Additive consistency of q-rung orthopair fuzzy preference relations with application to risk analysis

Preference relations have been extended to q-rung orthopair fuzzy environment, and the q-rung orthopair fuzzy preference relations (q-ROFPRs) with additive consistency are defined. Then, the concept of normalized q-rung orthopair fuzzy weight vector (q-ROFWV) is proposed, and the transformation method of constructing q-ROFPR with additive consistency is given. To obtain the weight vector of any q-ROFPRs, a goal programming model to minimize the deviation of the q-ROFPRs from the constructed additive consistent q-ROFPRs is established. The q-rung orthopair fuzzy weighted quadratic (q-ROFWQ) operator is selected to aggregate multiple q-ROFPRs, efficiently handling extreme values and satisfying monotonicity about the order relation. Further, a group decision-making (GDM) method is developed by combining the q-ROFWQ operator and the goal programming model. Finally, the practicality and feasibility of the developed GDM method are demonstrated by an example of rail bogie crucial component identification.