A group decision making method with intuitionistic triangular fuzzy preference relations and its application

This paper aims to offer an intuitionistic triangular fuzzy group decision making method by preference relations. For this purpose, the concept of intuitionistic triangular fuzzy preference relations (ITFPRs) is first offered. Then, an additive consistency concept for ITFPRs is introduced. Meanwhile, a programming model is built to check the consistency of ITFPRs. Considering the case where incomplete ITFPRs are obtained, two programming models are constructed, which aim at maximizing the consistency and minimizing the uncertainty of missing information. To achieve the goals of the minimum total adjustment and the smallest number of adjusted elements, two programming models are established to repair inconsistent ITFPRs. In addition, the weights of decision makers are considered, and the consensus levels of individual ITFPRs are studied to ensure the representativeness of decision results. When individual ITFPRs do not meet the consensus requirement, a programming model to reach the consensus threshold is constructed, which permits different intuitionistic triangular fuzzy variables (ITFVs) to have different adjustments and minimizes the total adjustment. Finally, a group decision making algorithm with ITFPRs is proposed, and its feasibility and efficiency are demonstrated through an example of evaluating the intelligent traditional Chinese medicine decocting centers.