Fuzzy Neural Networks (FNNs) are synergistic structures that aim to benefit from the properties of fuzzy logic in neural network structures. Yet, the traditional FNNs do not explicitly address the reliability aspect of uncertain real world applications. Here we propose a Reliable Fuzzy Neural Networks (ReFNNs) in which an information reliability measure is employed for rule training and robust decision making of the uncertain input data. The universal approximation property of the proposed structure is proved using the Stone-Weierstrass theorem. Furthermore, the resulting structure is continuous and differentiable. Hence, a backpropagation training algorithm is developed to optimize the proposed ReFNN’s parameters. Additionally, asymptotic stability analysis based on the Lyapunov theorem is shown for ReFNNs. Finally, this structure is first evaluated with several basic benchmark examples in function approximation (sine, increasing sinusoid, quadratic Hermite, and nonlinear functions). We then apply it to modeling several benchmark nonlinear systems (including a 3rd order nonlinear dynamical system, a continuous stirred tank reactor, a two cascaded tank problem, a Wiener-Hammerstein system, and wind speed prediction) and the adaptive control of nonlinear systems in both direct and indirect frameworks. Results confirm the superiority of the proposed structure over traditional FNNs in terms of error and sensitivity in the presence of noise.

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