Abstract
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.
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References
Dembczyński K, Greco S, Kotłowski W, Słowiński R (2006) Quality of rough approximation in multi-criteria classification problems. In: Greco S et al (eds) RSCTC 2006, LNCS (LNAI), vol 4259. Springer, Heidelberg, pp 318–327
Greco S, Matarazzo B, Slowinski R (2001) Rough set theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47
Greco S, Matarazzo B, Słowiński R (2005) Decision rule approach. In: Figueria J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis. Springer, New York, pp 507–561
Greco S, Hata Y, Hirano S, Inuiguchi M, Miyamoto S, Nguyen HS, Słowiński R (2006) RSCTC 2006, LNCS (LNAI) vol. 4259. Springer, Heidelberg
Inuiguchi M, Tsurumi M (2006) Measures based on upper approximations of rough sets for analysis of attribute importance and interaction. Int J Innov Comput Inf Control 2(1):1–12
Inuiguchi M, Yoshioka Y (2008) Several reducts in dominance-based rough set approach. In: Huynh VN et al (eds) Interval/probabilistic uncertainty and non-classical logics, ASC vol 46. Springer, Heidelberg, pp 163–175
Kryszkiewicz M (2001) Comparative study of alternative types of knowledge reduction in inconsistent systems. Int J Intell Syst 16:105–120
Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11(5):341–356
Pawlak Z, Słowiński R (1994) Rough set approach to multi-attribute decision analysis. Eur J Oper Res 72:443–459
Polkowski L, Skowron A (1998) Rough sets in knowledge discovery, vol 2, Applications, case studies and software systems. Physica-Verlag, Heidelberg
Shao MW, Zhang WX (2005) Dominance relation and rules in an incomplete ordered information system. Int J Intell syst 20:13–27
Ślęzak D (2000) Various approaches to reasoning with frequency based decision reducts: a survey. In: Polkowski L, Tsumoto S, Lin TY (eds) Rough set methods and applications. Physica-Verlag, Heidelberg, pp. 235–285
Słowiński R (1992) Intelligent decision support. Kluwer, Dordrecht
Susmaga R, Słowiński R, Greco S, Matarazzo B (2000) Generation of reducts and rules in multi-attribute and multi-criteria classification. Control Cybern 29(4):969–988
Yang X, Yang J, Wu C, Yu D (2008) Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf Sci 178(4):1219–1234
Acknowledgments
We acknowledge that this work has been partially supported by the Grant-in-Aid for Scientific Research (B) No.17310098.
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Kusunoki, Y., Inuiguchi, M. A unified approach to reducts in dominance-based rough set approach. Soft Comput 14, 507–515 (2010). https://doi.org/10.1007/s00500-009-0450-0
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DOI: https://doi.org/10.1007/s00500-009-0450-0