On a type of monotonicity for multidimensional operators

Abstract Two partial orderings on the set E of multidimensional ordered lists on [0, 1] are introduced based on a t-norm and on a t-conorm, respectively. We study the monotonicity condition for a function f from E to [0, 1] with respect to both orders. In the case when f is a t-norm we characterize the condition in terms of an equation that is solved in the very main context.