Institute of Information Theory and Automation

Publication details

On the definition of penalty functions in data aggregation

Journal Article

Bustince H., Beliakov G., Dimuro G. P., Bedregal B., Mesiar Radko

serial: Fuzzy Sets and Systems vol.323, 1 (2017), p. 1-18

keywords: Aggregation functions, Averaging aggregation function, Penalty functions, Quasi-penalty functions, Spread measures

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abstract (eng):

In this paper, we point out several problems in the different definitions (and related results) of penalty functions found in the literature. Then, we propose a new standard definition of penalty functions that overcomes such problems. Some results related to averaging aggregation functions, in terms of penalty functions, are presented, as the characterization of averaging aggregation functions based on penalty functions. Some examples are shown, as the penalty functions based on spread measures, which happen to be continuous. We also discuss the definition of quasi-penalty functions, in order to deal with non-monotonic (or weakly/directionally monotonic) averaging functions.


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Institute of Information Theory and Automation