Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

  • Authors:

  • Ju-Sheng Mi;Xiu-Min Li;Hui-Yin Zhao;Tao Feng

  • Affiliations:

  • College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, 050016, P.R. China;College of Science, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, P.R. China;College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, 050016, P.R. China and College of Science, Hebei College of Industry and Technology, Shijiazhuang, Heb ...;College of Science, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, P.R. China

  • Venue:
  • RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
  • Year:
  • 2009

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Abstract

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications. This paper studies the measurement of uncertainty in generalized fuzzy rough sets determined by a triangular norm. Based on information theory, the entropy of a generalized fuzzy approximation space is introduced, which is similar to Shannon's entropy. To measure uncertainty in generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T= min , it is proved that the measure of fuzziness of a generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.