An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making

In order to extend the best-worst method (BWM) to uncertain circumstances, in this paper, we propose an intuitionistic fuzzy multiplicative best-worst method (IFMBWM) with intuitionistic fuzzy multiplicative preference relations (IFMPRs) for multi-criteria group decision making. First of all, we aggregate individual IFMPRs provided by the decision makers to a collective one by using the intuitionistic fuzzy multiplicative weighted geometric aggregation (IFMWGA) operator. Afterwards, we design an algorithm to rank the criteria according to the membership degrees of the intuitionistic fuzzy assessments, which can be used to identify the best and worst criteria by calculating the out-degrees and in-degrees of the directed network about the collective IFMPR. Furthermore, based on the new definition of the multiplicative consistent IFMPR, we develop several max-min programming models to derive the weights of criteria, and then propose a consistency ratio to check the reliability of the derived results. The procedure of the IFMBWM is provided for the convenience of practical applications. Finally, a numerical example concerning the evaluation of the severity of pulmonary emphysema is given to illustrate the proposed method.