On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations

As a new preference structure, the hesitant fuzzy linguistic preference relation (HFLPR) was recently introduced by Rodriguez, Martinez, and Herrera to efficiently address situations in which the decision makers (DMs) are hesitant about several possible linguistic terms for the preference degrees over paired comparisons of alternatives. In this paper, we define the multiplicative consistency of HFLPRs to ensure that the DMs are being neither random nor illogical, and propose a characterization about the multiplicative consistency of HFLPRs. A consistency index is defined to measure the deviation degree between a HFLPR and its multiplicative consistent HFLPR. For a HFLPR with unacceptably multiplicative consistency, we develop a consistency-improving process to adjust it into an acceptably multiplicative one. Moreover, we use the hesitant fuzzy linguistic aggregation operators to aggregate preferences in the acceptably multiplicative HFLPR to obtain the ranking results. Several illustrative examples are further provided to verify the developed methods. Finally, a comparison with other methods in the existing literature is performed to illustrate the advantages of the new methods.