Pseudo-Additions and Shift Invariant Aggregation Functions

Abstract

Shift invariant aggregation functions are related to the shifts based on the standard addition + and their complete characterization is well known. We discuss the aggregation functions invariant with respect to a pseudo-addition ⊕. Our study has two directions. In the first one, we discuss ⊕-shift invariant aggregation functions with respect to a fixed pseudo-addition ⊕. In the second one, for a fixed aggregation function A, we discuss pseudo-additions ⊕ such that A is ⊕ -shift invariant.