Intuitionistic hesitant linguistic sets and their application in multi-criteria decision-making problems

In practice, the use of linguistic information is flexible and definite due to the complexity of problems, and therefore the linguistic models have been widely studied and applied to solve multi-criteria decision-making (MCDM) problems under uncertainty. In this paper, intuitionistic hesitant linguistic sets (IHLSs) are defined on the basis of intuitionistic linguistic sets (ILSs) and hesitant fuzzy linguistic sets (HFLSs). As an evaluation value of one reference object, an intuitionistic hesitant linguistic number (IHLN) contains a linguistic term, a set of membership degrees and a set of non-membership degrees. There can be a consensus on the linguistic term and then decision makers can express their opinions on membership or non-membership degrees depending on their preferences. Therefore, by means of IHLSs, the flexibility in generating evaluation information under uncertainty can be achieved to a larger extent than either ILSs or HFLSs do. Besides, the basic operations and comparison method of IHLNs are studied, which is followed by the definitions of several aggregation operators, including the intuitionistic hesitant linguistic hybrid averaging (IHLHA) operator, the intuitionistic hesitant linguistic hybrid geometric (IHLHG) operator and the corresponding generalized operators. Using these operators, an approach to MCDM problems with intuitionistic hesitant linguistic information is proposed. Finally, an illustrative example is provided to verify the proposed approach and its accuracy and effectiveness have been demonstrated through the comparative analysis with ILSs and HFLSs.