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)


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.


Probabilistic fuzzy rough set fuzzy compatibility relation Two universes 


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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

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