Stability of weighted penalty-based aggregation functions

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

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.

 

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s