  The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari,
IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the
generalized Shannon-Khinchin's axiom. In the present paper, this result is
generalized and simplified as follows: {\it Generalization}: The uniqueness
theorem for Tsallis relative entropy is shown by means of the generalized
Hobson's axiom. {\it Simplification}: The uniqueness theorem for Tsallis
entropy is shown by means of the generalized Faddeev's axiom.
