Hesitant extension of fuzzy-rough set to address uncertainty in classification

Abstract

Although fuzzy rough sets have been considered as a powerful theory to handle real-valued data with uncertainty, fuzzy rough sets 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 and uncertainty information. Thus, the fusion of hesitant fuzzy set and fuzzy-rough set is then explored and also applied it into the task of classification. The contributions of this paper include: 1) A dimensionality reduction of hesitant fuzzy sets by investigating the equivalence relation between hesitant fuzzy elements is studied. 2) A new definition of upper and lower approximations of the hesitant fuzzy rough set is given by studying the hesitant fuzzy similarities between hesitant fuzzy elements. 3) A hesitant fuzzy rough sets nearest neighbor (HFRNN) classification algorithm is proposed.The experiments show that the classification algorithm of HFRNN outperforms the existing algorithms of FRNN, VQNN, SNN and ASNN in classification accuracy and execution time.