Bustince Sola, HumbertoMesiar, RadkoKolesárová, AnnaPereira Dimuro, GraçalizFernández Fernández, Francisco JavierDíaz, IreneMontes Rodríguez, Susana2020-06-052022-05-0120200165-011410.1016/j.fss.2019.01.024https://academica-e.unavarra.es/handle/2454/37100In this work we consider some classes of functions with relaxed monotonicity conditions generalizing some other given classes of fusion functions. In particular, directionally increasing aggregation functions (called also pre-aggregation functions), directionally increasing conjunctors, or directionally increasing implications, etc., generalize the standard classes of aggregation functions, conjunctors, or implication functions, respectively. We analyze different properties of these classes of functions and we discuss a construction method in terms of linear combinations of t-norms.26 p.application/pdfeng© 2019 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0Directional monotonicityClasses of directionally increasing functionsPre-aggregation functionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess