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.
Highlights
Yager [1,2] introduced the concept of ordered weighted averaging (OWA) operator
O’Hagan [9] proposed another approach that determines a special class of OWA operators having maximal entropy for the OWA weights; this approach is algorithmically based on the solution of a constrained optimization problem
The model includes the least square deviation (LSD) OWA operators model suggested by Wang et al [1]
Summary
Yager [1,2] introduced the concept of ordered weighted averaging (OWA) operator. It is an important issue to the application and theory of OWA operators to determine the weights of the operators. Wang and Parkan [18] suggested a new method which generates the OWA operator weights by minimizing the maximum difference between any two adjacent weights. They transferred the minimax disparity problem to a linear programming problem, obtained weights for some special values of orness, and proved the dual property of OWA. We completely prove the optimization problem mathematically and consider the same numerical examples that Wang et al [1] and Sang and Liu [17] presented in their illustration of the application of the least square deviation model. We determine the solution OWA operator weights not for some discrete value of α but for all orness levels 0 ≤ α ≤ 1 as a function of α
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