OWA operators with maximal entropy

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal Shannon entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In this paper, using the method of Lagrange multipliers, we shall solve this constrained optimization problem analytically, furthermore, we represent the explicit solution when the entropy is defined as the Rényi’s entropy (with parameter value 2), the entropy of order introduced by Daróczy (when parameter is 2) and the 2-norm entropy (from entropy class R-norm entropies).