Hesitant distance set on hesitant fuzzy sets and its application in urban road traffic state identification

Since fuzziness lacks the distinction between a set and its complement, it is difficult to measure the distance between different hesitant fuzzy sets (HFSs) by a single value. In this study, a new concept "hesitant distance set (HDS)" is proposed, where the distance between different HFSs can be characterized by a series of different values. This study has three primary contributions. Firstly, most of the existing distance measures on HFSs are based on vector operation, while the novel proposed HDSs are based on set operation. Secondly, a statistical method is proposed to compare different HDSs, and some important properties of the comparison method are introduced. Thirdly, the characteristics of the novel HDSs and the classical hesitant distances are studied comparatively. Finally, the practicality and validity of the HDSs on HFSs are illustrated through an urban road traffic state identification example.