On the definition of penalty functions in data aggregation

0477083 - ÚTIA 2018 RIV NL eng J - Journal Article
Bustince, H. - Beliakov, G. - Dimuro, G. P. - Bedregal, B. - Mesiar, Radko
On the definition of penalty functions in data aggregation.
Fuzzy Sets and Systems. Roč. 323, č. 1 (2017), s. 1-18. ISSN 0165-0114. E-ISSN 1872-6801
Institutional support: RVO:67985556
Keywords : Aggregation functions * Averaging aggregation function * Penalty functions * Quasi-penalty functions * Spread measures
OECD category: Pure mathematics
Impact factor: 2.675, year: 2017
http://library.utia.cas.cz/separaty/2017/E/mesiar-0477083.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0274028