Abstract
This paper introduces a mechanism for computing approximations of Dominance-Based Rough Sets (DBRS) by bit-vector encodings. DBRS was introduced by Greco et al. as an extension of Pawlak’s classical rough sets theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes. Our formulation of dominance-based approximation spaces is based on the concept of indexed blocks introduced by Chan and Tzeng. Indexed blocks are sets of objects indexed by pairs of decision values where approximations of sets of decision classes are defined in terms of exclusive neighborhoods of indexed blocks. In this work, we introduced an algorithm for updating indexed blocks incrementally, and we show that the computing of dominance-based approximations can be accomplished more intuitively and efficiently by encoding indexed blocks as bit-vectors. In addition, bit-vector encodings can simplify the definitions of lower and upper approximations greatly. Examples are given to illustrate presented concepts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations, ICS Research Report 16/96, Warsaw University of Technology, Warsaw. European Journal of Operational Research 117(1), 63–83 (1999)
Greco, S., Matarazzo, B., Slowinski, R.: A new rough set approach to evaluation of bankruptcy risk. In: Zopounidis, C. (ed.) Operational Tools in the Management of Financial Risks, pp. 121–136. Kluwer Academic Publishers, Dordrecht (1998)
Greco, S., Matarazzo, B., Slowinski, R.: The use of rough sets and fuzzy sets in MCDM. In: Gal, T., Stewart, T., Hanne, T. (eds.) Advances in Multiple Criteria Decisions Making, ch. 14, pp. 14.1–14.59. Kluwer Academic Publishers, Dordrecht (1999)
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European Journal of Operational Research 138(2), 247–259 (2002)
Greco, S., Matarazzo, B., Slowinski, R., Stefanowski, J.: An algorithm for induction of decision rules consistent with the dominance principle. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 304–313. Springer, Heidelberg (2001)
Greco, S., Matarazzo, B., Slowinski, R., Stefanowski, J., Zurawski, M.: Incremental versus non-incremental rule induction for multicriteria classification. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 33–53. Springer, Heidelberg (2004)
Pawlak, Z.: Rough sets: basic notion. International Journal of Computer and Information Science 11(15), 344–356 (1982)
Pawlak, Z.: Rough sets and decision tables. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 186–196. Springer, Heidelberg (1985)
Pawlak, Z., Grzymala-Busse, J., Slowinski, R., Ziarko, W.: Rough sets. Communication of ACM 38(11), 89–95 (1995)
Roy, B.: Methodologie Multicritere d’Aide a la Decision. Economica, Paris (1985)
Fan, T.F., Liu, D.R., Tzeng, G.H.: Rough set-based logics for multicriteria decision analysis. European Journal of Operational Research 182(1), 340–355 (2007)
Chan, C.-C., Tzeng, G.-H.: Dominance-based rough sets using indexed blocks as granules. In: Wang, G., Li, T., Grzymała-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 244–251. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chan, CC., Tzeng, GH. (2008). Computing Approximations of Dominance-Based Rough Sets by Bit-Vector Encodings. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-88425-5_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88423-1
Online ISBN: 978-3-540-88425-5
eBook Packages: Computer ScienceComputer Science (R0)