三角型2模糊神经网络版的Stone-Weierstrass定理

2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD) Pub Date : 2013-07-23 DOI:10.1109/FSKD.2013.6816185

Saeed Panahian Fard, Z. Zainuddin

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引用次数: 0

摘要

2型模糊神经网络的通用逼近能力在2型模糊神经网络的逼近理论中占有重要地位。在本研究中，我们利用之前工作中引入的区间2型三角模糊数，提出了一个三角2型模糊数。此外，我们还引入了一些三角2型模糊运算。然后，我们利用这些概念构造了三层前馈三角形2型模糊神经网络。此外，我们还建立了一个主要定理，证明了这些网络具有普遍的逼近能力。主要定理可以看作是Stone-Weierstrass定理的三角型2模糊神经网络版本。

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Triangular type-2 fuzzy neural networks version of the Stone-Weierstrass theorem

The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main theorem that shows the universal approximation capability of these networks. The main theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass theorem.

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2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

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