New results on pre-aggregation functions: Introducing (light) pre-t-norms

The aim of this paper is to enlarge the knowledge about the promising concept of a pre-aggregation function introduced by Lucca et al., which is a kind of “aggregation” concept that no longer requires monotonicity in all the function domain. For that, we introduce the notion of pre-t-norm, based on the important concept of t-norm. We also study the case of the so-called light pre-t-norms, which are particular non necessarily associative, commutative functions with neutral element e =1, allowing for applications that do not require the associativity property, as it was extensively discussed in the literature. We analyse some properties of (light) pre-t-norms and the classes of (light) pre-t-norms, providing several examples.