Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS2,MoSe2,MoTe2,WS2{\mathrm{MoS}}_{2}, {\mathrm{MoSe}}_{2}, {\mathrm{MoTe}}_{2}, {\mathrm{WS}}_{2}, and WSe2{\mathrm{WSe}}_{2} are studied by means of density functional theory and path-integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modify