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Quantitative Comparison of Similarity Measure and Entropy for Fuzzy Sets

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Advanced Data Mining and Applications (ADMA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5678))

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Abstract

Comparison and data analysis to the similarity measures and entropy for fuzzy sets are studied. The distance proportional value between the fuzzy set and the corresponding crisp set is represented as fuzzy entropy. We also verified that the sum of the similarity measure and the entropy between fuzzy set and the corresponding crisp set constitutes the total information. Finally, we derive a similarity measure from entropy with the help of total information property, and illustrate a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.

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Author information

Authors and Affiliations

  1. School of Mechatronics, Changwon National University, Sarim-dong, Changwon, Gyeongnam, Korea

    Hongmei Wang, Sanghyuk Lee & Jaehyung Kim

Authors
  1. Hongmei Wang
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  2. Sanghyuk Lee
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  3. Jaehyung Kim
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Editor information

Editors and Affiliations

  1. Knowledge Science & Engineering Institute, School of Education Technology, Beijing Normal University, Xinjiekouwai Ave. 19, 100875, Beijing, China

    Ronghuai Huang

  2. The Hong Kong University of Science and Technology, Clear Water Bay,, Hong Kong, Hong Kong

    Qiang Yang

  3. School of Computing Science, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada

    Jian Pei

  4. Faculty of Economics, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    João Gama

  5. School of Information, Zhongguancum, Renmin University, 100872, Beijing, China

    Xiaofeng Meng

  6. School of Information Technology and Electrical Engineering, The University of Queensland, 4072, St. Lucia, Queensland, Australia

    Xue Li

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© 2009 Springer-Verlag Berlin Heidelberg

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Wang, H., Lee, S., Kim, J. (2009). Quantitative Comparison of Similarity Measure and Entropy for Fuzzy Sets. In: Huang, R., Yang, Q., Pei, J., Gama, J., Meng, X., Li, X. (eds) Advanced Data Mining and Applications. ADMA 2009. Lecture Notes in Computer Science(), vol 5678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03348-3_72

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  • DOI: https://doi.org/10.1007/978-3-642-03348-3_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03347-6

  • Online ISBN: 978-3-642-03348-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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