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

•A tolerance-based intuitionistic fuzzy rough set concept has been proposed.•Analogous results of rough set theory have proven with this model.•An algorithm for feature selection based on proposed approach is presented.•Comparison between fuzzy and proposed concept for feature selection is added. Due to technological advancement and the explosive growth of electrically stored information, automated methods are required to aid users in maintaining and processing this huge amount of information. Experts, as well as machine learning processes on large volumes of data, are the main sources of knowledge. Knowledge extraction is an important step in framing expert and intelligent systems. However, the knowledge extraction phase is very slow or even impossible due to noise and large size of data. To enhance the productivity of machine learning algorithms, feature selection or attribute reduction plays a key role in the selection of relevant and non-redundant features to improve the performance of classifiers and interpretability of data. Many areas like machine learning, image processing, data mining, natural language processing and Bioinformatics, etc., which have high relevancy to expert and intelligent systems, are applications of feature selection. 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-