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Ordered Weighted Averaging

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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

The focus of this chapter is on OWA functions. The formal definitions and the main properties of OWA are presented. Some extensions of the OWA functions are discussed in detail. Various methods of fitting OWA functions to empirical data are presented. This chapter ends with the discussion of the median functions and order statistics as the special cases of OWA functions.

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Notes

  1. 1.

    I.e., Q is a monotone increasing function \([0,1]\rightarrow [0,1]\), \(Q(0)=0,Q(1)=1\) whose value Q(t) represents the degree to which t satisfies the fuzzy concept represented by the quantifier.

  2. 2.

    This is an informal definition. The proper definition involves the concepts of distributions and measures, see, e.g., [Rud91].

  3. 3.

    Note that in OWA, weighted median and ordinal OWA, \(x_{(k)}\) denotes the k-th largest element of \(\mathbf {x}\).

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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). Ordered Weighted Averaging. 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_3

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  • DOI: https://doi.org/10.1007/978-3-319-24753-3_3

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