Abstract
In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered possibilistic information systems, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their possibilistic evaluations with respect to each criterion. This results in a fuzzy dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of an information system. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. The lower and upper approximations of the decision classes based on the fuzzy dominance relation are thus fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.
This work was partially supported by NSC (Taiwan) Grants: 99-2410-H-346-001 (T.F. Fan) and 98-2221-E-001-013-MY3(C.J. Liau).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)
Fan, T.F., Liau, C.J., Liu, D.R.: Dominance-based rough set analysis of uncertain data table. In: Proc. of the International Fuzzy Systems Association (IFSA) World Congress and the European Society for Fuzzy Logic and Technology (EUSFLAT) Conference, pp. 294–299 (2009)
Greco, S., Matarazzo, B., Słowiński, R.: Rough set theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Słowiński, 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., Słowiński, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158(2), 271–292 (2004)
Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach as a proper way of handling graduality in rough set theory. Transactions on Rough sets VII, 36–52 (2007)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Inuiguchi, M.: Rough set approach to rule induction from imprecise decision tables. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds.) WILF 2009. LNCS, vol. 5571, pp. 68–76. Springer, Heidelberg (2009)
Kryszkiewicz, M.: Properties of incomplete information systems in the framework of rough sets. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 422–450. Physica-Verlag, Heidelberg (1998)
Kryszkiewicz, M., Rybiński, H.: Reducing information systems with uncertain attributes. In: Raś, Z.W., Michalewicz, M. (eds.) ISMIS 1996. LNCS, vol. 1079, pp. 285–294. Springer, Heidelberg (1996)
Kryszkiewicz, M., Rybiński, H.: Reducing information systems with uncertain real value attributes. In: Proc. of the 6th IPMU, pp. 1165–1169 (1996)
Lipski, W.: On databases with incomplete information. Journal of the ACM 28(1), 41–70 (1981)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(15), 341–356 (1982)
Pawlak, Z.: Rough Sets–Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126(2), 137–155 (2002)
Sakai, H., Ishibashi, R., Nakata, M.: Lower and upper approximations of rules in non-deterministic information systems. In: Chan, C.C., Grzymala-Busse, J.W., Ziarko, W. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 299–309. Springer, Heidelberg (2008)
Słowiński, R., Greco, S., Matarazzo, B.: Rough set analysis of preference-ordered data. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 44–59. Springer, Heidelberg (2002)
Yao, Y.Y., Liu, Q.: A generalized decision logic in interval-set-valued information tables. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 285–293. Springer, Heidelberg (1999)
Zadeh, L.A.: The concept of a linguistic variable and its applications in approximate reasoning. Information Sciences 8, 199–251 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fan, TF., Liau, CJ., Liu, DR. (2011). Dominance-Based Rough Set Approach for Possibilistic Information Systems. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-21881-1_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21880-4
Online ISBN: 978-3-642-21881-1
eBook Packages: Computer ScienceComputer Science (R0)