A new intuitionistic fuzzy best worst method for deriving weight vector of criteria and its application

Intuitionistic fuzzy Best Worst method (IFBWM) is an effective method to deal with multi-criteria decision making problems via intuitionistic fuzzy reference comparisons of experts, which has attracted increasing attention from different decision fields. However, there are drawbacks in the existing IFBWMs, which can result in unreasoning and incorrect ranking order of criteria or alternatives. To overcome the existing drawbacks of the IFBWMs, we propose a new IFBWM considering the multiplicative consistency of intuitionistic fuzzy reference comparisons. First, combining the multiplicative consistent intuitionistic fuzzy preference relation with the fully multiplicative consistency of the intuitionistic fuzzy reference comparisons, we build the mathematical programming model for obtaining the normalized intuitionistic fuzzy weight vector. Then, we define the concept of the consistency ratio for evaluating the multiplicative consistency of intuitionistic fuzzy reference comparisons. Afterwards, an algorithm for repairing the inconsistency of intuitionistic fuzzy reference comparisons is developed, which only adjust the preference degree of the best criterion over the worst criterion. Subsequently we propose a new IFBWM with the multiplicative consistency. Furthermore, we apply the proposed method to Advanced Mathematics textbooks selection. The computational results show that the consistency ratio is 0.0091, implying the intuitionistic fuzzy reference comparisons are acceptable, and the ranking order of the alternatives C-1 > C-2 > C-4 > C-3 is consistent with the initial judgment of experts and the actual usage of Advanced Mathematics textbooks in universities of China. The computational results of the practical example through the other methods reveal that there are some troubles in the consistency ratio, the weights of alternatives or the ranking order of the alternative. Therefore, the results suggest that the proposed method may have significant effects on the theoretical development and practical application of IFBWM.