Abstract
This study discusses how to fuzzify a feedforward neural network (FNN) to generate a fuzzy forecast that contains the actual value, while minimizing the average range of fuzzy forecasts. This topic has rarely been investigated in past studies, but is an essential step to constructing a precise fuzzy FNN (FFNN). Existing methods fuzzify all parameters at the same time, which re-sults in a nonlinear programming (NLP) problem that is not easy to solve. In contrast, in this study, the parameters of a FNN are fuzzified independently. In this way, the optimal values of fuzzy parameters can be derived theoretically. An illustrative example is used to illustrate the ap-plicability of the proposed methodology. According to the experimental results, fuzzifying the thresholds on hidden-layer nodes or the connection weights between input and hidden layers may not guarantee that all fuzzy forecasts contain the corresponding actual values. In contrast, fuzzi-fying the threshold on the output node and the connection weights between the hidden and out-put layers is more likely to achieve a 100% hit rate. The results lay a foundation for establishing a precise deep FFNN in the future.