Quaternion neuro-fuzzy learning algorithm for generation of fuzzy rules
Quaternion neuro-fuzzy learning algorithm for generation of fuzzy rules
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DOI：
10.1016/j.neucom.2016.08.022
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发表时间：
2016-12
期刊：
影响因子：
6
通讯作者：
Ryusuke Hata;M. Islam;K. Murase
中科院分区：
文献类型：
--
作者：
Ryusuke Hata;M. Islam;K. Murase
传统的基于梯度下降法的高斯隶属度神经模糊学习算法可以产生或调整模糊规则。然而，增加输入的数量会大大增加参数的数量。因此，表示模糊规则表是困难的，学习时间增加，学习精度降低。为了克服这些问题，我们已经开发了一个复值神经模糊学习算法，扩展的神经模糊学习算法的复数。在该方法中，输入、前因隶属函数和后因单态是复数，但输出是真实的。为了将复数转化为真实的数，我们提出了两种类型的激活函数。复值方法减少了参数数目，并表现出更好的学习精度。在本文中，我们将该方法推广到四元数域。在四元数神经模糊学习算法中，输入、前件隶属度函数和后件单元数都是四元数，输出是真实的。对于参数调整，我们推导出四元数神经网络的四元数反向传播，输出真实的值的四元数值的输入。四元数反向传播比传统的反向传播具有更好的学习收敛性和准确性，并且调整过程更复杂，尽管它受益于四元数反向传播。该方法将四维真实的数分配给四元数的一个真实的部分和三个虚部，该四元数用作单个四元数输入。这个过程大大减少了调谐参数的数量，从而比传统方法更好地学习。我们比较了建议和传统的方法，使用几个功能识别问题，并表明所提出的方法优于其对应的，使其成为一个有用的工具，在模糊系统模型的学习。在最好的情况下，历元数减少到传统方法的四十分之一，误差减少到三十分之一。
The conventional neuro-fuzzy learning algorithm with Gaussian membership functions based on the gradient descent method can generate or tune fuzzy rules. However, increasing the number of inputs greatly increases the number of parameters. Thus, representing fuzzy rule tables is difficult, learning time increases, and learning accuracy decreases. To overcome these problems, we have developed a complex-valued neuro-fuzzy learning algorithm that extends the neuro-fuzzy learning algorithm to complex numbers. In the method, the inputs, antecedent membership functions, and consequent singletons are complex numbers, but the outputs are real. For converting complex to real numbers, we proposed two types of activation function. The complex-valued method reduced the parameter numbers and showed better learning accuracy. In this paper, we extend the method to the quaternion domain. In the quaternion neuro-fuzzy learning algorithm, the inputs, antecedent membership functions, and consequent singletons are quaternion, and the outputs are real. For parameter tuning, we derived the quaternion back propagation of quaternion neural networks that outputs real values for quaternion-valued inputs. The quaternion back propagation shows better learning convergence and accuracy than the conventional back propagation, and the tuning process is more complex, although it benefits from the quaternion back propagation. The method assigns a four-dimensional real number to one real and three imaginary parts of a quaternion number, which is used as a single quaternion input. This process greatly reduces the number of tuned parameters, leading to better learning than the conventional method. We compare the proposed and conventional methods using several function identification problems, and show that the proposed method outperforms its counterpart, making it a useful tool for learning in a fuzzy system model. In the best cases, the number of epochs was reduced to one-fortieth and the error to one-thirtieth of those in the conventional method.