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Soft Computing

, Volume 22, Issue 15, pp 5051–5071 | Cite as

Entropy measures for Atanassov intuitionistic fuzzy sets based on divergence

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Abstract

In the literature, there are two different approaches to define entropy of Atanassov intuitionistic fuzzy sets (AIFS, for short). The first approach, given by Szmidt and Kacprzyk, measures how far is an AIFS from its closest crisp set, while the second approach, given by Burrillo and Bustince, measures how far is an AIFS from its closest fuzzy set. On the other hand, divergence measures are functions that measure how different two AIFSs are. Our work generalizes both types of entropies using local measures of divergence. This results in at least two benefits: depending on the application, one may choose from a wide variety of entropy measures and the local nature provides a natural way of parallel computation of entropy, which is important for large data sets. In this context, we provide the necessary and sufficient conditions for defining entropy measures under both frameworks using divergence measures for AIFS. We show that the usual examples of entropy measures can be obtained as particular cases of our more general framework. Also, we investigate the connection between knowledge measures and divergence measures. Finally, we apply our results in a multi-attribute decision-making problem to obtain the weights of the experts.

Keywords

Atanassov intuitionistic fuzzy sets Divergence measures Entropy 

Notes

Acknowledgements

A shorter version of this paper was published at EUSFLAT Conference (Montes et al. 2018). The current version has been updated with additional results, comments and proofs. We acknowledge the financial support by project TIN2014-59543-P.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and O.R.University of OviedoOviedoSpain
  2. 2.Electronics and Communication Sciences UnitIndian Statistical InstituteCalcuttaIndia

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