  Tsallis' thermostatistics with the standard linear average energy is
revisited by employing $S_{2-q}$, which is the Tsallis entropy with $q$
replaced by $2-q$. We explore the connections among the $S_{2-q}$ approach and
the other different versions of Tsallis formalisms. It is shown that the
normalized $q$-average energy and the standard linear average energy are
related to each other. The relations among the Lagrange multipliers of the
different versions are revealed. The relevant Legendre transform structures
concerning the Lagrange multipliers associated with the normalization of
probability are studied. It is shown that the generalized Massieu potential
associated with $S_{2-q}$ and the linear average energy is related to one
associated with the normalized Tsallis entropy and the normalized $q$-average
energy.
