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Why Triangular Membership Functions are Often Efficient in F-transform Applications: Relation to Probabilistic and Interval Uncertainty and to Haar Wavelets

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 854))

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Abstract

Fuzzy techniques describe expert opinions. At first glance, we would therefore expect that the more accurately the corresponding membership functions describe the expert’s opinions, the better the corresponding results. In practice, however, contrary to these expectations, the simplest – and not very accurate – triangular membership functions often work the best. In this paper, on the example of the use of membership functions in F-transform techniques, we provide a possible theoretical explanation for this surprising empirical phenomenon.

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Acknowledgments

This work was supported in part by the US National Science Foundation grant HRD-1242122.

The authors are greatly thankful to the anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. University of Texas at El Paso, El Paso, TX, 79968, USA

    Olga Kosheleva & Vladik Kreinovich

Authors
  1. Olga Kosheleva
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  2. Vladik Kreinovich
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Corresponding author

Correspondence to Vladik Kreinovich .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Kosheleva, O., Kreinovich, V. (2018). Why Triangular Membership Functions are Often Efficient in F-transform Applications: Relation to Probabilistic and Interval Uncertainty and to Haar Wavelets. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-91476-3_11

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  • Online ISBN: 978-3-319-91476-3

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