Maximal Entropy and Minimal Variability OWA Operator Weights: A Short Survey of Recent Developments

Abstract

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, Fuller and Majlender solved this constrained optimization problem analytically and determined the optimal weighting vector. In 2003 Fuller and Majlender computed the exact minimal variability weighting vector for any level of orness using the Karush-Kuhn-Tucker second-order sufficiency conditions for optimality. The problem of maximizing an OWA aggregation of a group of variables that are interrelated and constrained by a collection of linear inequalities was first considered by Yager in 1996, where he showed how this problem can be modeled as a mixed integer linear programming problem. In 2003 Carlsson, Fuller and Majlender derived an algorithm for solving the constrained OWA aggregation problem under a simple linear constraint: the sum of the variables is less than or equal to one. In this paper we give a short survey of numerous later works which extend and develop these models.