Advertisement

Probabilistic Fuzzy Rough Set Model over Two Universes

  • Bingzhen Sun
  • Weimin Ma
  • Haiyan Zhao
  • Xinxin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7413)

Abstract

As a new generalization of Pawlak rough set, the theory and applications of rough set over two universes has brought the attention by many scholars in various areas. In this paper, we propose a new model of probabilistic fuzzy rough set by introducing the probability measure to the fuzzy compatibility approximation space over two universes. That is, the model defined in this paper included both of probabilistic rough set and fuzzy rough set over two universes. The probabilistic fuzzy rough lower and upper approximation operators of any subset were defined by the concept of the fuzzy compatible relation between two different universes. Since there has two parameters in the lower and upper approximations, we also give other definitions for probabilistic fuzzy rough set model under the framework of two universes with different combination of the parameters. Furthermore, we discuss the properties for the established model in detail and present several valuable conclusions. The results show that this model has more extensively applied fields.

Keywords

Probabilistic fuzzy rough set fuzzy compatibility relation Two universes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. Wiley, New York (1973)zbMATHGoogle Scholar
  2. 2.
    Gong, Z.T., Sun, B.Z.: Probability rough sets model between different universes and its applications. In: Proc. International Conference on Machine Learning and Cybernetics, pp. 561–565. IEEE Press, China (2008)Google Scholar
  3. 3.
    Gong, Z.T., Sun, B.Z., Chen, D.G.: Rough set theory for the interval-valued fuzzy information systems. Information Science (178), 1986–1985 (2008)Google Scholar
  4. 4.
    Ma, W.M., Sun, B.Z.: Probabilistic rough set over two universes and rough entropy. International Journal of Approximate Reasoning (53), 608–619 (2012)Google Scholar
  5. 5.
    Ma, W.M., Sun, B.Z.: On relationship between probabilistic rough set and Bayesian risk decision over two universes. International Journal of General Systems 41(3), 225–245 (2012)CrossRefGoogle Scholar
  6. 6.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Science (11), 341–356 (1982)Google Scholar
  7. 7.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  8. 8.
    Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Science (177), 3–27 (2007)Google Scholar
  9. 9.
    Pawlak, Z., Grzymala-Busse, J.W., Slowinski, R.: Rough sets. Communications of the ACM (38), 88–95 (1995)Google Scholar
  10. 10.
    Pei, D.W., Xu, Z.B.: Rough set models on two universes. International Journal of General Systems 33(5), 569–581 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Information (27), 245–253 (1996)Google Scholar
  12. 12.
    Sun, B.Z., Gong, Z.T., Chen, D.G.: Fuzzy rough set for the interval-valued fuzzy information systems. Information Science (178), 2794–2815 (2008)Google Scholar
  13. 13.
    Sun, B.Z., Ma, W.M.: Fuzzy rough set model on two different universes and its application. Applied Mathematical Modelling (35), 1798–1809 (2011)Google Scholar
  14. 14.
    Shafer, G.: Belief functions and possibility measures. In: Bezdek, J.C. (ed.) Analysis of Fuzzy Information, vol. (1), pp. 51–84. CRC Press, Boca Raton (1987)Google Scholar
  15. 15.
    Wong, S.K.M., Wang, L.S., Yao, Y.Y.: Interval structures: a framework for representing uncertain information. In: Proceeding of 8th Conference on Uncertainty Artificial Intelligent, pp. 336–343 (1993)Google Scholar
  16. 16.
    Wong, S.K.M., Wang, L.S., Yao, Y.Y.: On modeling uncertainty with interval structures. Computer Intelligent (11), 406–426 (1993)Google Scholar
  17. 17.
    Wu, W.Z., Zhang, W.X.: Constructive and axiomatic approaches of fuzzy approximation operators. Information Science (159), 233–254 (2004)Google Scholar
  18. 18.
    Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49(2), 255–271 (2008)zbMATHCrossRefGoogle Scholar
  19. 19.
    Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Science (109), 21–47 (1998)Google Scholar
  20. 20.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Science (111), 239–259 (1998)Google Scholar
  21. 21.
    Yao, Y.Y., Wong, S.K.M., Wang, L.S.: A non-numeric approach to uncertain reasoning. International Journal of General Systems (23), 343–359 (1995)Google Scholar
  22. 22.
    Yan, J.A.: Theory of measures. Science Press, Beijing (1998)Google Scholar
  23. 23.
    Zhang, H.Y., Zhang, W.Z., Wu, W.Z.: On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse. International Journal of Approximate Reasoning 51(1), 56–70 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Zhang, W.X., Wu, W.Z.: Rough set models based on random sets(I). Journal of Xi’an Jiaotong University (12), 75–79 (2000)Google Scholar
  25. 25.
    Zadeh, L.A.: Fuzzy sets. Information & Control (8), 338–353 (1965)Google Scholar
  26. 26.
    Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49(2), 272–284 (2008)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bingzhen Sun
    • 1
    • 2
  • Weimin Ma
    • 1
  • Haiyan Zhao
    • 1
    • 3
  • Xinxin Wang
    • 4
  1. 1.School of Economics and ManagementTongji UniversityShanghaiP.R. China
  2. 2.School of Traffic and TransportationLanzhou Jiaotong UniversityLanzhouP.R. China
  3. 3.Vocational Education DepartmentShanghai University of Engineering ScienceShanghaiP.R. China
  4. 4.School of Mathematics and StaticsLongdong UniversityQingyangP.R. China

Personalised recommendations