Optimal weighting models based on linear uncertain constraints in intuitionistic fuzzy preference relations

The priority weight vectors of an intuitionistic fuzzy preference relation (IFPR) with linear uncertainty distribution characteristics in group decision making (GDM) are determined in this study. On the basis of an IFPR, the assumptions of additive consistency and decision-making preference variables obeying the uncertainty distribution are defined. Afterward, a priority model is constructed with a chance constraint, and the ranking relations of the membership and non-membership matrices are analysed. The change in the confidence level of the chance constraint controls the flexibility of realising additive consistency. Moreover, it is proven that if the individual decision makers' IFPR has a linear distribution, the group IFPR aggregated by the weighted methodology still obeys this distribution. Finally, an uncertain linear ranking consensus model of the IFPR is developed, and a numerical example is used to verify its feasibility.