Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...

The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

In the note, the functions ̨ ̨ψ(i)(ex) ̨ ̨ for i ∈ N are proved to be sub-additive on (ln θi,∞) and super-additive on (−∞, ln θi), where θi ∈ (0, 1) is the unique root of equation 2 ̨ ̨ψ(i)(θ) ̨