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On the existence of aggregation functions with given super-additive and sub-additive transformations

Šipošová, Alexandra; Šipeky, Ladislav and Širáň, Jozef (2017). On the existence of aggregation functions with given super-additive and sub-additive transformations. Fuzzy Sets and Systems, 324 pp. 117–126.

DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.fss.2016.11.009
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Abstract

In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, AA and AA, 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 fg 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
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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