Uncertainty and Equivalence Relation Analysis for Hesitant Fuzzy-Rough Sets and Their Applications in Classification
Résumé
Fuzzy-rough based algorithms reached their limit of conveying hesitation information in the processes of making classification decision. Hesitant fuzzy set plays an important role in handling hesitant information. Thus, the fusion of hesitant fuzzy set and fuzzy-rough set is then explored and applied. In this paper, on the basis of studying the equivalence relations between hesitant fuzzy elements, hesitant fuzzy set operation updation, and hesitant fuzzy rough properties, the target instances are classified by employing the lower and upper approximations in hesitant fuzzy-rough set theory. Extensive performance analysis has been conduct 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 outperform current leading algorithms in terms of fuzzy-rough nearest-neighbor (FRNN), vaguely-quantified rough sets (VQNN), similarity nearest-neighbor (SNN), and aggregated-similarity nearest-neighbor (ASNN).