Nonlinear Function Approximation Based on Least Wilcoxon Takagi-Sugeno Fuzzy Model

Sun, Tsung-Ying; Tsai, Shang-Jeng; Tsai, Cheng-Han; Huo, Chih-Li; Liu, Chan-Cheng

doi:10.1109/isda.2008.261

Cited by 7 publications

(12 citation statements)

References 5 publications

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“…This experiment is conducted to show the advantage of our proposed combinatorial method over a fuzzing system [20], a regression approximation method, NWKR, and two known neural network methods, ANNBP and DNN model [18], for small samples problem with a few number of training points. In Table 5, the results of our experiments with a function y = x 2 in the domain [−32768, 32767], is presented.…”

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

“…The proposed combinatorial method has resolved the overfitting and under-fitting phenomena by smoothing down the fluctuations caused by the differences in the degree of the real function and its approximations. Proposes method in [20] LS-Based method Combinatorial-curve-fitting RMSE 0.0087 0.0843 0.0062 Figure 3: approximated results for ((x − 2)(2x − 1))/(1 + x 2 ),"O" in this figure shows approximated value for testing points and "." shows the actual value of testing points and "×" shows 50 random training points.…”

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

“…In Table 6, root minimum square error (RMSE) for approximations of a nonlinear function ((x − 2)(2x − 1))/(1 + x 2 ), using fuzzy method presented in [20], LS-Based, and our combinational method. As shown in Figure 2, the fuzzy method outperforms the LS-Based function approximation method.…”

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

“…In Figure 3, white bullet points represent all the approximated points, provided by our combinatorial method. The function ((x − 2)(2x − 1))/(1 + x 2 ) is also used in [20] to show the advantage of the fuzzy function approximation method in comparison with the LS-Based method. The number of samples used in [20] are 50 points within the interval (−8, 12) and the RMSE is 0.0087.…”

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

“…For instance, in order to reduce approximation error, it is observed that some function approximation methods, using neural networks [10], have modified their learning engine and its weight of neurons by changing or modifying their sigmoidal function [7] or feed-forward network and back-propagation learning algorithm [10]. To promote the accuracy of neural network fuzzing methods have been applied to the approximations provided by neural networks [20]. Also in certain situations, the approximation provided by a fuzzy system is used as input to neural networks [8].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A combination of curve fitting algorithms to collect a few training samples for function approximation

Parsa¹,

Alaeiyan²

2017

J. Math. Computer Sci.

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The aim of this paper is to approximate the numerical result of executing a program/function with a number of input parameters and a single output value with a small number of training points. Curve fitting methods are preferred to nondeterministic methods such as neural network and fuzzing system methods, because they can provide relatively more accurate results with the less amount of member in the training dataset. However, curve fitting methods themselves are most often function specific and do not provide a general solution to the problem. These methods are most often targeted at fitting specific functions to their training dataset. To provide a general curve fitting method, in this paper, the use of a combination of Lagrange, Spline, and trigonometric interpolation methods are suggested. The Lagrange method fits polynomial functions of degree N to its training values. In order to improve the resultant fitted polynomial our combinatorial method combines Lagrange with the polynomial resulted from the Spline method. If the absolute error of the actual value and the predicted value of a function are not desired, the trigonometric interpolation methods that fit trigonometric functions can be applied. Our experiments with a number of benchmark examples demonstrate the relatively high accuracy of our combinational fitting method.

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Section: Numerical Experiments and Resultsmentioning

confidence: 99%

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A combination of curve fitting algorithms to collect a few training samples for function approximation

Parsa¹,

Alaeiyan²

2017

J. Math. Computer Sci.

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Sparse regressions and particle swarm optimization in training high-order Takagi–Sugeno fuzzy systems

Wiktorowicz

Krzeszowski

Przednówek

2020

Neural Comput & Applic

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This paper proposes a method for training Takagi–Sugeno fuzzy systems using sparse regressions and particle swarm optimization. The fuzzy system is considered with Gaussian fuzzy sets in the antecedents and high-order polynomials in the consequents of the inference rules. The proposed method can be applied in two variants: without or with particle swarm optimization. In the first variant, ordinary least squares, ridge regression, or sparse regressions (forward selection, least angle regression, least absolute shrinkage and selection operator, and elastic net regression) determine the polynomials in the fuzzy system in which the fuzzy sets are known. In the second variant, we have a hybrid method in which particle swarm optimization determines the fuzzy sets, while ordinary least squares, ridge regression, or sparse regressions determine the polynomials. The first variant is simpler to implement but less accurate, the second variant is more complex, but gives better results. A new quality criterion is proposed in which the goal is to make the validation error and the model density as small as possible. Experiments showed that: (a) the use of sparse regression and/or particle swarm optimization can reduce the validation error and (b) the use of sparse regression may simplify the model by zeroing some of the coefficients.

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RFIS: regression-based fuzzy inference system

Wiktorowicz

2022

Neural Comput & Applic

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Nonlinear Function Approximation Based on Least Wilcoxon Takagi-Sugeno Fuzzy Model

Cited by 7 publications

References 5 publications

A combination of curve fitting algorithms to collect a few training samples for function approximation

A combination of curve fitting algorithms to collect a few training samples for function approximation

Sparse regressions and particle swarm optimization in training high-order Takagi–Sugeno fuzzy systems

RFIS: regression-based fuzzy inference system

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