On obtaining OWA operator weights: a short survey of recent developments

The determination of ordered weighted averaging (OWA) operator weights is a very important issue of applying the OWA operator for decision making. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In 2001, using the method of Lagrange multipliers, Fullér and Majlender solved this constrained optimization problem analytically and determined the optimal weighting vector. In 2003 Fullér and Majlender also suggested a minimum variance method to obtain the minimal variability OWA operator weights. In this paper we give a short survey of some later works that extend and develop these models. I. OBTAINING OWA OPERATOR WEIGHTS An OWA operator of dimension n is a mapping F : R → R that has an associated weighting vector W = (w1, . . . , wn) of having the properties w1 + · · ·+ wn = 1, 0 ≤ wi ≤ 1, i = 1, . . . , n,