  Given two continuous functions $f,g:I\to\mathbb{R}$ such that $g$ is positive
and $f/g$ is strictly monotone, a measurable space $(T,A)$, a measurable family
of $d$-variable means $m: I^d\times T\to I$, and a probability measure $\mu$ on
the measurable sets $A$, the $d$-variable mean $M_{f,g,m;\mu}:I^d\to I$ is
defined by $$
  M_{f,g,m;\mu}(\pmb{x})
  :=\left(\frac{f}{g}\right)^{-1}\left(
  \frac{\int_T f\big(m(x_1,\dots,x_d,t)\big) d\mu(t)}
  {\int_T g\big(m(x_1,\dots,x_d,t)\big) d\mu(t)}\right)
  \qquad(\pmb{x}=(x_1,\dots,x_d)\in I^d). $$ The aim of this paper is to study
the local and global comparison problem of these means, i.e., to find
conditions for the generating functions $(f,g)$ and $(h,k)$, for the families
of means $m$ and $n$, and for the measures $\mu,\nu$ such that the comparison
inequality $$
  M_{f,g,m;\mu}(\pmb{x})\leq M_{h,k,n;\nu}(\pmb{x}) \qquad(\pmb{x}\in I^d) $$
be satisfied.
