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On the Use of Divergences for Defining Entropies for Atanassov Intuitionistic Fuzzy Sets

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

Abstract

In the literature we find two different approaches to define entropies of AIFSs. On the one hand, Szmidt and Kacprzyk’s entropy measures how far is an AIFS from a crisp set; on the other hand, Burrillo and Bustince’s approach measures how far is an AIFS from a fuzzy set. In this work we use divergence measures to define both types of entropies. We also show the conditions that we must impose on the divergence to define entropy measures of AIFSs and use our results to build several examples.

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Acknowledgment

The research in this communication has been supported in part by project MINECO-TIN2014-59543-P. Its financial support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Statistics and O.R., University of Oviedo, Oviedo, Spain

    Ignacio Montes & Susana Montes

  2. Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India

    Nikhil Pal

Authors
  1. Ignacio Montes
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  2. Susana Montes
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  3. Nikhil Pal
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Corresponding author

Correspondence to Ignacio Montes .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Montes, I., Montes, S., Pal, N. (2018). On the Use of Divergences for Defining Entropies for Atanassov Intuitionistic Fuzzy Sets. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_49

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  • DOI: https://doi.org/10.1007/978-3-319-66824-6_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

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