Research review on Saaty's comments on fuzzy logic is not applicable to analytic hierarchy process

Fuzzy analytic hierarchy process has been widely used in many fields, but Thomas L. Saaty, the architect of AHP, questioned the validity of fuzzy AHP and had published three articles which show the invalidity of using fuzziness with the AHP. In this paper, we review Saaty's comments on fuzzy AHP from three aspects: fuzzy AHP is lack of mathematical validity; the judgments in AHP are themselves already fuzzy and fuzzy them again has no meaning; improving inconsistency need not improve the validity of the outcome. Through this paper, we do further analysis on both AHP and fuzzy. We hope it will make some help for decision-makers when using AHP.