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Calculation of Data Reliability with Entropy for Fuzzy Sets

Wang, Hongmei    (School of Mechatronics, Changwon National University   ); Lee, Sang-Hyuk    (School of Mechatronics, Changwon National University  );
  • 초록

    Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary characteristics that the fuzzy entropies of fuzzy set and complementary fuzzy set have the same entropies. Discrepancy that low fuzzy entropy did not guarantee the data certainty was overcome by modifying fuzzy entropy formulation. Obtained fuzzy entropy is analyzed and discussed through simple example.


  • 주제어

    Uncertainty .   Fuzzy entropy .   distance measure.  

  • 참고문헌 (10)

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    4. S.H. Lee, J.M. Kim, and Y.K. Choi, 'Similarity measure construction using fuzzy entropy and distance measure', LNAI, vol. 4114, pp. 952?958, 2006 
    5. S.H. Lee, W. Pedrycz, and Gyoyong Sohn, 'Design of Similarity and Dissimilarity Measures for Fuzzy Sets on the Basis of Distance Measure', International Journal of Fuzzy Systems, vol. 11, no. 2, pp.67-72, 2009 
    6. N.R. Pal and S.K. Pal, 'Object-background segmentation using new definitions of entropy', IEEE Proc,. vol. 36, pp. 284?295, 1989 
    7. A. Ghosh, 'Use of fuzziness measure in layered networks for object extraction: a generalization', Fuzzy Sets and Systems, vol. 72, pp. 331?348, 1995 
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    9. Liu Xuecheng, 'Entropy, distance measure and similarity measure of fuzzy sets and their relations,' Fuzzy Sets and Systems, vol. 52, pp. 305-318, 1992 
    10. D. Bhandari and N.R. Pal, 'Some new information measure of fuzzy sets', Inform. Sci. vol. 67, pp. 209?228, 1993 

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