Existence of solutions for implicit fuzzy differential inclusions

A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions (FDIs) and fuzzy differential equations (FDEs), which might be helpful in the analysis of fuzzy dynamic systems.