The core of artificial intelligence (AI) research is intelligent information processing, and fuzzy reasoning and fuzzy neural networks are significant research areas in models of intelligent information processing. The study examines the robustness of fuzzy reasoning by using the property characteristics of triangular modal operators and implication operators, which are used to analyse the Lipschitz property of fuzzy operators and its corresponding property characteristics of triangular modal operators and implication operators. Inference operators are used to investigate the robustness and error-control capabilities of fuzzy operators for fuzzy reasoning. The results showed that the robustness of quasi-copula fuzzy reasoning with fusion rules is better, and the corresponding maximum output perturbation is lowest at 0.36 when the fuzzy operator is T[Formula: see text]&R[Formula: see text] and the corresponding maximum output error is lowest at 0.41 when the fuzzy operators are T[Formula: see text]&R[Formula: see text] and T[Formula: see text]&R[Formula: see text]. This shows the optimal performance of the fuzzy associative memory model with fuzzy rule for quasi-copula fuzzy operators and can improve the theoretical technology. The best-performance fuzzy copula operator of the fuzzy associative memory model can enhance the theoretical foundation and technical support for the processing of intelligent information.