Solving the problem of anomalous J/ ψ\psi suppression by the MPD experiment on the NICA collider

The meassurements of charmonium states production via their decay on lepton pairs by the MPD experiment on the NICA collider at the energies $\sqrt{s_{NN}}$ = 4-11 GeV per nucleon could provide important data for solving the problem of anomalous J/$\psi$ suppression first observed in central Pb-Pb collisions by the NA50 Collaboration at 158 GeV/nucleon. The anomalous J/$\psi$ suppression could be due to the formation of the QGP in the central heavy-ion collisions. However, this effect could be also interpreted as the result of the comover interactions in nuclear matter. The recent experiments at the SPS, at the RHIC, and the LHC reviewed in this article indicate a more complicated picture of the J/$\psi$ production including the recombination, medium effects, parton shadowing, and the coherent energy loss mechanism. A more simple production mechanism could be expected at low colliding energies. However, no data were obtained at energies below $\sqrt{s_{NN}}=17$ GeV for heavy-ion collisions. After the short review of the whole set of the data of charmonium states observation the estimation of the production rate for the MPD/NICA is made