen.  Pawlak's Information Systems in Terms of Galois Connections and Functional Dependencies , 2007, Fundam. Informaticae.

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