Šipošová, Alexandra; Šipeky, Ladislav and Širáň, Jozef
(2017).
| DOI (Digital Object Identifier) Link: | https://doi.org/10.1016/j.fss.2016.11.009 |
|---|---|
| Google Scholar: | Look up in Google Scholar |
Abstract
In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, A → A∗ and A → A∗, of an aggregation function A. We prove that if A∗ has a slightly stronger property of being strictly directionally convex, then A = A∗ and A∗ is linear; dually, if A∗ is strictly directionally concave, then A = A∗ and A∗ is linear. This implies, for example, the existence of pairs of functions f≤g sub-additive and super-additive on [0, ∞[n, respectively, with zero value at the origin and satisfying relatively mild extra conditions, for which there exists no aggregation function A on [0, ∞[n such that A∗=f and A∗=g.
| Item Type: | Journal Item |
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| Copyright Holders: | 2016 Elsevier B.V. |
| ISSN: | 0165-0114 |
| Keywords: | aggregation function; sub-additive and super-additive transformation |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 48783 |
| Depositing User: | Jozef Širáň |
| Date Deposited: | 01 Mar 2017 16:07 |
| Last Modified: | 30 Jun 2020 05:05 |
| URI: | http://oro.open.ac.uk/id/eprint/48783 |
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