Preference rationality analysis for the best–worst method and its application to quality assessment

Abstract

A primary concern in most decision-making problems using pairwise comparisons is the consistency issue of individual preference information. The existence of inconsistencies may lead to unrealistic and unreasonable results. This paper focuses on the consistency improvements for the best–worst method (BWM), which seeks to retain the original preference information as much as possible. To do this, some optimization models are designed as a preference-modification advice tool to interact with a decision maker (DM). Firstly, several systems of constraints are designed to explicitly control the ordinal consistency for the BWM. A mixed-integer linear programming model is proposed to provide optimal suggestions of preference-modification for ensuring the ordinal consistency. Furthermore, an optimization model is constructed to offer optimal suggestions of preference-modification for simultaneously meeting an acceptable cardinal consistency level and the ordinal consistency. Then, a framework for preference rationality analysis based on the two optimization-based advice tools is designed for the BWM. Finally, a real case study about the quality assessment of airline baggage handling systems is used to validate the proposed approach.