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Analytic hierarchy process (AHP), as one of the most important methods to tackle multiple criteria decision-making problems, has achieved much success over the past several decades. Given that linguistic expressions are much closer than numerical values or single linguistic terms to a human way of thinking and cognition, this paper investigates the AHP with comparative linguistic expressions. After providing the snapshot of classical AHP and its fuzzy extensions, we propose the framework of hesitant fuzzy linguistic AHP, which shows how to yield a decision for qualitative decision-making problems with complex linguistic expressions. First, the comparative linguistic expressions over criteria or alternatives are transformed into hesitant fuzzy linguistic elements and then the hesitant fuzzy linguistic preference relations (HFLPRs) are constructed. Considering that HFLPRs may be inconsistent, we conduct consistency checking and improving processes after obtaining priorities from the HFLPRs based on a linear programming method. Regarding the consistency-improving process, we develop a new way to establish a perfectly consistent HFLPR. The procedure of the hesitant fuzzy linguistic AHP is given in stepwise. Finally, a numerical example concerning the used-car management in a lemon market is given to illustrate the efficiency of the proposed hesitant fuzzy linguistic AHP method.

Hesitant Fuzzy Linguistic Analytic Hierarchical Process With Prioritization, Consistency Checking, and Inconsistency Repairing