A unified approach to reducts in dominance-based rough set approach

The Dominance-based Rough Set Approach (DRSA), which is an extension of the Rough Set Approach (RSA), analyzes a sorting problem for a given data set. Attribute reduction is one of major topics in RSA as well as DRSA. By attribute reduction, we can find an important attribute set, which is called a reduct. In this paper, we propose a new approach to reducts in DRSA. A few kinds of reducts have been already proposed in DRSA, therefore, we clarify relations among the proposed and previous ones. We prove that they are consolidated into four kinds. Moreover, we show that all kinds of reducts can be enumerated based on two discernibility matrices.

[1]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

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

[3]  Andrzej Skowron,et al.  Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems , 1998 .

[4]  Ming-Wen Shao,et al.  Dominance relation and rules in an incomplete ordered information system , 2005 .

[5]  S. Greco,et al.  Decision Rule Approach , 2005 .

[6]  Z. Pawlak,et al.  Rough set approach to multi-attribute decision analysis , 1994 .

[7]  Roman Słowiński,et al.  Generation of reducts and rules in multi-attribute and multi-criteria classification , 2000 .

[8]  Jing-Yu Yang,et al.  Dominance-based rough set approach and knowledge reductions in incomplete ordered information system , 2008, Inf. Sci..

[9]  Marzena Kryszkiewicz.  Comparative study of alternative types of knowledge reduction in inconsistent systems , 2001, Int. J. Intell. Syst..

[10]  Wojciech Kotlowski,et al.  Quality of Rough Approximation in Multi-criteria Classification Problems , 2006, RSCTC.

[11]  Dominik Ślęzak,et al.  Various approaches to reasoning with frequency based decision reducts: a survey , 2000 .

[12]  Masahiro Inuiguchi,et al.  Several Reducts in Dominance-Based Rough Set Approach , 2008, Interval / Probabilistic Uncertainty and Non-Classical Logics.

[13]  Roman Słowiński,et al.  Intelligent Decision Support , 1992, Theory and Decision Library.

[14]  Lech Polkowski,et al.  Rough Sets in Knowledge Discovery 2 , 1998 .