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Šipošová, Alexandra; Šipeky, Ladislav and Širáň, Jozef
(2017).
DOI: https://doi.org/10.1016/j.fss.2016.11.009
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.
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About
- Item ORO ID
- 48783
- Item Type
- Journal Item
- ISSN
- 0165-0114
- Keywords
- aggregation function; sub-additive and super-additive transformation
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2016 Elsevier B.V.
- Depositing User
- Jozef Širáň