“…For this reason, many authors have studied in last years operations defined on a finite chain L n , usually called discrete operations. For instance, tnorms and t-conorms were characterized in [20], uninorms and nullnorms in [14], idempotent uninorms in [9], a non-commutative version of nullnorms in [10], weighted means in [13], smooth aggregation functions in [17], copulas in [19] and also implications functions in [15] and [16]. It is proved in [20] that only the number of elements of the finite chain L n is relevant when we deal with monotonic operations on L n , and so the finite chain used in many of the mentioned works is the most simple one L n = {0, 1, .…”