A theoretical/computational methodology for the analysis of the FGM is introduced, and its application is made to the problem of a dynamically propagating crack running transversely in the FGM, where the intensity of the estimated crack-tip severity is managed to keep in valance with the graded material toughness in the FGM during the propagation. To detect the crack-tip severity, an integral fracture parameter, T*, is used. The crack is propagated so that the value of T* is equated to the prescribed varying critical values of T*. Emphasis is placed on the use of a fuzzy inference algorithm to control the crack speed deduced from a few T* values immediately preceding the current crack position. As to describing the constitutive law for the FGM, spherical particles of arbitrary size in mesoscale are supposed to be randomly dispersed in the matrix medium. By assuming that the volume fraction of the inclusion is continuously varied, the grading is modeled. For modeling the constitutive law for the FGM composite media of thermo-elastoplasticity, a closed form SCC-LRM constitutive model describing the nonlinear material mechanics of the particle-dispersed medium is used. The model is based on the self-consistent scheme and uses Eshelby's equivalent inclusion method. Unprecedented analytical results of crack speed of a crack running transversely in the FGM plate are shown. In some cases of material grading, apparent crack arresting is observed as the crack runs into the metal rich area of the FGM.