A Novel Extension of Best-Worst Method With Intuitionistic Fuzzy Reference Comparisons

Best-worst method (BWM) has attracted increasing attention. It has been generalized to different fuzzy environments and applied to various real-life decision problems. This article develops a new intuitionistic fuzzy (IF) BWM (IFBWM) for multicriteria decision-making. When a decision maker (DM) makes comparisons, there may be some hesitancies. Thus, the reference comparisons are represented as intuitionistic fuzzy values (IFVs), the Best-to-Others vector and the Others-to-Worst vector are IF vectors. According to the multiplicative consistency of intuitionistic fuzzy preference relation, this article gives the consistency equations and views them as IF equations. The derivation of optimal IF weights of criteria is formulated as an IF decision-making problem. Thereby, a mathematical programming model is constructed to assure that the derived optimal IF weights of criteria is a normalized IF weight vector. Depending on the risk preference of DM, four linear programming models are presented to obtain the optimal IF weights based on the constructed mathematical programming model for the optimistic DM, the pessimistic DM, and the neutral DM, respectively. Furthermore, this article investigates the process of improving the consistency. Several examples are demonstrated to show the application and effectiveness of the proposed IFBWM.

I. Introduction

Analytic hierarchy process (AHP) [1] is a special kind of multicriteria decision-making (MCDM) technique. AHP can determine the weights of criteria (or alternatives) via preference relations (PRs) constructed by pairwise comparisons. Owing to the flexible structure and innate ability of humans to make pairwise comparisons, PRs have been widely applied to many decision-making problems. Various types of PRs have been proposed, such as fuzzy preference relations [2]–[4], interval fuzzy preference relations (IVFPRs) [5]–[9], intuitionistic fuzzy (IF) preference relations (IFPRs) [7], [10], [11] and interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs) [12]–[14], etc.