Forward-Backward System for Fuzzy Doubly Stochastic Differential Equations

Our main goal in this work is to study a general class of forward-backward fuzzy double stochastic differential equations systems ( in short FBFDSDEs ) in a precise manner, not relaying the equations on the solution process only, but rather on their law. By verifying the existence and uniqueness of the solution to the forward equation of the general system FBFDSDEs as well as the backward equation under Lipschitz conditions, we prove the existence of the maximum solution of the general system FBFDSDEs under monotonic continuity conditions.