  Basic idea presented in Parts (I)-(III) for the deformed boson scheme is
applied to the case of the su(2)- and su(1,1)-algebras for describing many-body
systems consisting of four kinds of boson operators. A possible form of the
coherent state given by the present authors is generalized and the su(2)_q- and
the su(1,1)_q-algebras are obtained in the form expressed in terms of four
kinds of boson operators. As an illustrative example of the application, the
framework for describing thermal effects observed in two-level shell model
under the pairing correlation is proposed.
