This paper just accepted for publication in Fuzzy Sets and Systems. We look at aggregation functions whose output does not change when a new input is introduced that is equal to the aggregated value of the original inputs. Some of the more novel results concern the conditions on weighting vectors associated with functions like the OWA that involve a reordering of the inputs.
Title: Stability of weighted penalty-based aggregation functions
Authors: G. Beliakov and S. James
In many practical applications, the need arises to aggregate data of varying dimension. Following from the self-identity property, some recent studies have looked at the stability of aggregation operators in terms of their behavior as the dimensionality is increased from n-1 to n. We use the penalty-based representation of aggregation functions in order to investigate the conditions for weighting vectors associated with some important weighted families, extending on the results already established for quasi-arithmetic means. In particular, we obtain results for quasi-medians and functions that involve a reordering of the inputs such as the OWA and order statistics.