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Entropy for Interval-Valued Fuzzy Sets

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Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 54))

Abstract

A non-probabilistic-type entropy measure for interval-valued fuzzy set (IVFS) is proposed. It is a result of a geometric interpretation of IVFS and uses a ratio of distances between them. It is also shown that the proposed measure can be defined in terms of the ratio of interval-valued fuzzy cardinalities: of F ∩ F c and F ∪ F c.

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References

  1. Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  2. Zadeh, L.A.: Fuzzy Sets and Systems. In: Proc. Systems Theory, Polytechnic Institute of Brooklyn, New York, pp. 29–37 (1965)

    Google Scholar 

  3. De Luca, A., Termini, S.: A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inform. And Control 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  4. Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Fundamental Theoretical Elements, vol. 1. Academic Press, New York (1975)

    MATH  Google Scholar 

  5. Yager, R.R.: On the measure of fuzziness and negation. Part I: Membership in the unit interval. Internat. J. General Systems 5, 189–200 (1979)

    Article  MathSciNet  Google Scholar 

  6. Kosko, B.: Fuzzy entropy and conditioning. Inform. Sci. 40(2), 165–174 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kosko, B.: Fuzziness vs. probability. Internat. J. General Systems 17(2-3), 211–240 (1990)

    Article  MATH  Google Scholar 

  8. Kacprzyk, J.: Multistage Fuzzy Control. Wiley, New York (1997)

    MATH  Google Scholar 

  9. Dubios, D., Ostasiewicz, W., Prade, H.: Fuzzy sets: history and basic notions[M]. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 80–93. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

  10. Iczany, G.: A method of inference in approximate reasoning based on interval valued fuzzy set[J]. Fuzzy Sets and Systems 21(1), 1–17 (1987)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information, Beijing Wuzi University, Beijing, P.R. China

    Hong-mei Ju

Authors
  1. Hong-mei Ju
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Editor information

Editors and Affiliations

  1. Guangzhou Higher Education Mega Center, Guangzhou University, 230Wai Huan Xi Road, 510006, China

    Bing-yuan Cao

  2. Department of Mathematics, Hainan Normal University, Haikou, 571158, Hainan, P.R. China

    Cheng-yi Zhang

  3. Department of Electronic Information Engineering, Chongqing University of Science & Technology, 401331, Chongqing

    Tai-fu Li

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© 2009 Springer-Verlag Berlin Heidelberg

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Ju, Hm. (2009). Entropy for Interval-Valued Fuzzy Sets. In: Cao, By., Zhang, Cy., Li, Tf. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88914-4_45

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  • DOI: https://doi.org/10.1007/978-3-540-88914-4_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88913-7

  • Online ISBN: 978-3-540-88914-4

  • eBook Packages: EngineeringEngineering (R0)

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