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More Types of Averaging and Construction Methods

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A Practical Guide to Averaging Functions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 329))

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Abstract

This chapter treats some advanced topics, including a number of construction methods, such as idempotization, graduation curves and flying parameter. It also presents various related functions, such as the overlap and grouping functions. The recent extensions of the Bonferroni mean are treated in detail. The issue of consistency and stability of weighted averages is presented.

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Notes

  1. 1.

    Intervals \({\mathbb I}\) other than [0, 1] can be easily accommodated.

  2. 2.

    See p. 22 for definitions of various norms.

  3. 3.

    The standard OWA and OWG functions were defined on pp. 101, 133.

  4. 4.

    Here we allow the relationship \(w^n_i = 0, \forall i \ne n, w^n_n > 0\) that results for \(\lambda _n =0\).

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Authors and Affiliations

  1. School of Information Technology, Deakin University, Burwood, VIC, Australia

    Gleb Beliakov

  2. Departamento de Automática y Computación, Universidad Pública de Navarra, Pamplona, Spain

    Humberto Bustince Sola

  3. Departamento de Ciencias de la Computación, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain

    Tomasa Calvo Sánchez

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  1. Gleb Beliakov
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  3. Tomasa Calvo Sánchez
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Correspondence to Gleb Beliakov .

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Beliakov, G., Bustince Sola, H., Calvo Sánchez, T. (2016). More Types of Averaging and Construction Methods. In: A Practical Guide to Averaging Functions. Studies in Fuzziness and Soft Computing, vol 329. Springer, Cham. https://doi.org/10.1007/978-3-319-24753-3_6

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