Nonlinear PLS modeling with fuzzy inference system

We propose a new nonlinear partial least squares (NLPLS) algorithm that embeds the Takagi–Sugeno–Kang (TSK) fuzzy model into the regression framework of the partial least squares (PLS) method. We call the new algorithm fuzzy partial least squares (FPLS). Several NLPLS algorithms have been proposed. However, they can lead to overfitting and contain ambiguities in the meaning of regression parameters. The proposed FPLS algorithm applies the TSK fuzzy model to the PLS inner regression. Using this approach, the interpretability of the TSK fuzzy model overcomes some of the handicaps of previous NLPLS algorithms. The proposed method uses the PLS method to solve the problems of high dimensionality and collinearity and the TSK fuzzy model is used to capture the nonlinearity and to increase the use of expertsʹ knowledge. As a result, the FPLS model gives a more favorable modeling environment in which the knowledge of experts can be easily applied. In addition, we propose a new input and output weight update algorithm to enhance the regression performance of FPLS. The power of the proposed method is illustrated by application to a simple mathematical simulation data set and a real near infrared spectral data set.