Formulae of proton and neutron boson structure functions (BSFs) are deduced in terms of a microscopic approach of sdgIBM (namely, microscopic sdgIBM). For the nucleus 190Os, the value of BSFs is worked out. Due to the high similarity, the maximum F-spin truncation is made under the full-symmetry approximation. Thereafter,calculations of E2 and E4 transition charge densities (TCDs) are performed in the sdgIBM-1. It is found that the E2 and E4 TCDs can be reproduced quite satisfactorily in the uniform frame of microscopic sdgIBM-1.