Deep Fuzzy Min-Max Neural Network: Analysis and Design

Fuzzy min-max neural network (FMNN) is one kind of three-layer models based on hyperboxes that are constructed in a sequential way. Such a sequential mechanism inevitably leads to the input order and overlap region problem. In this study, we propose a deep FMNN (DFMNN) based on initialization and optimization operation to overcome these limitations. Initialization operation that can solve the input order problem is to design hyperboxes in a simultaneous way, and side parameters have been proposed to control the size of hyperboxes. Optimization operation that can eliminate overlap region problem is realized by means of deep layers, where the number of layers is immediately determined when the overlap among hyperboxes is eliminated. In the optimization process, each layer consists of three sections, namely, the partition section, combination section, and union section. The partition section aims to divide the hyperboxes into a nonoverlapping hyperbox set and an overlapping hyperbox set. The combination section eliminates the overlap problem of overlapping hyperbox set. The union section obtains the optimized hyperbox set in the current layer. DFMNN is evaluated based on a series of benchmark datasets. A comparative analysis illustrates that the proposed DFMNN model outperforms several models previously reported in the literature.