Reduction method for concept lattices based on rough set theory and its application

Rough set theory and formal concept analysis are two complementary mathematical tools for data analysis. In this paper, we study the reduction of the concept lattices based on rough set theory and propose two kinds of reduction methods for the above concept lattices. First, we present the sufficient and necessary conditions for justifying whether an attribute and an object are dispensable or indispensable in the above concept lattices. Based on the above justifying conditions, we propose a kind of multi-step attribute reduction method and object reduction method for the concept lattices, respectively. Then, on the basis of the defined discernibility functions of the concept lattices, we propose a kind of single-step reduction method for the concept lattices. Additionally, the relations between the attribute reduction of the concept lattices in FCA and the attribute reduction of the information system in rough set theory are discussed in detail. At last, we apply the above multi-step attribute reduction method for the concept lattices based on rough set theory to the reduction of the redundant premises of the multiple rules used in the job shop scheduling problem. The numerical computational results show that the reduction method for the concept lattices is effective in the reduction of the multiple rules.

[1]  Piero Pagliani,et al.  From Concept Lattices to Approximation Spaces: Algebraic Structures of Some Spaces of Partial Objects , 1993, Fundam. Informaticae.

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

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

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

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

[6]  R. Słowiński.  Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory , 1992 .

[7]  LIUMin,et al.  An Iterative Layered Tabu Search Algorithm for Complex Job Shop Scheduling Problem , 2005 .

[8]  Marc Roubens,et al.  Theory and Applications of Relational Structures as Knowledge Instruments II, International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers , 2006, Theory and Applications of Relational Structures as Knowledge Instruments.

[9]  Rokia Missaoui,et al.  An Incremental Concept Formation Approach for Learning from Databases , 1994, Theor. Comput. Sci..

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

[11]  Zdzislaw Pawlak,et al.  Rough Set Theory and its Applications to Data Analysis , 1998, Cybern. Syst..

[12]  Robert E. Kent,et al.  Rough Concept Analysis: A Synthesis of Rough Sets and Formal Concept Analysis , 1996, Fundam. Informaticae.

[13]  Karl Erich Wolff,et al.  A Conceptual View of Knowledge Bases in Rough Set Theory , 2000, Rough Sets and Current Trends in Computing.

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

[15]  Jitender S. Deogun,et al.  Monotone concepts for formal concept analysis , 2004, Discret. Appl. Math..

[16]  Andrzej Skowron,et al.  EXTRACTING LAWS FROM DECISION TABLES: A ROUGH SET APPROACH , 1995, Comput. Intell..

[17]  Rudolf Wille.  Knowledge acquisition by methods of formal concept analysis , 1989 .

[18]  Hiroshi Ohta,et al.  A heuristic for job shop scheduling to minimize total weighted tardiness , 2002 .

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

[20]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

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

[22]  Ming-Wen Shao,et al.  Approximation in Formal Concept Analysis , 2005, RSFDGrC.

[23]  Olivier Ridoux,et al.  A Logical Generalization of Formal Concept Analysis , 2000, ICCS.

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

[25]  Peter Brucker,et al.  Scheduling Algorithms , 1995 .

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

[27]  Rudolf Wille,et al.  A Triadic Approach to Formal Concept Analysis , 1995, ICCS.