An adaptive double-parameter softmin based Takagi-Sugeno-Kang fuzzy system for high-dimensional data

Abstract

Fuzzy or neuro-fuzzy systems have been widely applied across numerous fields. However, they still face significant challenges when addressing high-dimensional problems. This is primarily due to the use of product T-norm, minimum T-norm and its softer variants. In this context, we construct an adaptive double-parameter softmin (ADP-softmin) based Takagi-Sugeno-Kang fuzzy model, called ADPTSK, where ADP-softmin is proposed to overcome the drawbacks of “numeric underflow” and “fake minimum” prevalent in existing fuzzy systems (FSs) when handling high-dimensional data. During the design process of ADP-softmin, we discover that the traditional Gaussian membership function (Gaussian TMF) may lead to ADPTSK FS crash due to its not having a positive infimum, prompting us to give a Gaussian membership function with a positive infimum (Gaussian PIMF). The effective combination of ADP-softmin and Gaussian PIMF enables ADPTSK to handle data with over one hundred thousand features. The ADPTSK is evaluated on 14 classification datasets with feature dimensions ranging from 1,024 to 120,432. The experimental results indicate that ADPTSK exhibits competitive performance in handling high-dimensional problems.