Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4943791 | Fuzzy Sets and Systems | 2017 | 10 Pages |
Abstract
In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, Aâ¦Aâ and Aâ¦Aâ, of an aggregation function A. We prove that if Aâ has a slightly stronger property of being strictly directionally convex, then A=Aâ and Aâ is linear; dually, if Aâ is strictly directionally concave, then A=Aâ and Aâ is linear. This implies, for example, the existence of pairs of functions fâ¤g sub-additive and super-additive on [0,â[n, respectively, with zero value at the origin and satisfying relatively mild extra conditions, for which there exists no aggregation function A on [0,â[n such that Aâ=f and Aâ=g.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Alexandra Å ipoÅ¡ová, Ladislav Å ipeky, Jozef Å iráÅ,