Halaš, RadomírMesiar, RadkoKolesárová, AnnaSaadati, RezaHerrera, FranciscoRodríguez Martínez, IosuBustince Sola, Humberto2024-10-312024-10-01Halas, R., Mesiar, R., Kolesárová, A., Saadati, R., Herrera, F., Rodriguez-Martinez, I., Bustince, H. (2024) Extremal values-based aggregation functions. Fuzzy Sets and Systems, 493-494, 1-16. https://doi.org/10.1016/j.fss.2024.109097.0165-011410.1016/j.fss.2024.109097https://academica-e.unavarra.es/handle/2454/52419We introduce and study aggregation functions based on extremal values, namely extended (𝑙, 𝑢)- aggregation functions whose outputs only depend on a fixed number 𝑙 of extremal lower input values and a fixed number 𝑢 of extremal upper input values, independently of the arity of the input 𝑛-tuples (𝑛 ≥ 𝑙 + 𝑢). We discuss several general properties of (𝑙, 𝑢)-aggregation functions and we study special (𝑙, 𝑢)-aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study (𝑙, 𝑢)-aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as (𝑙, 𝑢)-ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.application/pdfeng© 2024 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0.Aggregation functionChoquet integralClassificationExtended aggregation functionOrdered weighted quasi-arithmetic meanSugeno integralSymmetric discrete fuzzy measuret-conormt-norminfo:eu-repo/semantics/article2024-10-31info:eu-repo/semantics/embargoedAccess