Uncertainty and Equivalence Relation Analysis for Hesitant Fuzzy-Rough Sets and Their Applications in Classification

The fusion of hesitant fuzzy set (HFS) and fuzzy-rough set (FRS) is explored and applied into the task of classification due to its capability of conveying hesitant and uncertainty information. In this paper, on the basis of studying the equivalence relations between hesitant fuzzy elements and HFS operation updating, the target instances are classified by employing the lower and upper approximations in hesitant FRS theory. Extensive performance analysis has been conducted including classification accuracy results, execution time, and the impact of k parameter to evaluate the proposed hesitant fuzzy-rough nearest-neighbor (HFRNN) algorithm. The experimental analysis has shown that the proposed HFRNN algorithm significantly outperforms current leading algorithms in terms of fuzzy-rough nearest-neighbor, vaguely quantified rough sets, similarity nearest-neighbor, and aggregated-similarity nearest-neighbor.