Multihead Takagi–Sugeno–Kang Fuzzy System

Fuzzy systems are widely used for their strong ability to handle uncertainty; however, they often struggle with high-dimensional problems. Here, a novel scalable model, the multihead Takagi–Sugeno–Kang fuzzy system (MHTSK), is proposed to efficiently handle high-dimensional data while maintaining strong interpretability. Unlike traditional fuzzy systems that construct a single antecedent using all features, MHTSK builds multiple subantecedents by randomly sampling subsets of features to address high-dimensional challenges. The rules generated by these subantecedents are jointly optimized, resulting in a naturally sparse consequent structure that enhances interpretability. Since the size and number of feature subsets directly influence the length and complexity of fuzzy rules, we propose an optimal parameter configuration scheme that balances: first, preventing “numeric underflow” in high-dimensional data, and second, ensuring sufficient coverage of the original feature space. Furthermore, considering the randomness introduced by sampling, a rule extraction scheme is proposed to eliminate redundant rules. The refined rule base obtained after the extraction process is used to retrain the model, resulting in a new variant model called MHTSK_RE. The effectiveness of MHTSK and MHTSK_RE is demonstrated on eleven high-dimensional datasets. The results confirm their superior performance and outstanding interpretability in handling high-dimensional data.