Decision making with multiplicative hesitant fuzzy linguistic preference relations

This study introduces a new type of preference relations called multiplicative hesitant fuzzy linguistic preference relations (MHFLPRs) to denote the asymmetrically qualitative hesitancy information of decision makers. Unlike hesitant fuzzy linguistic preference relations, MHFLPRs are defined on unbalanced scaled linguistic sets. Considering the application of MHFLPRs, a consistency concept is introduced that extends the consistency definition for multiplicative fuzzy linguistic preference relations. A consistency probability-based method for deriving the hesitant fuzzy linguistic priority weight vector is presented on the basis of the consistency analysis. The concept of consistent probabilistic multiplicative fuzzy linguistic preference relations is then proposed, by which the same the ranking values can be derived similarly to the above method. To address an incomplete case, consistency-based programming models are constructed by which the missing values can be determined. A consensus index is defined to measure the agreement degree between individual MHFLPRs. When the consensus requirement is unsatisfied, an interactive method for improving the consensus is offered that can guarantee the consistency of individual and comprehensive MHFLPRs. An algorithm for group decision making with MHFLPRs is subsequently developed, and a practical example is offered to show the efficiency and feasibility of the new method.