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Ordered Novel  Weighted Averages

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Type-2 Fuzzy Logic and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 362))

Abstract

The novel weighted averages (NWAs) are extensions of the linear arithmetic weighted average and are powerful tools in aggregating diverse inputs including numbers, intervals, type-1 fuzzy sets (T1 FSs), words modeled by interval type-2 fuzzy sets, or a mixture of them. In contrast to the linear arithmetic weighted average, the ordered weighed average (OWA) is a nonlinear operator that can implement more flexible mappings, and hence it has been widely used in decision-making. In many situations, however, providing crisp numbers for either the sub-criteria or the weights is problematic (there could be uncertainties about them), and it is more meaningful to provide intervals, T1 FSs, words, or a mixture of all of these, for the sub-criteria and weights. Ordered NWAs are introduced in this chapter. They are also compared with NWAs and Zhou et al’s fuzzy extensions of the OWA. Examples show that generally the three aggregation operators give different results.

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Author information

Authors and Affiliations

  1. School of Automation, Huazhong University of Science and Technology, Wuhan, Hubei, China

    Dongrui Wu & Jian Huang

Authors
  1. Dongrui Wu
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  2. Jian Huang
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Corresponding author

Correspondence to Dongrui Wu .

Editor information

Editors and Affiliations

  1. LUCID Research Group, School of Computer Science, The University of Nottingham, Jubilee Campus, Nottingham, Nottinghamshire, United Kingdom

    Robert John

  2. School of Computer Science and Electronic Engineering, The Computational Intelligence Centre, University of Essex, Colchester, United Kingdom

    Hani Hagras

  3. Division of Graduate Studies, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

Ranking Methods for T1 FSs

Ranking Methods for T1 FSs

Wang and Kerre [41,42,43,44] performed a very comprehensive study on ranking methods for T1 FSs. They partitioned over 35 ranking methods for T1 FSs into three classes:

  1. 1.

    Class 1: Reference set(s) is (are) set up, and each T1 FS is mapped into a crisp number based on the reference(s). The T1 FSs are then ranked according to the corresponding crisp numbers.

  2. 2.

    Class 2: A function \(f(A_i)\) is used to map a T1 FS \(A_i\) to a crisp number, which can then be ranked. No reference set(s) is (are) used in the mapping.

  3. 3.

    Class 3: T1 FSs \(A_i\) (\(i=1,\ldots ,M\)) are ranked through pairwise comparisons.

They then proposed seven reasonable properties that a ranking method should satisfy [41]. Some simple ranking methods, which are also the most reasonable ones according to the seven properties [41, 42], are summarized in Table 1.

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Wu, D., Huang, J. (2018). Ordered Novel  Weighted Averages. In: John, R., Hagras, H., Castillo, O. (eds) Type-2 Fuzzy Logic and Systems. Studies in Fuzziness and Soft Computing, vol 362. Springer, Cham. https://doi.org/10.1007/978-3-319-72892-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-72892-6_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-72892-6

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