模糊分数型多s型函数激活神经网络逼近

IF 1.3 Q3 COMPUTER SCIENCE, THEORY & METHODS Mathematical foundations of computing Pub Date : 2023-01-01 DOI:10.3934/mfc.2022031
G. Anastassiou
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引用次数: 1

摘要

本文研究了基于模糊神经网络算子的拟插值arc切-代数-古德曼-广义对称激活函数在紧区间上模糊实值函数的单变量模糊分数定量逼近。这些近似是通过建立涉及所涉函数的左右Caputo模糊分数阶导数的连续性模糊模的模糊Jackson型不等式得到的。该近似是模糊点化和模糊均匀化的。相关的前馈模糊神经网络只有一个隐藏层。我们还研究了模糊整数导数和仅仅模糊连续的情况。采用高阶模糊微分的模糊分数逼近结果比模糊刚连续情况下收敛性更好。
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Fuzzy fractional more sigmoid function activated neural network approximations revisited
Here we study the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study also the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.
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