  We propose a two-parametric non-distributive algebraic structure that follows
from $(q,q')$-logarithm and $(q,q')$-exponential functions. Properties of
generalized $(q,q')$-operators are analyzed. We also generalize the proposal
into a multi-parametric structure (generalization of logarithm and exponential
functions and the corresponding algebraic operators). All $n$-parameter
expressions recover $(n-1)$-generalization when the corresponding $q_n\to1$.
Nonextensive statistical mechanics has been the source of successive
generalizations of entropic forms and mathematical structures, in which this
work is a consequence.
