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 $q_nto1$. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence.
