Distance and entropy measures for dual hesitant fuzzy sets

Dual hesitant fuzzy sets (DHFSs), which consist of the membership and the nonmembership hesitancy function, offer a flexible tool when decision makers give their opinions. The main aim of this paper is to investigate distance and entropy measures for DHFSs. We first propose new distance measures between hesitant fuzzy sets (HFSs), which avoid the issue of extension process in the existing distance measures. On this basis, we propose several distance measures for DHFSs, where the dual hesitant fuzzy elements (DUHEs) of the corresponding DHFSs need not have the same length. In addition, we construct several entropy measures for DHFSs, which describe the fuzziness of DHFSs. Finally, a numerical example about pattern recognition is provided to verify the practicality and effectiveness of the developed measures.