Improving the Best-Worst Method Based on Optimal Completion of Incomplete Pairwise Comparison Matrix

In this paper, the pairwise comparison matrix (PCM) of the best-worst method (BWM) is regarded as a special incomplete PCM (IPCM), and an improved method based on the optimal completion of the IPCM, called BWM-IPCM, is proposed. Firstly, as a special IPCM, BWM-IPCM has been proven to be effective/acceptable and ordinally consistent. Then, with the best consistency as the objective function, the optimization model of BWM-IPCM is established to achieve the optimal completion of incomplete elements, and the optimal weights and rankings are obtained from the completed PCM. In order to deal with possible inconsistencies in BWM, two methods are proposed: one is to invite experts to supplement a small amount of comparison information among inconsistent criteria found; the other is to fine-tune known elements to improve consistency without the participation of experts. Finally, illustrative examples show that compared with the original BWM, the proposed method can make more effective use of additional comparison information, has better consistency description and interpretation, and is easier to solve.