Consistency and stability in aggregation operators: An application to missing data problems

Abstract

In this work we analyze the key issue of the relationship that should hold between the operators in a family {An} of aggregation operators in order to understand they properly define a consistent whole. Here we extend some of the ideas about stability of a family of aggregation operators into a more general framework, formally defining the notions of i – L and j – R strict stability for families of aggregation operators. The notion of strict stability of order k is introduced as well. Finally, we also present an application of the strict stability conditions to deal with missing data problems in an information aggregation process. For this analysis, we have focused in the weighted mean family and the quasi-arithmetic weighted means families.