Upper and lower probabilities of fuzzy events induced by a fuzzy set-valued mapping

  • Authors:
  • Wei-Zhi Wu

  • Affiliations:
  • Information College, Zhejiang Ocean University, Zhoushan, Zhejiang, P.R. China

  • Venue:
  • RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
  • Year:
  • 2005

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Abstract

In this paper, we study rough set approximations under fuzzy and random environments. A fuzzy set-valued mapping defines a pair of upper and lower fuzzy rough approximations. Properties of fuzzy approximation operators are examined and the crisp representations of fuzzy approximation operators are presented. A fuzzy random variable from a universe U to a universe W carries a probability measure defined over subsets of U into a system of upper and lower probabilities over subsets of W. The connections between fuzzy approximation spaces and fuzzy belief structures are also established.