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.
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
Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. Wiley, New York (1973)
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)
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)
Ma, W.M., Sun, B.Z.: Probabilistic rough set over two universes and rough entropy. International Journal of Approximate Reasoning (53), 608–619 (2012)
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)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Science (11), 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Science (177), 3–27 (2007)
Pawlak, Z., Grzymala-Busse, J.W., Slowinski, R.: Rough sets. Communications of the ACM (38), 88–95 (1995)
Pei, D.W., Xu, Z.B.: Rough set models on two universes. International Journal of General Systems 33(5), 569–581 (2004)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Information (27), 245–253 (1996)
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)
Sun, B.Z., Ma, W.M.: Fuzzy rough set model on two different universes and its application. Applied Mathematical Modelling (35), 1798–1809 (2011)
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)
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)
Wong, S.K.M., Wang, L.S., Yao, Y.Y.: On modeling uncertainty with interval structures. Computer Intelligent (11), 406–426 (1993)
Wu, W.Z., Zhang, W.X.: Constructive and axiomatic approaches of fuzzy approximation operators. Information Science (159), 233–254 (2004)
Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49(2), 255–271 (2008)
Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Science (109), 21–47 (1998)
Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Science (111), 239–259 (1998)
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)
Yan, J.A.: Theory of measures. Science Press, Beijing (1998)
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)
Zhang, W.X., Wu, W.Z.: Rough set models based on random sets(I). Journal of Xi’an Jiaotong University (12), 75–79 (2000)
Zadeh, L.A.: Fuzzy sets. Information & Control (8), 338–353 (1965)
Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49(2), 272–284 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sun, B., Ma, W., Zhao, H., Wang, X. (2012). Probabilistic Fuzzy Rough Set Model over Two Universes. In: Yao, J., et al. Rough Sets and Current Trends in Computing. RSCTC 2012. Lecture Notes in Computer Science(), vol 7413. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32115-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-32115-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32114-6
Online ISBN: 978-3-642-32115-3
eBook Packages: Computer ScienceComputer Science (R0)