Programming-Based OWA Operator Weights With Quadratic Objective Function

Yager's ordered weighted averaging (OWA) operators are extensively employed to perform mean-type aggregations. Their success heavily depends on proper determination of the associated weights that characterize the operators. Several methods have been established to determine the weights and, thereby, to support successful OWA aggregation. In this study, the least square method, which is one of the nonlinear programs with a quadratic objective function, is reformulated by using the extreme points that correspond to its constraints and then solved by a few steps of matrix operations. Finally, we present a new weighting method called the minimizing distances from the extreme points (MDP) wherein the OWA operator weights that minimize the expected quadratic distance with respect to the set of extreme points are chosen. A different attitudinal character leads to different extreme points, and thus, the MDP seeks to find the OWA operator weights that are dynamically adjusted to be at the center of attitude-dependent polytope.