Implementing Batch Least Squares for Training Takagi-Sugeno Fuzzy Systems
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Resource Overview
Batch least squares method for training Takagi-Sugeno fuzzy systems with linear parameter optimization and error minimization
Detailed Documentation
The batch least squares method for training Takagi-Sugeno fuzzy systems involves organizing input-output data into paired datasets and performing linear regression to fit the fuzzy system's parameters. During training, the system optimizes performance by minimizing fitting errors through matrix operations typically implemented using pseudoinverse calculations (e.g., MATLAB's pinv() function or Python's numpy.linalg.lstsq()). This approach constructs a design matrix where each row corresponds to a data point with weighted membership functions, while the output vector contains target values. The core algorithm solves the linear equation: parameters = (X^T * X)^(-1) * X^T * Y, where X is the regression matrix and Y is the output vector. This method is particularly effective for developing fuzzy controllers, fuzzy inference systems, and optimizing various fuzzy models through offline batch processing of complete datasets.
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