Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction

Rough set theory has been successfully applied for attribute reduction, but this theory is inadequate in the case of attribute reduction of real-valued data set as it may lose some information during the discretization process. Fuzzy and rough set theories have been combined and various attribute selection techniques were proposed, which can easily handle the real-valued data. An intuitionistic fuzzy set possesses a strong ability to represent information and better describing the uncertainty when compared to the classical fuzzy set theory as it considers positive, negative and hesitancy degree simultaneously for an object to belong to a set. This paper proposes a novel mechanism of attribute selection using tolerance-based intuitionistic fuzzy rough set theory. For this, we present tolerance-based intuitionistic fuzzy lower and upper approximations and formulate a degree of dependency of decision features over the set of conditional features. Moreover, the basic results on lower and upper approximations based on rough sets are extended for intuitionistic fuzzy rough sets and analogous results are established. In the end, the proposed algorithm is applied to an example data set and the comparison between tolerance-based fuzzy rough and intuitionistic fuzzy rough sets approaches for feature selection is presented. The proposed concept is found to be better performing in the form of selected attributes.