To study various relaxation phenomena of $Pb(Mg_{1/3}Nb_{2/3})O_3$ relaxor ferroelectrics, weak electric-field properties as well as strong electric-field properties were investigated in the frequency range from 1 Hz to 100 kHz. The temperature dependence of the dielectric properties were measured under the low electric-field of 1 V/mm in the phase transition temperature range from $-40^{circ}C$ to $90^{circ}C$. The dielectric properties obtained from the slope of the dielectric hysteresis loop and the temperature dependence of the pyroelectric properties were also investigated. When fitting all the experimental data with the Vogel-Fulcher relation, experimental data were agreed with the equation closely. Thus, dielectric relaxations could be modeled by the Vogel-Fulcher relation not only for the low electric-field but also for the high electric-field.