A New Pythagorean Fuzzy Analytic Hierarchy Process Based on Interval-Valued Pythagorean Fuzzy Numbers

Abstract

The Analytic Hierarchy Process (AHP) is one of the most widely used techniques 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, several researchers extend the AHP to the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP). In the existing methods, an interval-valued Pythagorean fuzzy pairwise comparison matrix is transformed into a crisp matrix. 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 existing methods, violates the reciprocal propriety of pairwise comparison matrices, and the obtained normalized priority weights are the weights of non-pairwise comparison matrices. Therefore, this paper discusses the shortcomings of the existing method, 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.