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Mathematics 2019, 7(4), 326; https://doi.org/10.3390/math7040326

The General Least Square Deviation OWA Operator Problem

1
Department of Mathematics, Myongji University, Yongin 449-728, Kyunggido, Korea
2
Department of Managment, Nagoya University of Commerce & Business, 4-4 Sagamine Komenoki, Nisshin 470-0193, Aichi, Japan
*
Author to whom correspondence should be addressed.
Received: 8 March 2019 / Revised: 25 March 2019 / Accepted: 1 April 2019 / Published: 3 April 2019
(This article belongs to the Special Issue Special Polynomials)
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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. View Full-Text
Keywords: decision making; OWA operator; operator weights; degree of orness; absolute disparity; least convex deviation model decision making; OWA operator; operator weights; degree of orness; absolute disparity; least convex deviation model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Hong, D.H.; Han, S. The General Least Square Deviation OWA Operator Problem. Mathematics 2019, 7, 326.

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