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The General Least Square Deviation OWA Operator Problem

Author

Listed:
  • Dug Hun Hong

    (Department of Mathematics, Myongji University, Yongin 449-728, Kyunggido, Korea)

  • Sangheon Han

    (Department of Managment, Nagoya University of Commerce & Business, 4-4 Sagamine Komenoki, Nisshin 470-0193, Aichi, Japan)

Abstract

A crucial issue in applying the ordered weighted averaging (OWA) operator for decision making is the determination of the associated weights. This paper proposes a general least convex deviation model for OWA operators which attempts to obtain the desired OWA weight vector under a given orness level to minimize the least convex deviation after monotone convex function transformation of absolute deviation. The model includes the least square deviation (LSD) OWA operators model suggested by Wang, Luo and Liu in Computers & Industrial Engineering, 2007, as a special class. We completely prove this constrained optimization problem analytically. Using this result, we also give solution of LSD model suggested by Wang, Luo and Liu as a function of n and α completely. We reconsider two numerical examples that Wang, Luo and Liu, 2007 and Sang and Liu, Fuzzy Sets and Systems, 2014, showed and consider another different type of the model to illustrate our results.

Suggested Citation

  • Dug Hun Hong & Sangheon Han, 2019. "The General Least Square Deviation OWA Operator Problem," Mathematics, MDPI, vol. 7(4), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:326-:d:219658
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    Citations

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    Cited by:

    1. Jing Wang & Huafei Sun & Simone Fiori, 2019. "Empirical Means on Pseudo-Orthogonal Groups," Mathematics, MDPI, vol. 7(10), pages 1-20, October.
    2. Dug Hun Hong, 2019. "The General Model for Least Convex Disparity RIM Quantifier Problems," Mathematics, MDPI, vol. 7(7), pages 1-12, June.
    3. Luis A. Perez-Arellano & Fabio Blanco-Mesa & Ernesto Leon-Castro & Victor Alfaro-Garcia, 2020. "Bonferroni Prioritized Aggregation Operators Applied to Government Transparency," Mathematics, MDPI, vol. 9(1), pages 1-19, December.

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