Strictly stable families of aggregation operators
In this paper we analyze the notion of family of aggregation operators (FAO), also refereed to as extended aggregation functions (EAF), i.e., a set of aggregation operators defined in the unit interval which aggregate several input values into a single output value. In particular, we address the key issue of the relationship that should hold between the operators in a family in order to understand that they properly define a consistent FAO. We focus on the idea of strict stability of a family of aggregation operators in order to propose an operative notion of consistency between operators of such a family. In this way, robustness of the aggregation process can be guaranteed. Some strict stability definitions for FAOs are proposed, leading to a classification of the main aggregation operators in terms of the properties they satisfy. Furthermore, we apply this approach to analyze the stability of some families of aggregation operators based on weights.
In this paper we study a notion of consistency based on the robustness of the aggregation process. In this sense, we introduce the strict stability property for a family of aggregation functions by extending the self-identity property defined by other authors. Such strict stability property tries to force a family to have a stable/continuous definition, in the sense that an operator defined for n elements should not differ too much from an operator of the same family defined for n - 1 elements, when the last n-th element of information added is the aggregation of the previous n - 1 elements. Therefore this property gives us some restrictions to take into account in order to maintain the logical consistency of the operators of a given family, so as to guarantee the robustness of the aggregation process when there is a change in the cardinality of the data. of the data.
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