An analytic approach to obtain the least square deviation OWA operator weights

An important issue in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weights. One important approach, suggested by Wang, Luo and Liu in 2007 determines a special class of OWA operators with the least square deviation (LSD) of OWA weights for a given orness level. In this paper, using the method of Lagrange multipliers, we solve this constrained optimization problem analytically, and derive a polynomial equation to determine the optimal weighting vector. Numerical examples illustrate our proposed approach.