A Discussion on “Pythagorean fuzzy AHP based risk assessment methodology for hazardous material transportation: an application in Istanbul”

Ayyildiz et al. (Environmental Science and Pollution Research (2021), 1-13) pointed out that it is important to identify and minimize the critical risks in the transportation of hazardous material. For the same, Ayyildiz et al. proposed an effective integrated decision-making methodology by combining the Modified Delphi Method (MDM) and Pythagorean fuzzy analytic hierarchy process (PF-AHP). In this integrated methodology, PF-AHP method is utilized to obtain weights of main and sub-risk factors in order to rank these factors. In Step 5 of PF-AHP method an interval valued Pythagorean fuzzy pairwise comparison matrix is transformed into a crisp matrix and then crisp AHP is applied to obtain the normalized weights from the transformed crisp matrix. It is quite evident that the crisp AHP is used only for crisp pairwise comparison matrix. However, after a deep study, it is observed that the transformed crisp matrix, obtained on applying the steps of Ayyildiz et al. methodology, violates the reciprocal propriety of pairwise comparison matrix. Therefore, to apply crisp AHP on the transformed crisp matrix is mathematically incorrect and will lead to problematic decision-making approach. Hence, may result in a heavy loss in any value-added model such as hazardous material transportation problems. Therefore, the Ayyildiz et al. methodology is not valid in its present form and cannot be used to find the solution of such type of real-life problem. Keeping the same in mind, the focus of this discussion is to make the researchers aware about these mathematical incorrect assumptions and the necessary modification is suggested.