Fuzzy Rough Sets Reduct Based On Discernibility Matrix

Fuzzy rough sets are mathematical theories that combines rough sets with fuzzy sets together to deal with imprecise and uncertain information. The existing research about fuzzy rough sets mainly concentrate on definitions of fuzzy rough sets, and there are few work on fuzzy rough sets reduct. There are two primary fuzzy rough sets reduct methods--- one is based on dependency function and another based on discernibility matrix. Both of them are extended from rough sets reduct methods. The lower approximation of the former is not accordance with that of fuzzy rough sets, and the latter uses a different way from the former and avoids the problem of the former. However, both of them can only deal with data sets with continuous condition attributes and discreet decision attributes. There is no method to deal with data sets with continuous condition attributes and decision attributes using fuzzy rough sets reduct. By analyzing the latter's work, we extend the theory of fuzzy rough sets reduct using discernibility matrix. We propose a fuzzy rough sets reduction method to deal with data sets with continuous condition and decision attributes. We do some experiments on several datasets, and the experimental results show our method in this paper is feasible and effective.