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Choquet integration by Simpson’s rule with application in Hellinger distance

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Abstract

In non-additive measure theory, there are a few studies on the numerical Choquet integral in continuous case on real line. Recently, based on the statistics software R, Torra and Narukawa (Inf Fusion 31:137–145, 2016) considered the problem of computing a numerical Choquet integral and some algorithms for Hellinger distance between two monotone measures. In this paper, the composite Simpson rule for numerical Choquet integration is proposed. Then some algorithms in Mathematica software are given. As well as, CPU time of the Examples in terms of seconds is reported which shows, in computational view, the presented method has a high speed.

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Acknowledgements

The author’s are very grateful to the anonymous reviewers for their comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Shariati Ave., Babol, 47148-71167, Iran

    Hamzeh Agahi & Mahmoud Behroozifar

Authors
  1. Hamzeh Agahi
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  2. Mahmoud Behroozifar
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Correspondence to Mahmoud Behroozifar.

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Communicated by V. Loia.

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Agahi, H., Behroozifar, M. Choquet integration by Simpson’s rule with application in Hellinger distance. Soft Comput 24, 14463–14470 (2020). https://doi.org/10.1007/s00500-020-04798-8

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  • DOI: https://doi.org/10.1007/s00500-020-04798-8

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