A New Approach to Solve the Constrained OWA Aggregation Problem

Constrained ordered weighted averaging (OWA) aggregation attempts to optimize the OWA aggregation problem with multiple constraints. It is inherently nonlinear, and Yager presented a novel method to transform the nonlinear problem to a mixed integer linear problem. Later, a simple algorithm for exact computation of optimal solutions to a single constrained OWA aggregation problem was presented. In this paper, we deal with the same problem, but in completely different ways in a sense that it is linearized by utilizing the reordering property of the OWA operators. We attempt to solve the linear programming problem via the extreme points in lieu of using a linear programming package for the purpose of deriving an explicit formula for the optimal solution. Furthermore, we consider its dual problem that leads to an equivalent optimal solution. Finally, the proposed method is extended to the OWA optimization problem with multiple constraints including the attitudinal character as well as a range of incomplete arguments.