  A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal
with high-dimensional datasets. This happens primarily due to the use of
T-norm, particularly, product or minimum (or a softer version of it). Thus,
there are hardly any work dealing with datasets with dimensions more than
hundred or so. Here, we propose a neuro-fuzzy framework that can handle
datasets with dimensions even more than 7000! In this context, we propose an
adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of
``numeric underflow" and ``fake minimum" that arise for existing fuzzy systems
while dealing with high-dimensional problems. We call it an Adaptive
Takagi-Sugeno-Kang (AdaTSK) fuzzy system. We then equip the AdaTSK system to
perform feature selection and rule extraction in an integrated manner. In this
context, a novel gate function is introduced and embedded only in the
consequent parts, which can determine the useful features and rules, in two
successive phases of learning. Unlike conventional fuzzy rule bases, we design
an enhanced fuzzy rule base (En-FRB), which maintains adequate rules but does
not grow the number of rules exponentially with dimension that typically
happens for fuzzy neural networks. The integrated Feature Selection and Rule
Extraction AdaTSK (FSRE-AdaTSK) system consists of three sequential phases: (i)
feature selection, (ii) rule extraction, and (iii) fine tuning. The
effectiveness of the FSRE-AdaTSK is demonstrated on 19 datasets of which five
are in more than 2000 dimension including two with dimension greater than 7000.
This may be the first time fuzzy systems are realized for classification
involving more than 7000 input features.
