Comments on “Generalization of Shannon–Khinchin Axioms to Nonextensive Systems and the Uniqueness Theorem for the Nonextensive Entropy”

In this comment, we consider a generalization of the Shannon–Khinchin axioms (GSK axioms) and the uniqueness theorem for the entropy determined by GSK axioms proposed in [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783–1787, Aug. 2004]. It is shown that the class of entropy functions determined by the axioms from the mentioned paper is wider than the one proposed in this paper, and a counterexample is given. We also derive a new class of entropies by fixing the incorrectness which occurs in the mentioned paper.