scholarly journals Training High-Order Takagi-Sugeno Fuzzy Systems Using Batch Least Squares and Particle Swarm Optimization

2019 ◽  
Vol 22 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Krzysztof Wiktorowicz ◽  
Tomasz Krzeszowski
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Piecewise Linear ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Takagi Sugeno

AbstractThis paper proposes two methods for training Takagi–Sugeno (T-S) fuzzy systems using batch least squares (BLS) and particle swarm optimization (PSO). The T-S system is considered with triangular and Gaussian membership functions in the antecedents and higher-order polynomials in the consequents of fuzzy rules. In the first method, the BLS determines the polynomials in a system in which the fuzzy sets are known. In the second method, the PSO algorithm determines the fuzzy sets, whereas the BLS determines the polynomials. In this paper, the ridge regression is used to stabilize the solution when the problem is close to the singularity. Thanks to this, the proposed methods can be applied when the number of observations is less than the number of predictors. Moreover, the leave-one-out cross-validation is used to avoid overfitting and this way to choose the structure of a fuzzy model. A method of obtaining piecewise linear regression by means of the zero-order T-S system is also presented.

A PSO-Based Fuzzy c-Regression Model Applied to Nonlinear Data Modeling

2015 ◽  
Vol 23 (06) ◽  
pp. 881-891 ◽  
Author(s):  
Moez Soltani ◽  
Abdelkader Chaari
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Regression Models ◽  
Clustering Algorithm ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Identification Procedure ◽  
Swarm Optimization

This paper presents a new method for fuzzy c-regression models clustering algorithm. The main motivation for this work is to develop an identification procedure for nonlinear systems using weighted recursive least squares and particle swarm optimization. The fuzzy c-regression models algorithm is sensitive to initialization which leads to the convergence to a local minimum of the objective function. In order to overcome this problem, particle swarm optimization is employed to achieve global optimization of FCRM and to finally tune parameters of obtained fuzzy model. The weighted recursive least squares is used to identify the unknown parameters of the local linear model. Finally, validation results involving simulation of two examples have demonstrated the effectiveness and practicality of the proposed algorithm.

scholarly journals Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

2018 ◽  
Vol 8 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Sheriff Sadiqbatcha ◽  
Saeed Jafarzadeh ◽  
Yiannis Ampatzidis
Keyword(s):  
Particle Swarm Optimization ◽  
Fuzzy Sets ◽  
Nonlinear Equations ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Fuzzy Variables ◽  
Modified Particle Swarm Optimization ◽  
Fuzzy Polynomials ◽  
Exponential Equations

Abstract This paper proposes a modified particle swarm optimization (PSO) algorithm that can be used to solve a variety of fuzzy nonlinear equations, i.e. fuzzy polynomials and exponential equations. Fuzzy nonlinear equations are reduced to a number of interval nonlinear equations using alpha cuts. These equations are then sequentially solved using the proposed methodology. Finally, the membership functions of the fuzzy solutions are constructed using the interval results at each alpha cut. Unlike existing methods, the proposed algorithm does not impose any restriction on the fuzzy variables in the problem. It is designed to work for equations containing both positive and negative fuzzy sets and even for the cases when the support of the fuzzy sets extends across 0, which is a particularly problematic case.

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