Multi-granulation hesitant fuzzy rough sets and corresponding applications

This paper develops a single-granulation hesitant fuzzy rough set (SGHFRS) model from the perspective of granular computing. In the multi-granulation framework, we propose two types of multi-granulation rough sets model called the optimistic multi-granulation hesitant fuzzy rough sets (OMGHFRSs) and pessimistic multi-granulation hesitant fuzzy rough sets (PMGHFRSs). In the models, the multi-granulation hesitant fuzzy lower and upper approximations are defined based on multiple hesitant fuzzy tolerance relations. The relationships among the SGHFRSs, OMGHFRSs and PMGHFRSs are also established. In order to further measure the uncertainty of multi-granulation hesitant fuzzy rough sets (MGHFRSs), the concepts of rough measure and rough measure about the parameters α and β are presented and some of their interesting properties are examined. Finally, we give a decision-making method based on the MGHFRSs, and the validity of this approach is illustrated by two practical applications. Compared with the existing results, we also expound its advantages.