Intuitionistic Fuzzy Analytic Hierarchy Process

TLDR

Intuitionistic fuzzy sets better handle vagueness and uncertainty than fuzzy sets, enabling the IFAHP to address complex decision problems with uncertain preference assignments. The study extends AHP and FAHP to an intuitionistic fuzzy AHP (IFAHP) that represents preferences with intuitionistic fuzzy values, introduces a consistency‑checking and repair procedure, and proposes a normalizing rank‑summation method for priority derivation. The IFAHP procedure incorporates consistency verification, automatic repair, and the new rank‑summation technique, and is illustrated with a global supplier‑development example. The proposed IFAHP method autonomously improves inconsistent preference relations, saves decision‑maker time, and outperforms AHP and FAHP, as demonstrated in the supplier‑development case.

Abstract

The intuitionistic fuzzy set has shown definite advantages in handling vagueness and uncertainty over a fuzzy set. Taking the powerfulness of the analytic hierarchy process (AHP) and the fuzzy AHP (FAHP) into account when tackling comprehensive multi-criteria decision-making problems, in this paper, we extend the classic AHP and the FAHP into the intuitionistic fuzzy AHP (IFAHP) in which the preferences are represented by intuitionistic fuzzy values. The IFAHP can be used to handle more complex problems, where the decision maker has some uncertainty in assigning preference values to the objects considered. The paper proposes a new way to check the consistency of an intuitionistic preference relation and then introduces an automatic procedure to repair the inconsistent one. It is worth pointing out that our proposed method can improve the inconsistent intuitionistic preference relation without the participation of the decision maker, and thus, it can save much time and show some advantages over the AHP and the FAHP. This paper also develops a novel normalizing rank summation method to derive the priority vector of an intuitionistic preference relation, on which the priorities of the hierarchy in the IFAHP are derived. The procedure of the IFAHP is given in detail, and an example concerning global supplier development is used to demonstrate our results.