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New fuzzy mean codeword length and similarity measure

Abstract

In this paper, based on the concept of Renyi–Tsallis entropy, we propose an inaccuracy measure for a pair of probability distribution and discuss its relationship with mean codeword length. Furthermore, we propose a new fuzzy entropy measure in the setting of fuzzy set theory and its several properties are examined. Comparison with several existing entropies shows that the proposed fuzzy information measure has a greater ability in discriminating different FSs (fuzzy sets). Furthermore, we introduce a new fuzzy mean codeword length and give their relationship with fuzzy information measure. The upper bounds of these entropies in terms of mean codeword lengths have been provided and some basic properties of the proposed codeword length have been studied. In addition, we introduce a new similarity measure for fuzzy sets and give its applications in pattern recognition and cluster analysis. To implement the application of proposed similarity measure in real life problem, we have taken real data from the repository of machine learning. These practical examples are given to support the findings and also show the availability of similarity measure between fuzzy sets.

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Acknowledgements

The authors are thankful to the editor and the anonymous reviewers for their precious suggestions and comments which improved this manuscript and enhanced our knowledge.

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Correspondence to Ratika Kadian.

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Kadian, R., Kumar, S. New fuzzy mean codeword length and similarity measure. Granul. Comput. 7, 461–478 (2022). https://doi.org/10.1007/s41066-021-00278-y

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  • DOI: https://doi.org/10.1007/s41066-021-00278-y

Keywords

  • Divergence measure
  • Mean codeword length
  • Holder’s inequality
  • Similarity measure
  • Bacteria detection