In this paper, the uniqueness of a solution to the fuzzy system of equations is proved by employing the fuzzy B-contraction Principle in fuzzy metric space. The fuzzy system of equations is transformed into an operator form and then applied to the contraction principle, which leads to a B-contraction in fuzzy Banach space. We also revisited the notion of fuzzy systems in norm space and Banach spaces, the fixed point and contraction along with the B-contrition principle. The main contribution of this study is to the analytical proof of the uniqueness of the fuzzy system of equations using the contraction principle in the fuzzy Banach space.
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