Interactively iterative group decision-making method with interval-valued intuitionistic fuzzy preference relations based on a new additively consistent concept

Abstract

Interval-valued intuitionistic fuzzy preference relation (IVIFPR) is a powerful instrument for describing uncertain judgement of expert in preference group decision making (PGDM). Nevertheless, the extant additive consistency definitions for IVIFPRs violate the invariance regarding arrangement of objectives. In addition, the modification for comparative judgments in the consensus reaching process (CRP) of existing PGDMs with IVIFPRs do not involve the interaction or communication with experts. Therefore, we propose an PGDM to avoid these situations. First, a new additive consistency definition for IVIFPRs is given satisfying the invariance regarding arrangement of objectives. Then, an interactively iterative algorithm considering minimum information loss is developed to enhance the consistency of IVIFPRs. Next, as to group decision making (GDM) with IVIFPRs, a bi-objective optimization model is constructed to determine the experts’ weights, and an interactively iterative algorithm considering minimum information loss is developed to enhance the consensus level among experts. Furthermore, a fuzzy optimization model is constructed to derive the interval priority weights of objectives from an IVIFPR. Finally, the feasibility and superiority of the proposed GDM method are verified by application examples and analyses. The proposed GDM method has obtained an average of 0.0432 for information deviations and 22/72 for modified judgments on two datasets, respectively, which is one of the best results compared to state-of-art.