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Canonical form of ordered weighted averaging operators

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Abstract

Discrete Ordered Weighted Averaging (OWA) operators as one of the most representative proposals of Yager (1988) have been widely used and studied in both theoretical and application areas. However, there are no effective and systematic corresponding methods for continuous input functions. In this study, using the language of measure (capacity) space we propose a Canonical Form of OWA operators which yield some common properties like Monotonicity and Idempotency and thus serve as a generalization of Discrete OWA operators. We provide also a representation of the Canonical Form by means of asymmetric Choquet integrals. The Canonical Form of OWA operators can effectively handle some input functions defined on ordered sets.

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Acknowledgements

The authors would like to express their thanks to anonymous reviewers for valuable comments helping to improve the paper. The work of Martin Kalina was supported from the VEGA grant agency, Grant No. 1/0006/19. The work of Martin Kalina and Radko Mesiar was supported from the APVV grant agency, grant No. 18-0052 and from the project of Grant Agency of the Czech Republic (GAČR) no. 18-06915S.

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Authors and Affiliations

  1. Business School, Nanjing Normal University, Nanjing, China

    LeSheng Jin

  2. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar & Martin Kalina

  3. Faculty of Science, Department of Algebra and Geometry, Palacký University Olomouc, 17 Listopadu 12, 77146, Olomouc, Czech Republic

    Radko Mesiar

  4. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald R. Yager

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  1. LeSheng Jin
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  2. Radko Mesiar
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  3. Martin Kalina
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  4. Ronald R. Yager
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Correspondence to Martin Kalina.

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Jin, L., Mesiar, R., Kalina, M. et al. Canonical form of ordered weighted averaging operators. Ann Oper Res 295, 605–631 (2020). https://doi.org/10.1007/s10479-020-03802-6

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