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

Abstract

This 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 leaveone-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 review on type-2 fuzzy neural networks for system identification

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Design and optimization of TS firefly algorithm based on the nonhomogeneous linear polygonal T‐S fuzzy system

“…Actually, most MHAs belong to the combination of Random Search and Hill Clipping. For some recent works, see References [30–36].…”

Fuzzy Decision-Making Soft Model for Family Financial Planning in The Post COVID-19 World

“…A wealth management bank begins with the people' financial advisor to understand the people' preferred lifestyle and then helps the investor deal with threats, such as taxes, volatility, inflation, creditors, and lawsuits, to maintain this lifestyle. With the development of personal financial services in domestic banks, the personal finance business has become a key area of domestic commercial banking products and services innovation (Arunraj and Maiti 2010;Chang et al 2011;Chen et al 2012;Wiktorowicz and Krzeszowski 2020;.…”