Abstract
Fuzzy rule-based models are widely employed to tackle regression problems due to their simplicity and comprehensibility. Numeric functions (e.g., linear ones) are generally utilized to represent the conclusion part of a rule, but this simple module cannot well describe the behavior of data located within local area defined by the premise part. In this study, a novel reinforced fuzzy clustering-based rule model (RFCRM) is presented to address this issue. First, information granulation (Fuzzy C-Means) approach is used to reveal the structure in the data and divide the input space into local regions, as well as form the premise parts. Second, the augmented Random Vector Functional Link Networks (RVFLNs) are employed as the conclusion parts to strengthen the description and representation of the behavior of data positioned within the local regions. Weighted Least Squares Error estimation with regularization is exploited to estimate the coefficients of the connection weights of RVFLN. Also, an exponential weight method benefited from the weight function theory encountered in harmonic analysis is introduced to improve the penalty strategy of regularization in coefficient estimation. More specifically, an exponential weighted ℓ2 regularization (EWℓ2) strategy equipped with the exponential functions as the penalty terms is proposed to realize the targeted penalty on coefficients. The merit of EWℓ2 over ordinary ℓ2 is that different types of polynomial terms can be identified and penalized separately in coefficient estimation. This strategy not only prevents the decline of generalization ability, but also effectively enhances the prediction potential of the model. By combining weighted LSE based on EWℓ2 with FCM partition and the augmented RVFLN leads to better prediction accuracy as well as lower complexity (viz., number of rules). Finally, detailed experimental studies are conducted to demonstrate the effectiveness of the proposed RFCRM.