  The aim of this paper is to introduce several notions of homogenization in
various classes of weighted means, which include quasiarithmetic and
semideviation means. In general, the homogenization is an operator which
attaches a homogeneous mean to a given one. Our results show that, under some
regularity or convexity assumptions, the homogenization of quasiarithmetic
means are power means, and homogenization of semideviation means are
homogeneous semideviation means. In other results, we characterize the
comparison inequality, the Jensen concavity, and Minkowski- and H\"older-type
inequalities related to semideviation means.
