This paper investigates linear time varying fuzzy controlled systems with fuzzy boundary conditions, and fuzzy optimal control systems where the boundary conditions are described by fuzzy numbers. We use the α-cut sets of fuzzy system and Heaviside functions as well to find the solution of so-called fuzzy systems, while we profit the generalized Hukuhara differentiability concept.Three theorems are proved for the richness of the theory. Finally three numerical examples are given to verify the reliability and efficiency of the proposed approach.

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