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Evolutionary algorithm-based learning of fuzzy neural networks. Part 2: Recurrent fuzzy neural networks

机译：基于进化算法的模糊神经网络学习。第2部分：递归模糊神经网络

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Fuzzy neural networks (FNN) as opposed to neuro-fuzzy systems, whose main task is to process numerical relationships, can process both numerical (measurement based) information and perception based information. In spite of great importance of fuzzy feed-forward and recurrent neural networks for solving wide range of real-world problems, today there are no effective training algorithm for them. Currently there are two approaches for training of FNN. First approach is based on application of the level-sets of fuzzy numbers and the back-propagation (BP) algorithm. The second approach involves using evolutionary algorithms to minimize error function and determine the fuzzy connection weights and biases. The method based on the second approach was proposed by the authors and published in Part 1 of this paper [R.A. Aliev, B. Fazlollahi, R. Vahidov, Genetic algorithm-based learning of fuzzy neural networks. Part 1: feed-forward fuzzy neural networks. Fuzzy Sets and Systems 118 (2001) 351-358]. In contrast to the BP and other supervised learning algorithms, evolutionary algorithms do not require nor use information about differentials, and hence, they are most effective in case where the derivative is very difficult to obtain or even unavailable. However, the main deficiency of the existing FNN based on the feed-forward architecture is its adherence to static problems. In case of dynamic or temporal problems there is a need for recurrent fuzzy neural networks (RFNN). Designing efficient training algorithms for RFNN has recently become an active research direction. In this paper we propose an effective differential evolution optimization (DEO) based learning algorithm for RFNN with fuzzy inputs, fuzzy weights and biases, and fuzzy outputs. The effectiveness of the proposed method is illustrated through simulation of benchmark forecasting and identification problems and comparisons with the existing methods. The suggested approach has also been used for real applications in an oil refinery plant for petrol production forecasting.
机译：与神经模糊系统相反，模糊神经网络（FNN）的主要任务是处理数字关系，它可以处理数字（基于测量）信息和基于感知的信息。尽管模糊前馈神经网络和递归神经网络对于解决各种各样的现实问题非常重要，但如今还没有有效的训练算法。当前有两种训练FNN的方法。第一种方法是基于模糊数水平集的应用和反向传播（BP）算法。第二种方法涉及使用进化算法来最小化误差函数并确定模糊连接权重和偏差。作者提出了基于第二种方法的方法，并在本论文的第1部分中发表。 Aliev，B.Fazlollahi，R.Vahidov，基于遗传算法的模糊神经网络学习。第1部分：前馈模糊神经网络。模糊集和系统118（2001）351-358]。与BP和其他监督学习算法相反，进化算法不需要也不使用有关微分的信息，因此，在导数很难获得甚至不可用的情况下，它们是最有效的。然而，基于前馈架构的现有FNN的主要缺陷在于其对静态问题的坚持。在动态或时间问题的情况下，需要递归模糊神经网络（RFNN）。为RFNN设计有效的训练算法最近已成为活跃的研究方向。在本文中，我们为RFNN提出了一种有效的基于差分进化优化（DEO）的学习算法，该算法具有模糊输入，模糊权重和偏差以及模糊输出。通过模拟基准预测和识别问题并与现有方法进行比较，说明了该方法的有效性。建议的方法也已在炼油厂的实际应用中用于预测汽油产量。

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