  Takagi-Sugeno-Kang (TSK) fuzzy system with Gaussian membership functions
(MFs) is one of the most widely used fuzzy systems in machine learning.
However, it usually has difficulty handling high-dimensional datasets. This
paper explores why TSK fuzzy systems with Gaussian MFs may fail on
high-dimensional inputs. After transforming defuzzification to an equivalent
form of softmax function, we find that the poor performance is due to the
saturation of softmax. We show that two defuzzification operations, LogTSK and
HTSK, the latter of which is first proposed in this paper, can avoid the
saturation. Experimental results on datasets with various dimensionalities
validated our analysis and demonstrated the effectiveness of LogTSK and HTSK.
