we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class o...

Modes are idempotent and entropic algebras. More precisely, an algebra (A,Ω) of type τ : Ω −→ Z is called a mode if it is idempotent and entropic, i.e. each singleton in A is a subalgebra and each operation ω ∈ Ω is actually a homomorphism from an appropriate power of the algebra. Both properties can also be expressed by the following identities: (I) ∀ω ∈ Ω, x . . . xω = x (E) ∀ω, φ ∈ Ω, with m...