Stability of weighted penalty-based aggregation functions

Authors:
Gleb Beliakov;Simon James
Affiliations:
Deakin University, School of Information Technology, 221 Burwood Hwy, Burwood, Victoria 3125, Australia;Deakin University, School of Information Technology, 221 Burwood Hwy, Burwood, Victoria 3125, Australia
Venue:
Fuzzy Sets and Systems
Year:
2013

Citing 11
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Abstract

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.