Advertisement

Dominance-Based Rough Set Approach for Possibilistic Information Systems

  • Tuan-Fang Fan
  • Churn-Jung Liau
  • Duen-Ren Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6743)

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.

Keywords

Dominance Relation Fuzzy Subset Possibility Distribution Decision Class Linguistic Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)CrossRefzbMATHGoogle Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough set theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    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)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)CrossRefzbMATHGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Kryszkiewicz, M., Rybiński, H.: Reducing information systems with uncertain real value attributes. In: Proc. of the 6th IPMU, pp. 1165–1169 (1996)Google Scholar
  12. 12.
    Lipski, W.: On databases with incomplete information. Journal of the ACM 28(1), 41–70 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(15), 341–356 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pawlak, Z.: Rough Sets–Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  15. 15.
    Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126(2), 137–155 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: The concept of a linguistic variable and its applications in approximate reasoning. Information Sciences 8, 199–251 (1975)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tuan-Fang Fan
    • 1
  • Churn-Jung Liau
    • 2
  • Duen-Ren Liu
    • 3
  1. 1.Department of Computer Science and Information EngineeringNational Penghu University of Science and TechnologyPenghuTaiwan
  2. 2.Institute of Information ScienceAcademia SinicaTaipeiTaiwan
  3. 3.Institute of Information ManagementNational Chiao-Tung UniversityHsinchuTaiwan

Personalised recommendations