Rational means, weak associativity of means, invariance with respect to mean-type and t-(norm,conorm) mappings and applications

Abstract

The means and t-norms are considered. A weak associativity property of the weighted quasi-arithmetic means, connecting these two families of functions, is introduced. It is observed that the symmetry of every t-norm follows from a modified system of the remaining axioms. The conditions under which a rational function is a bivariate homogeneous mean in $(0,\infty )$ are given. The invariance of means and functions with respect to the mean-type mappings and t-(norm,conorm)-type mappings is considered with some applications.