On stability of maximal entropy OWA operator weights

The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear programming problem for obtaining MEOWA weights is well-posed: it has a unique solution and each MEOWA weight changes continuously with the initial level of orness. Using the implicit function theorem we will show that MEOWA weights are Lipschitz-continuous functions of the orness level. The stability property of the MEOWA weights under small changes of the orness level guarantees that small rounding errors of digital computation and small errors of measurement of the orness level can cause only a small deviation in MEOWA weights, i.e. every successive approximation method can be applied to the computation of the approximation of the exact MEOWA weights.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This paper discusses the approximation of maximal entropy OWA weights using a nonlinear programming problem with a linear constraint. The well-posedness and continuity of the problem are proved, and the stability of the weights under small changes in the level of orness is demonstrated.