Hesitant Linguistic Intuitionistic Fuzzy Sets and Their Application in Multicriteria Decision-Making Problems

This paper introduces hesitant linguistic intuitionistic fuzzy sets (HLIFSs) based on hesitant fuzzy sets (HFSs) and linguistic intuitionistic fuzzy numbers (LIFNs). HLIFSs can serve as a useful tool to depict complex and uncertain decision-making information and reflect the hesitancy of decision-makers. This paper focuses on the development of an innovative method to address multicriteria decision-making (MCDM) problems, in which the criteria are in different priority levels and the weight information is completely unknown. Handling qualitative information requires the effective support of quantitative tools, after which the linguistic scale function (LSF) can be employed to deal with linguistic information. First, the comparison method and operations of HLIFNs are proposed. Second, two prioritized aggregation operators, including the hesitant linguistic intuitionistic generalized weighted prioritized average (HLIGWPA) operator and the hesitant linguistic intuitionistic generalized weighted prioritized geometric (HLIGWPG) operator, are defined and further extended to accommodate to a grouping prioritized situation. Then, an MCDM method which contains the proposed operators is developed. Finally, an illustrative example regarding coal mine safety evaluation is provided for demonstrating the presented method. Moreover, a sensitivity analysis and comparisons with some other existing methods are furnished to verify the feasibility and validity of the proposed method.