Approximation of fuzzy neural networks based on Choquet integral

被引：5

作者：

Cao, Shan ^{[1
]}

Wang, Yuhuan ^{[1
]}

Li, Jun ^{[1
]}

机构：

[1] Commun Univ China, Sch Sci, Beijing 100024, Peoples R China

来源：

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2016年 / 31卷 / 02期

关键词：

Capacity; Choquet integral; regular fuzzy neural network; submodularity; MEASURE-SPACES; UNIVERSAL APPROXIMATION; EGOROFFS THEOREMS; LUSINS THEOREM; METRIC-SPACES; REGULARITY;

D O I：

10.3233/JIFS-169001

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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.

引用

页码：691 / 698

页数：8

共 41 条

[1]

[Anonymous], 1992, Fuzzy measure theory

[2]

[Anonymous], 1994, Metric Spaces of Fuzzy Sets: Theory and Applications

[3] Approximations of functions by a multilayer perceptron: a new approach [J].

Attali, JG ;

Pages, G .

NEURAL NETWORKS, 1997, 10 (06) :1069-1081

[4] CAN FUZZY NEURAL NETS APPROXIMATE CONTINUOUS FUZZY FUNCTIONS [J].

BUCKLEY, JJ ;

HAYASHI, Y .

FUZZY SETS AND SYSTEMS, 1994, 61 (01) :43-51

[5] FUZZY INPUT-OUTPUT CONTROLLERS ARE UNIVERSAL APPROXIMATORS [J].

BUCKLEY, JJ ;

HAYASHI, Y .

FUZZY SETS AND SYSTEMS, 1993, 58 (03) :273-278

[6] Universal approximation in p-mean by neural networks [J].

Burton, RM ;

Dehling, HG .

NEURAL NETWORKS, 1998, 11 (04) :661-667

[7] Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction [J].

Castillo, Oscar ;

Castro, Juan R. ;

Melin, Patricia ;

Rodriguez-Diaz, Antonio .

SOFT COMPUTING, 2014, 18 (06) :1213-1224

[8]

Castro J.R., 2008, J INF SCI, V179, P2175

[9] Hybrid learning algorithm for interval type-2 fuzzy neural networks [J].

Castro, Juan R. ;

Castillo, Oscar ;

Melin, Patricia ;

Rodriguez-Diaz, Antonio .

GRC: 2007 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, PROCEEDINGS, 2007, :157-162

[10]

Castro JR, 2008, LECT NOTES COMPUT SC, V4750, P104

← 1 2 3 4 5 →