A novel modified fuzzy best-worst multi-criteria decision-making method

One of the latest multi-criteria decision-making methods is best-worst method (BWM). In the procedure of BWM, decision maker (DM) identifies the most and the least important criteria namely, best and worst. Thereafter, DM identifies the degrees which he believes the best criterion is better than the other criteria, and identifies the degrees which he believes the other criteria are better than the worst criterion. Because of uncertainties in comparisons due to using linguistic variables for pairwise comparisons and also the lack of complete information, the crisp values of pairwise comparisons cannot appropriately model the problems. This paper develops the BWM for considering fuzzy pairwise comparisons (FBWM) by proposing a new fuzzy mathematical model which yields crisp weights from a fuzzy pairwise comparison matrix. Unlike to some previous papers that obtains fuzzy weights from fuzzy pairwise comparison matrix, the crisp weights of the proposed method of this paper eliminates the supplementary aggregation of fuzzy weights and ranking procedures. Moreover, the proposed method avoids obtaining the different ranking results due to the different ranking procedures of fuzzy numbers. Another outstanding advantage of this paper is that the obtained weights of the proposed method better satisfy the initial judgments compared to previous methods, while as we know, the satisfaction of the initial judgments is essential for pairwise comparison judgments. This paper presents several numerical examples to prove the good performance and the merit of the proposed method. According to the provided numerical examples, the proposed method of this paper absolutely outperforms the two well-known previous methods.