The Concept of Reducts in Pawlak Three-Step Rough Set Analysis

Rough set approaches to data analysis involve removing redundant attributes, redundant attribute-value pairs, and redundant rules in order to obtain a minimal set of simple and general rules. Pawlak arranges these tasks into a three-step sequential process based on a central notion of reducts. However, reducts used in different steps are defined and formulated differently. Such an inconsistency in formulation may unnecessarily affect the elegancy of the approach. Therefore, this paper introduces a generic definition of reducts of a set, uniformly defines various reducts used in rough set analysis, and examines several mathematically equivalent, but differently formulated, definitions of reducts. Each definition captures a different aspect of a reduct and their integration provides new insights.

[1]  Troels Andreasen,et al.  Foundations of Intelligent Systems , 2014, Lecture Notes in Computer Science.

[2]  Chris Cornelis,et al.  Rough Sets and Intelligent Systems Paradigms , 2014, Lecture Notes in Computer Science.

[3]  Yiyu Yao,et al.  Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model , 2009, Inf. Sci..

[4]  Dominik Slezak,et al.  Utilization of attribute clustering methods for scalable computation of reducts from high-dimensional data , 2012, 2012 Federated Conference on Computer Science and Information Systems (FedCSIS).

[5]  Mikhail Ju. Moshkov,et al.  Partial Covers, Reducts and Decision Rules in Rough Sets - Theory and Applications , 2009, Studies in Computational Intelligence.

[6]  Dominik Slezak,et al.  Association Reducts: A Framework for Mining Multi-attribute Dependencies , 2005, ISMIS.

[7]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[8]  Andrzej Skowron,et al.  Dynamic Reducts as a Tool for Extracting Laws from Decisions Tables , 1994, ISMIS.

[9]  Wei-Zhi Wu,et al.  Approaches to knowledge reductions in inconsistent systems , 2003, Int. J. Intell. Syst..

[10]  Dominik Slezak,et al.  Approximate Reducts and Association Rules - Correspondence and Complexity Results , 1999, RSFDGrC.

[11]  Yiyu Yao,et al.  Level-wise Construction of Decision Trees for Classification , 2006, Int. J. Softw. Eng. Knowl. Eng..

[12]  Wei-Zhi Wu.  Knowledge Reduction in Random Incomplete Decision Tables via Evidence Theory , 2012, Fundam. Informaticae.

[13]  Andrzej Skowron,et al.  New Directions in Rough Sets, Data Mining, and Granular-Soft Computing , 1999, Lecture Notes in Computer Science.

[14]  Yiyu Yao,et al.  A Granular Computing Paradigm for Concept Learning , 2013 .

[15]  Yiyu Yao,et al.  Interpreting Low and High Order Rules: A Granular Computing Approach , 2007, RSEISP.

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

[17]  Jerzy W. Grzymala-Busse,et al.  Approximation Space and LEM2-like Algorithms for Computing Local Coverings , 2008, Fundam. Informaticae.

[18]  Yiyu Yao,et al.  On Reduct Construction Algorithms , 2006, RSKT.

[19]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[20]  JOHANNES FÜRNKRANZ,et al.  Separate-and-Conquer Rule Learning , 1999, Artificial Intelligence Review.

[21]  Ryszard S. Michalski,et al.  Categories and Concepts: Theoretical Views and Inductive Data Analysis , 1993 .

[22]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[23]  Fgit,et al.  Future Generation Information Technology, First International Conference, FGIT 2009, Jeju Island, Korea, December 10-12, 2009. Proceedings , 2009, FGIT.

[24]  Zbigniew W. Ras,et al.  Methodologies for Intelligent Systems , 1991, Lecture Notes in Computer Science.

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

[26]  Jadzia Cendrowska,et al.  PRISM: An Algorithm for Inducing Modular Rules , 1987, Int. J. Man Mach. Stud..

[27]  Roman Słowiński,et al.  Sequential covering rule induction algorithm for variable consistency rough set approaches , 2011, Inf. Sci..

[28]  Jerzy W. Grzymala-Busse,et al.  LERS-A System for Learning from Examples Based on Rough Sets , 1992, Intelligent Decision Support.

[29]  Dominik Slezak,et al.  Ensembles of Bireducts: Towards Robust Classification and Simple Representation , 2011, FGIT.

[30]  Yee Leung,et al.  Dependence-space-based attribute reduction in consistent decision tables , 2011, Soft Comput..

[31]  Yiyu Yao,et al.  Partitions, Coverings, Reducts and Rule Learning in Rough Set Theory , 2011, RSKT.

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