Some Properties of Consistency in the Families of Aggregation Operators

Abstract

Properties related with aggregation operators functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. What should be the relationship among the members of a family of aggregation operators? Is it possible to build the aggregation of n data with aggregation operators of lower dimension? Should it exist some consistency in the family of aggregation operators? In this work, we analyze two properties of consistency in a family of aggregation operators: Stability and Structural Relevance. The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n items should be similar to the aggregation of n + 1 items if the last item is the aggregation of the previous n items. Following this idea some definitions and results are given. The second concept presented in this work is related with the construction of the aggregation operator when the data that have to be aggregated has an inherent structure. The Structural Relevance property tries to give some ideas about the construction of the aggregation operator when the items are related by means of a graph.