IT2 Fuzzy-Rough Sets and Max Relevance-Max Significance Criterion for Attribute Selection

One of the important problems in pattern recognition, machine learning, and data mining is the dimensionality reduction by attribute or feature selection. In this regard, this paper presents a feature selection method, based on interval type-2 (IT2) fuzzy-rough sets, where the features are selected by maximizing both relevance and significance of the features. By introducing the concept of lower and upper fuzzy equivalence partition matrices, the lower and upper relevance and significance of the features are defined for IT2 fuzzy approximation spaces. Different feature evaluation criteria such as dependency, relevance, and significance are presented for attribute selection task using IT2 fuzzy-rough sets. The performance of IT2 fuzzy-rough sets is compared with that of some existing feature evaluation indices including classical rough sets, neighborhood rough sets, and type-1 fuzzy-rough sets. The effectiveness of the proposed IT2 fuzzy-rough set-based attribute selection method, along with a comparison with existing feature selection and extraction methods, is demonstrated on several real-life data.