Enhancing the scalability of fuzzy rough set approximate reduct computation through fuzzy min–max neural network and crisp discernibility relation formulation

Abstract

Fuzzy rough sets (FRS) framework is proven to be useful in computing predictive features in the presence of incompleteness and uncertainty in hybrid systems. However, the existing FRS methods for feature subset selection (reduct computation) are not scalable to large datasets due to higher space and time complexities. Towards increasing the scalability of FRS reduct computation, FMNN-FRS approach is proposed earlier, utilizing fuzzy min–max neural network (FMNN) preprocessing to enable reduct computation in fuzzy hyperbox space instead of object space. FMNN-FRS approach considers fuzzy discernibility matrix (DM) for computation of an approximate reduct. However, it is observed that the space utilization of fuzzy DM limits the scalability of FMNN-FRS. To further increase the scalability of FMNN-FRS method by the reduction in the space complexity, in this work, a novel way of crisp DM construction is proposed from the knowledge derived from FMNN preprocessing (CDM-FMFRS). Extended overlapping criteria, with tolerance parameter, are also designed for arriving at the crisp discernibility relation through fuzzy hyperboxes. The proposed CDM-FMFRS approach computes an approximate reduct using SFS strategy on the generated crisp DM. Empirically, the experimental results established that the classifiability of the induced model from the proposed algorithm is similar or better than FMNN-FRS and other state-of-the-art FRS reduct approaches with a significant reduction in computational time. Results also established better scalability achieved by CDM-FMFRS than FMNN-FRS.