  By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo
average (KN-averages) or quasilinear mean and further imposing the additivity
constraint, R\'{e}nyi proposed the first formal generalization of Shannon
entropy. Using this recipe of R\'{e}nyi, one can prepare only two information
measures: Shannon and R\'{e}nyi entropy. Indeed, using this formalism R\'{e}nyi
characterized these additive entropies in terms of axioms of quasilinear mean.
As additivity is a characteristic property of Shannon entropy,
pseudo-additivity of the form $x \oplus_{q} y = x + y + (1-q)x y$ is a
characteristic property of nonextensive (or Tsallis) entropy. One can apply
R\'{e}nyi's recipe in the nonextensive case by replacing the linear averaging
in Tsallis entropy with KN-averages and thereby imposing the constraint of
pseudo-additivity. In this paper we show that nonextensive entropy is unique
under the R\'{e}nyi's recipe, and there by give a characterization.
