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Strictly stable families of aggregation operators Rojas Patuelli, Karina Gómez González, Daniel Montero De Juan, Francisco Javier Rodríguez González, Juan Tinguaro 519.2 Aggregation operators Stability Consistency Self-identity Fuzzy sets Estadística matemática (Matemáticas) 1209 Estadística 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. Depto. de Estadística e Investigación Operativa Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-19T13:22:04Z 2023-06-19T13:22:04Z 2013-10-01 journal article https://hdl.handle.net/20.500.14352/33356 0165-0114 10.1016/j.fss.2012.12.010 eng Rojas, K., Gómez, D., Montero, J., Tinguaro Rodríguez, J.: Strictly stable families of aggregation operators. Fuzzy Sets and Systems. 228, 44-63 (2013). https://doi.org/10.1016/j.fss.2012.12.010 restricted access application/pdf Elsevier Science Bv