Document Type : Research Paper


School of Mathematics, Thapar Institute of Engineering & Technology, Patiala, Punjab, India



The analytic hierarchy process (AHP), is one of the well-known and most widely used technique to determine the priority weights of alternatives from pairwise comparison matrices. Several fuzzy and intuitionistic fuzzy extensions of AHP have been proposed in the literature. However, these extensions are not appropriate to present some real-life situations. For this reason, Ilbahara et al. extend the AHP to Pythagorean fuzzy analytic hierarchy process (PFAHP). In this 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 priority weights from the transformed crisp matrix. However, it is observed that the transformed crisp matrix, obtained on applying the step of Ilbahara et al.’s method, violates the reciprocal propriety of pairwise comparison matrices and the obtained normalized priority weights are the weights of non-pairwise comparison matrices. Therefore, in this paper, the shortcomings of the existing method are discussed and a modified method is proposed to overcome these shortcomings. Finally, based on a real-life decision-making problem, the superiority of the proposed method over the existing method is shown.


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