To describe nonlinear behavior of MR dampers as established semi-active devices employed to control vibrations, various models have been proposed which could be classified in hard and soft computing fields. However, only some could mimic hysteretic and highly dynamic characteristics of MR dampers appropriately directly and inversely which is a principle control attribute; more precisely, choosing a qualified invertible model plays a prominent role in a semi-active control, which has not come into sharp focus so far.  Thus in this article, first, some best-proposed hard computing (parametric) MR damper models are chosen and identified by genetic optimization under the same conditions. Second, two fuzzy-genetic and neuro-fuzzy models using soft computing techniques are constructed. Then a pseudo static model is proposed, which unlike to accurate dynamic models, have no differential equations and is invertible. Finally, all models subjected to filtered Iranian and foreign earthquakes would be compared. During all phases, experimental data is generated utilizing a benchmark program equipped with large-scale MR dampers, which is proposed by American Society of Civil Engineering (ASCE). Comparisons bring two results: the fuzzy-genetic model is more precise than hard computing ones; and the proposed model performs more effectively than dynamic ones, as it not only demonstrates desirable accuracy and much higher rate, but could easily be inverted.