In practical engineering, fuzzy failure criteria can reflect the actual conditions of the normal use and durability of structures. Therefore, this topic has garnered considerable research attention. First, a fuzzy set and a membership function were proposed in this study. A fuzzy reliability mathematical model of structures was obtained by means of the fuzzy random event probability. Second, the distribution forms of common membership functions were introduced, and the optimal membership function was selected based on the Akaike information criterion. Third, considering the difficulty of calculating multiple integrals in the fuzzy reliability mathematical model, a direct integration method based on dual neural networks was introduced. This method provides a new approach for calculating structural reliability with the fuzzy failure criteria. Finally, the proposed method was verified by numerical examples. The results showed that this method could solve structural fuzzy reliability problems with multidimensional random variables with high computational efficiency and accuracy.
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