Probabilistic rough sets characterized by fuzzy sets

  • Authors:

  • Li-Li Wei;Wen-Xiu Zhang

  • Affiliations:

  • Institute of Information and System Science, Faculty of Science, Xi'an Jiaotong University, Xi'an, People's Republic of China;Institute of Information and System Science, Faculty of Science, Xi'an Jiaotong University, Xi'an, People's Republic of China

  • Venue:
  • RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
  • Year:
  • 2003

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Abstract

In this paper, fuzziness in probabilistic rough set is studied by fuzzy sets. we show that the variable precision approximation of a probabilistic rough set can be generalized from the vantage point of the cuts of a fuzzy set which is determined by the rough membership function. As a result, the fuzzy set can be used conveniently to describe the feature of rough set. Moreover we give a measure of fuzziness, fuzzy entropy, induced by roughness in a probabilistic rough set and make some characterizations of this measure. For three well-known entropy functions, we show that the finer the information granulation is, the less the fuzziness in a rough set. The superiority of fuzzy entropy to Pawlak's accuracy measure is illustrated with examples. Finally, the fuzzy entropy of a rough classification is defined by the fuzzy entropy of corresponding rough sets, and show that one possible application of it is to measure the inconsistency in a decision table.