A smoothing Group Lasso based interval type-2 fuzzy neural network for simultaneous feature selection and system identification

Inspired by the life philosophy, an ingenious gate (membership) function, which can mimic the open and close of the gate in the real world, is proposed to realize feature selection (FS) for interval type-2 fuzzy neural network. Based on the widths of gate functions, a smoothing integrated learning strategy is designed, and in the regularized FS error function the gate widths corresponding to one feature are grouped as one Group Lasso (GL) regularization term. During the training procedure of feature selection, all the group terms with respect to bad features will be punished, but for the good features the corresponding group terms converge to different nonzero values. When feature selection is finished, using the selected features, the interpretable clustering algorithm based initial interval type-2 rule generation method is detailedly introduced firstly, then a simple and efficient memory-based gradient method is presented for the tuning of rule structure parameters. Lastly, employing the simulation results of four regression problems and four classification problems, the effectiveness on simultaneous feature selection and system identification of our proposed model, i.e., the smoothing Group Lasso based interval type-2 fuzzy neural network (SGLIT2FNN), is proved, which illustrates that SGLIT2FNN not only simplifies the model structure by deleting the bad features, but also maintains the performance.