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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| Published in | Fuzzy sets and systems Vol. 291; pp. 40 - 53 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
15.05.2016
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| Subjects | |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Greco, Salvatore Mesiar, Radko Rindone, Fabio Šipeky, Ladislav |
| Author_xml | – sequence: 1 givenname: Salvatore surname: Greco fullname: Greco, Salvatore email: salgreco@unict.it organization: Department of Economics and Business, 95029 Catania, Italy – sequence: 2 givenname: Radko surname: Mesiar fullname: Mesiar, Radko email: radko.mesiar@stuba.sk organization: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 810 05 Bratislava, Slovakia – sequence: 3 givenname: Fabio surname: Rindone fullname: Rindone, Fabio email: frindone@unict.it organization: Department of Economics and Business, 95029 Catania, Italy – sequence: 4 givenname: Ladislav surname: Šipeky fullname: Šipeky, Ladislav email: ladislav.sipeky@stuba.sk organization: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 810 05 Bratislava, Slovakia |
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| Cites_doi | 10.1007/BF02589354 10.1017/CBO9781139644150 10.1016/j.ijar.2013.02.001 10.1007/s10700-014-9182-4 10.1016/j.fss.2014.05.003 10.5802/aif.53 10.1007/s00199-007-0302-z |
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| Keywords | Superadditive and subadditive transformations Aggregation function Fuzzy integrals |
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| References | Hörmander (br0050) 1955; 3 Shephard, Gale, Kuhn (br0130) 1970 Mesiar, Stupňanová (br0110) 2013; 54 Mishra (br0120) 2010; 8 Choquet (br0020) 1953/54; 5 Yang (br0180) 1985; 3 Klement, Mesiar, Spizzichino, Stupňanová (br0080) 2014; 13 Lehrer (br0090) 2009; 39 Grabisch, Marichal, Mesiar, Pap (br0040) 2009 Sugeno (br0160) 1974 Klement, Mesiar, Pap (br0070) 2000 Stupňanová (br0150) 2012 Wang, Klir (br0170) 2009 Mesiar, Li, Pap (br0100) 2015; 259 Shilkret (br0140) 1971; vol. 74 Jehle, Reny (br0060) 2001 Aliprantis, Border (br0010) 1999 Coelli, Rao, O'Donnell, Battese (br0030) 2005 Aliprantis (10.1016/j.fss.2015.08.006_br0010) 1999 Shilkret (10.1016/j.fss.2015.08.006_br0140) 1971; vol. 74 Stupňanová (10.1016/j.fss.2015.08.006_br0150) 2012 Choquet (10.1016/j.fss.2015.08.006_br0020) 1953; 5 Grabisch (10.1016/j.fss.2015.08.006_br0040) 2009 Mesiar (10.1016/j.fss.2015.08.006_br0110) 2013; 54 Sugeno (10.1016/j.fss.2015.08.006_br0160) 1974 Mesiar (10.1016/j.fss.2015.08.006_br0100) 2015; 259 Mishra (10.1016/j.fss.2015.08.006_br0120) 2010; 8 Klement (10.1016/j.fss.2015.08.006_br0080) 2014; 13 Jehle (10.1016/j.fss.2015.08.006_br0060) 2001 Yang (10.1016/j.fss.2015.08.006_br0180) 1985; 3 Klement (10.1016/j.fss.2015.08.006_br0070) 2000 Wang (10.1016/j.fss.2015.08.006_br0170) 2009 Coelli (10.1016/j.fss.2015.08.006_br0030) 2005 Hörmander (10.1016/j.fss.2015.08.006_br0050) 1955; 3 Lehrer (10.1016/j.fss.2015.08.006_br0090) 2009; 39 Shephard (10.1016/j.fss.2015.08.006_br0130) 1970 |
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| SubjectTerms | Agglomeration Aggregation function Fuzzy integrals Fuzzy set theory Integrals Links Superadditive and subadditive transformations Transformations Transformations (mathematics) Transforms |
| Title | Superadditive and subadditive transformations of integrals and aggregation functions |
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