On the definition of penalty functions in data aggregation

• Published in: Fuzzy sets and systems Vol. 323; pp. 1 - 18
• Main Authors: Bustince, Humberto, Beliakov, Gleb, Pereira Dimuro, Graçaliz, Bedregal, Benjamín, Mesiar, Radko
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15-09-2017
• Subjects: Aggregation functions; Averaging aggregation function; Penalty functions; Quasi-penalty functions; Spread measures; Aggregation functions; Quasi-penalty functions; Penalty functions; Averaging aggregation function; Spread measures
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2016.09.011

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.