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Canonical form of ordered weighted averaging operators

Author

Listed:
  • LeSheng Jin

    (Nanjing Normal University)

  • Radko Mesiar

    (Slovak University of Technology
    Palacký University Olomouc)

  • Martin Kalina

    (Slovak University of Technology)

  • Ronald R. Yager

    (Iona College)

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.

Suggested Citation

  • LeSheng Jin & Radko Mesiar & Martin Kalina & Ronald R. Yager, 2020. "Canonical form of ordered weighted averaging operators," Annals of Operations Research, Springer, vol. 295(2), pages 605-631, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03802-6
    DOI: 10.1007/s10479-020-03802-6
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    References listed on IDEAS

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    1. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    2. Hamzeh Agahi, 2020. "On fractional continuous weighted OWA (FCWOWA) operator with applications," Annals of Operations Research, Springer, vol. 287(1), pages 1-10, April.
    3. Yasuo Narukawa & Vicenç Torra & Michio Sugeno, 2016. "Choquet integral with respect to a symmetric fuzzy measure of a function on the real line," Annals of Operations Research, Springer, vol. 244(2), pages 571-581, September.
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