On Stability of Families for Improper Aggregation Operators.

This work extends the notion of consistency in terms of stability for Families of Aggregation Operators (FAO), as defined in previous works. The notion of stability proposed in this work, not only extends the previous one, but it can be applied to a wider set of FAOs, particularly, to those that we name here as Family of Improper Aggregation Operators (FIAO), or improper FAOs. When the aggregated value cannot be considered as a new item from the input, the present definition of consistency cannot be applied. This is usual in several areas, namely in the development of social, economic and political indexes, as far as the aggregation process typically yield a new and different concept from the input elements.