Shift invariant binary aggregation operators

When applying an information fusion method, usually the output results are required to be a scalar value. In multiple situations, the application of the fusion method to input values shifted by a constant should result in an output that is shifted likewise. In this paper, we present a study of the shift invariance property of aggregation operators. The relationship between shift invariant binary aggregation operators and 1-Lipschitz aggregation operators is shown, and a full description of shift invariant aggregation operators is given.