Generalized Shannon-Khinchin axioms and uniqueness theorem for pseudo-additive entropies

We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as the Sharma-Mittal and Frank-Daffertshofer entropies. We provide the generalization of the Shannon-Khinchin axioms and give the corresponding uniqueness theorem. The previous attempts at such axiomatizations are also discussed.