Approximation of fuzzy neural networks based on Choquet integral

Issue title: ICNC-FSKD 2015

Guest editors: Zheng Xiao and Kenli Li

Article type: Research Article

Authors: Cao, Shan | Wang, Yuhuan | Li, Jun^*

Affiliations: School of Sciences, Communication University of China, Beijing, China

Correspondence: [*] Corresponding author. Jun Li, School of Sciences, Communication University of China, Beijing 100024, China. Tel./Fax: +86 10 65783583; E-mail: lijun@cuc.edu.cn.

Abstract: In this paper, we shall introduce a metric on the space of fuzzy-valued measurable functions by means of a kind of nonlinear integral — Choquet integral with respect to a capacity. We called it as Choquet integral norm. By using the metric between fuzzy-valued measurable functions, we discuss the mean approximation of regular fuzzy neural networks in the sense of Choquet integral. It is shown that any fuzzy-valued measurable function on ℝ can be approximated in mean by four-layer regular fuzzy neural networks in the sense of Choquet integral norm.

Keywords: Capacity, Choquet integral, regular fuzzy neural network, submodularity

DOI: 10.3233/JIFS-169001

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 2, pp. 691-698, 2016