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On the definition of penalty functions in data aggregation. (English) Zbl 1409.68288

Summary: 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.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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