A Discussion on Consistency of Global Aggregation Operators

Several authors have introduced global aggregation operators as families of aggregation operators {Tn}n, being each one of these Tn the n-ary operator in charge of aggregation, if and only if the number of items being actually aggregated is n. But according to this general definition, it is clear that operators within the same family may be not related at all. In this paper we shall point out the absolute need of an additional condition allowing some kind of consistency for such a family of operators, in order to be considered an aggregation rule. In particular, we shall discuss some advantages and limits of the concept of recursiveness, which basically assumes that the aggregation can be worked out by means of a recursive process. A comparative analysis with some alternative consistency conditions is also presented.