scholarly journals Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Oscar Castillo ◽  
Juan R. Castro ◽  
Patricia Melin ◽  
Antonio Rodriguez-Diaz
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Nonlinear Function ◽  
Fuzzy Neural Networks ◽  
Universal Approximation ◽  
Fuzzy Logic Systems ◽  
Fuzzy Neural ◽  
Logic Systems ◽  
Interval Type

Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.

Design of back propagation optimized Nagar-Bardini structure-based interval type-2 fuzzy logic systems for fuzzy identification

2021 ◽  
pp. 014233122110066
Author(s):  
Yang Chen ◽  
Jiaxiu Yang
Keyword(s):  
Fuzzy Logic ◽  
Back Propagation ◽  
Membership Functions ◽  
Identification Problems ◽  
Fuzzy Logic Systems ◽  
Fuzzy Identification ◽  
Logic Systems ◽  
Academic Topic ◽  
Interval Type

In recent years, fuzzy identification based on system identification theory has become a hot academic topic. Interval type-2 fuzzy logic systems (IT2 FLSs) have become a rising technology. This paper designs a type of Nagar-Bardini (NB) structure-based singleton IT2 FLSs for fuzzy identification problems. The antecedents of primary membership functions of IT2 FLSs are chosen as Gaussian type-2 primary membership functions with uncertain standard deviations. Then, the back propagation algorithms are used to tune the parameters of IT2 FLSs according to the chain rule of derivation. Compared with the type-1 fuzzy logic systems, simulation studies show that the proposed IT2 FLSs can obtain better abilities of generalization for fuzzy identification problems.

Sliding mode incremental learning algorithm for interval type-2 Takagi–Sugeno–Kang fuzzy neural networks

2012 ◽  
Vol 3 (3) ◽  
pp. 179-188 ◽  
Author(s):  
Sevil Ahmed ◽  
Nikola Shakev ◽  
Andon Topalov ◽  
Kostadin Shiev ◽  
Okyay Kaynak
Keyword(s):  
Neural Networks ◽  
Incremental Learning ◽  
Sliding Mode ◽  
Learning Algorithm ◽  
Fuzzy Neural Networks ◽  
Fuzzy Neural ◽  
Interval Type ◽  
Takagi Sugeno

Application of Interval Type-2 Fuzzy Logic Systems for Control of the Coiling Entry Temperature in a Hot Strip Mill

2009 ◽  
pp. 352-359 ◽  
Author(s):  
Gerardo M. Méndez ◽  
Luis Leduc-Lezama ◽  
Rafael Colas ◽  
Gabriel Murillo-Pérez ◽  
Jorge Ramírez-Cuellar ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Hot Strip Mill ◽  
Fuzzy Logic Systems ◽  
Hot Strip ◽  
Logic Systems ◽  
Interval Type

System Identification Based on Dynamical Training for Recurrent Interval Type-2 Fuzzy Neural Network

2013 ◽  
pp. 188-205
Author(s):  
Tsung-Chih Lin ◽  
Yi-Ming Chang ◽  
Tun-Yuan Lee
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
System Identification ◽  
Nonlinear System ◽  
Fuzzy Neural Networks ◽  
Training Data ◽  
Fuzzy Neural ◽  
Interval Type ◽  
Recurrent Interval

This paper proposes a novel fuzzy modeling approach for identification of dynamic systems. A fuzzy model, recurrent interval type-2 fuzzy neural network (RIT2FNN), is constructed by using a recurrent neural network which recurrent weights, mean and standard deviation of the membership functions are updated. The complete back propagation (BP) algorithm tuning equations used to tune the antecedent and consequent parameters for the interval type-2 fuzzy neural networks (IT2FNNs) are developed to handle the training data corrupted by noise or rule uncertainties for nonlinear system identification involving external disturbances. Only by using the current inputs and most recent outputs of the input layers, the system can be completely identified based on RIT2FNNs. In order to show that the interval IT2FNNs can handle the measurement uncertainties, training data are corrupted by white Gaussian noise with signal-to-noise ratio (SNR) 20 dB. Simulation results are obtained for the identification of nonlinear system, which yield more improved performance than those using recurrent type-1 fuzzy neural networks (RT1FNNs).

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