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The analytic hierarchy process (AHP) is widely employed to guide the decision-maker to rank or evaluate the alternatives in decision activities. Its fuzzy set-based version, i.e., the fuzzy AHP, has also been widely studied and applied since its inception. The essential distinction between the AHP and fuzzy AHP comes from the diverse transformation methods between the linguistic and numeric judgments. In this article, we conduct a thorough comparative study between the AHP and fuzzy AHP methods in the framework of two linguistic models, i.e., the linguistic model based on the membership functions and two-tuple linguistic model. First, four AHP and three fuzzy AHP methods are revisited with the involvement of two linguistic models. Then, the comparison criteria are involved by calculating the cardinal or ordinal deviation between the original information and decision solutions, and the effects of the transitivity of the reciprocal matrix are also discussed in the comparative study. Finally, the detailed experiments along with a thorough comparative analysis are conducted based on the random and publicly available data to show the difference between the AHP and fuzzy AHP methods.
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