Best-worst method (BWM) extended to uncertain situations, generalized interval-valued trapezoidal fuzzy best-worst method (GITrFBWM) is proposed by using generalized interval-valued trapezoidal fuzzy multiplicative preference relation for multiple criteria group decision-making problems. The reference comparison of the best criterion and the worst criterion are described by the linguistic terms, which are expressed in generalized interval-valued trapezoidal fuzzy numbers, of the decision-makers. Weights of criteria are calculated by using graded mean integration representation method. Using the concept of BWM, nonlinearly constrained optimization problems are formed to obtain generalized interval-valued trapezoidal fuzzy weights of different criteria and alternatives. To check the reliability of the GITrFBWM, consistency ratio is proposed. The advantage and suitability of the proposed GITrFBWM are determined by three case studies. The results indicate that the GITrFBWM, due to higher comparison consistency as compared to BWM and fuzzy-best worst method, obtain plausible preference ranking for alternatives.
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