Superadditive and subadditive transformations of integrals and aggregation functions

We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Su...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 291; pp. 40 - 53
Main Authors Greco, Salvatore, Mesiar, Radko, Rindone, Fabio, Šipeky, Ladislav
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.05.2016
Subjects
Agglomeration
Aggregation function
Fuzzy integrals
Fuzzy set theory
Integrals
Links
Superadditive and subadditive transformations
Transformations
Transformations (mathematics)
Transforms
Superadditive and subadditive transformations
Aggregation function
Fuzzy integrals
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Summary:We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Superadditive transformation of the Choquet integral, as well as of the Shilkret integral, is shown to coincide with the corresponding concave integral recently introduced by Lehrer. Similarly the transformation of the Sugeno integral is studied. Moreover, subadditive transformation of distinguished integrals is also discussed.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2015.08.006