On some classes of directionally monotone functions

In 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.H. Bustince and J. Fernandez were supported by research project TIN2016-77356-P of the Spanish Government. G. Dimuro was supported by CNPq/Brazil Proc.305882/2016-3. R. Mesiar was supported by the project APVV14-0013 and by the project of Grant Agency of the Czech Republic (GACR) no. 18-06915S. A. Kolesárová was supported by the project VEGA 1/0614/18. I. Díaz was supported by research project TIN2017-87600-P of the Spanish Government. S. Montes was supported by research project TIN2014-59543-P of the Spanish Government