Additive generators of discrete conjunctive aggregation operations

This paper deals with a class of conjunction-like binary operations defined on a finite totally ordered set. The concept of additive generator of a discrete conjunctive aggregation operation is introduced and we obtain a description of those operations having an additive generator by means of nonstrict Archimedean t-norms. The main goal is to give a procedure for deciding whether a conjunctive aggregation operation is additively generated or not. The problem of the existence of additive generators for discrete t-norms is also discussed.