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.
Highlights
Fuzzy feedforward neural networks (FFNNs) combines the advantages of fuzzy logic and feedforward neural networks (FNNs) [1], and have been widely applied to forecasting in many fields [2,3,4,5].There are various types of fuzzy FNN (FFNN) with fuzzy or crisp inputs, parameters, and outputs.The numbers of layers and activation functions in these FFNNs are different [6]
Past studies have shown that FFNNs can improve the forecasting accuracy, that is, each forecast is close to the actual value [14,15,16]
This study considers an FFNN with a single hidden layer in which all network parameters can be fuzzified and nonlinear transformation functions are adopted
Summary
Fuzzy feedforward neural networks (FFNNs) combines the advantages of fuzzy logic (in uncertainty modelling) and feedforward neural networks (FNNs) (in nonlinear approximation) [1], and have been widely applied to forecasting in many fields [2,3,4,5]. The present study aims to construct an FFNN to improve the forecasting precision, that is, every actual value is included in the narrowest possible fuzzy forecast. This topic has rarely been discussed in the past, which constitutes the motivation of this research. Chen and Wang [20] showed that the problem of deriving the values of fuzzy parameters in an FFNN was a nonlinear programming (NLP). We aim to optimize the values of fuzzy parameters theoretically without solving an NLP problem, while guaranteeing that all actual values are contained in the corresponding fuzzy forecasts.
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