Disjunctive Fuzzy Neural Networks: A New Splitting-Based Approach to Designing a T–S Fuzzy Model

This article proposes a new network approach toward the implementation of Takagi–Sugeno (T–S) fuzzy models referred to as disjunctive fuzzy neural networks (DJFNNs). The proposed DJFNN involves a novel network architecture and a greedy learning algorithm. Being different from the existing grid-based and clustering-based network architectures, the proposed architecture adds an OR neural layer positioned between the fuzzification layer and the rule layer. In this way, the implied constraint between the number of rules and the number of fuzzy labels is excluded so that a curse of dimensionality can be overcome and more interpretable models are formed. Furthermore, inspired by the core algorithm for building a decision tree, a top–down, nonbacktracking, and greedy algorithm is proposed to learn the unknown parameters of the networks. The input space splits into smaller and smaller subspace along the predefined fuzzy grids in a supervised manner meanwhile the associated conditions of the T–S fuzzy model are identified. The greedy algorithm is applicable to high-dimensional problems since there is no exponential growth in time or space as the dimensionality increases. The new network architecture and greedy learning algorithm make the proposed DJFNN a regression model of high interpretability and good prediction capability, particularly suitable for solving the high-dimensional problems. The DJFNN was experimented with using a synthetic dataset and 28 real-world datasets and compared with classical and state-of-the-art methods through nonparametric statistical tests. The results confirmed the effectiveness of the DJFNN in terms of accuracy, interpretability, and computational cost.