On interval pseudo-homogeneous uninorms

Abstract

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-norms, that is, T M and we also prove that only interval t-conorm which is pseudo-homogeneous is S M and that there are no interval pseudo-homogeneous proper uninorms.

On some classes of nullnorms and h-pseudo homogeneity

“…Theorem 2.5). This notion was also adapted and investigated for other classes of aggregation functions, such as overlap functions in [29], t-subnorms in [25] or even interval-valued uninorms, t-norms and t-conorms in [23,24].…”

“…We have also presented a notion of pseudohomogeneity for nullnorms. In general, the pseudo-homogeneity of a function F , as considered in [23,24,29,37] is defined by F (λx, λy) = G(λ, F (x, y)). But here the function "F " on the right side (in our case V S,T,min(1, k λ ) ) is different from the "F " on the left side (in our case V S,T,k ).…”

“…We will also consider admissible orders [33], as it was done in [38]. In both cases, the relation to the interval-valued pseudo-homogeneity as introduced in [23,24] will be considered.…”