ADMTSK: A High-Dimensional Takagi-Sugeno-Kang Fuzzy System Based on Adaptive Dombi T-Norm

Fuzzy systems have been employed in many fields and achieved remarkable results. However, due to the inherent characteristics, there is still a challenge for them to deal with high-dimensional data which includes a large number of features and becomes very common in the current era of Big Data. Most of the literature employ the product, minimum, softmin and its adaptive versions to compute the firing strengths in fuzzy system modeling, where only the first two are standard T-norms conforming to the theoretical basis of fuzzy logic reasoning. But easy to cause numeric underflow and nondifferentiability are their disadvantages, respectively. To comply with fuzzy theory basis and alleviate the aforementioned predicament of dimensionality, this article investigates how to design high-dimensional Takagi-Sugeno-Kang (TSK) fuzzy system based on Dombi T-norm, which has not been explored for fuzzy system modeling to the best of our knowledge. We first build Dombi T-norm based TSK (DombiTSK) model, then an adaptive strategy is designed for the index parameter of Dombi T-norm to enhance the performance of DombiTSK, which results in so-called adaptive DombiTSK (ADMTSK) fuzzy system. To further improve the design and performance of ADMTSK, we give a novel membership function with positive lower bound to match the use of adaptive Dombi T-norm, which is constructed based on Gaussian membership function (GMF) and named as composite GMF (CGMF). The experiments are conducted on high-dimensional classification datasets with feature dimensions varying from 1024 to 120 432 to evaluate the proposed methodologies. Experimental results verify the advantages of adaptive Dombi T-norm and CGMF. The comparison results and statistical tests among ADMTSK and other state-of-the-art fuzzy algorithms demonstrate that our proposed model outperforms its rivals.