Ferrero Jaurrieta, MikelHoranská, LubomíraLafuente López, JulioMesiar, RadkoPereira Dimuro, GraçalizTakáč, ZdenkoGómez Fernández, MarisolFernández Fernández, Francisco JavierBustince Sola, Humberto2024-04-182023Ferrero-Jaurrieta, M., Horanská, L., Lafuente, J., Mesiar, R., Dimuro, G.P., Takác, Z., Gómez, M., Fernández, J., Bustince, H. (2023) Degree of totalness: How to choose the best admissible permutation for vector fuzzy integration. Fuzzy Sets and Systems, 466, 1-15. https://doi.org/10.1016/j.fss.2022.12.017.0165-011410.1016/j.fss.2022.12.017https://academica-e.unavarra.es/handle/2454/47989The use of aggregation operators that require ordering of the data brings a problem when the structures to be aggregated are multi-valued, since there may be several admissible orders. To addressing this problem, the concept of admissible permutation was introduced for intervals. In this paper we extend this concept to vector domain. However, the problem of selecting the best possible permutation is still an open problem. In this paper we present a novel concept in order to choose the best admissible permutation for vectors: the degree of totalness. This concept allows us to represent to which degree the admissible permutation reorder given vectors as a chain with respect to the partial order. Finally, from the best admissible permutation we construct the Choquet integral.application/pdfeng© 2022 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0Admissible permutationBest admissible permutationDegree of totalnessFuzzy integrationVector Choquet integralinfo:eu-repo/semantics/article2024-04-18info:eu-repo/semantics/embargoedAccess