bipolar-valued hesitant fuzzy sets (BVHFSs). The HBVFSs encompass bipolar-valued fuzzy
sets (BVFSs) and hesitant fuzzy sets (HFSs) as special cases. The BVHFS is the
generalization of the concept of HFS in which the membership degrees of an element to a
given set are not exactly defined, but denoted by several possible bipolar-valued fuzzy
values. Then, we investigate the basic operations, properties, and comparison laws of …