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: 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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

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