Dependence and Algebraic Structure of Formal Contexts

Formal concept analysis is an important approach of knowledge representation and data analysis. This paper focus on the dependence among formal contexts with common object set. A partial order relation among formal contexts is first introduced and its properties are examined. Subsequently, The notion of independence of a formal context is proposed by which attribute reduction of formal context is investigated. An useful conclusion is obtained, that is, all formal contexts with common object set form a lattice.

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

[2]  E. Turunen.  Mathematics Behind Fuzzy Logic , 1999 .

[3]  Bernard De Baets,et al.  Inducing decision trees via concept lattices , 2009, CLA.

[4]  Qinghua Hu,et al.  Mixed feature selection based on granulation and approximation , 2008, Knowl. Based Syst..

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

[6]  Bernard Monjardet,et al.  The Lattices of Closure Systems, Closure Operators, and Implicational Systems on a Finite Set: A Survey , 2003, Discret. Appl. Math..

[7]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

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

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

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

[11]  Xindong Wu.  EIC Editorial: Introducing the New Editor-in-Chief and Four New Associate Editors , 2009, IEEE Trans. Knowl. Data Eng..

[12]  Jun Xia,et al.  Development of distributed time-variant gain model for nonlinear hydrological systems , 2005 .

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

[14]  Qiang Wu,et al.  Real formal concept analysis based on grey-rough set theory , 2009, Knowl. Based Syst..

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

[16]  Yee Leung,et al.  Knowledge acquisition in incomplete information systems: A rough set approach , 2006, Eur. J. Oper. Res..