research-article

Wasserstein distance for OWA operators

Authors:

István Á. Harmati,

Lucian Coroianu,

Robert FullérAuthors Info & Claims

Volume 484, Issue C

https://doi.org/10.1016/j.fss.2024.108931

Published: 15 May 2024 Publication History

Abstract

We suggest a distance measure for OWA operators. First we associate an OWA operator with a unique regular increasing monotone quantifier and then define the distance between two OWA operators as the Wasserstein-1 distance between their associated quantifiers.

References

[1]

L.S. Jin, R. Mesiar, The metric space of ordered weighted average operators with distance based on accumulated entries, Int. J. Intell. Syst. 32 (2017) 665–675.

Google Scholar

[2]

R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets Syst. 136 (2) (2003) 203–215.

Google Scholar

[3]

S.S. Vallender, Calculation of the Wasserstein distance between probability distributions on the line, Theory Probab. Appl. 18 (4) (1974) 784–786.

Google Scholar

[4]

C. Villani, Optimal Transport: Old and New, vol. 338, Springer, Berlin, 2009.

Google Scholar

[5]

L.N. Wasserstein, Markov processes with countable state space describing large systems of automata, Probl. Pereda. Inf. 5 (1969) 64–73. (in Russian).

Google Scholar

[6]

R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybern. 18 (1988) 183–190.

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Google Scholar

[7]

R.R. Yager, Quantifier guided aggregation using OWA operators, Int. J. Intell. Syst. 11 (1) (1996) 49–73.

Google Scholar

[8]

S.T. Rachev, S.V. Stoyanov, F.J. Fabozzi, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures, Wiley, 2008.

Google Scholar

[9]

J. Wu, B.L. Sun, C.Y. Liang, S.L. Yang, A linear programming model for determining ordered weighted averaging operator weights with maximal Yager's entropy, Comput. Ind. Eng. 57 (3) (2009) 742–747.

Google Scholar

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Published In

Fuzzy Sets and Systems Volume 484, Issue C

May 2024

205 pages

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Elsevier B.V.

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Elsevier North-Holland, Inc.

United States

Publication History

Published: 15 May 2024

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Constructing Choquet integral-based operators that generalize weighted means and OWA operators

On the properties of OWA operator weights functions with constant level of orness

Distance measures, weighted averages, OWA operators and Bonferroni means

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Constructing Choquet integral-based operators that generalize weighted means and OWA operators

On the properties of OWA operator weights functions with constant level of orness

Distance measures, weighted averages, OWA operators and Bonferroni means

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