A consistency-based approach to group decision making with uncertain multiplicative linguistic fuzzy preference relations

To denote the uncertainty and fuzziness of the decision makers' qualitative judgments, uncertain multiplicative linguistic fuzzy preference relations (UMLFPRs) are proposed. This paper focuses on the consistency of this type of preference relations, which can guarantee the reasonable ranking orders. To do this, we first analyze the differences between the operations on linguistic variables and on uncertain linguistic variables. Then, we give the concepts of quasi UMLFPRs (QUMLFPRs) and consistent QUMLFPRs. Subsequently, we introduce a consistency concept for UMLFPRs. Using this consistency concept, goal programming models are constructed to judge the consistency of UMLFPRs. Then, an approach to deriving consistent UMLFPRs from inconsistent ones is introduced. Furthermore, goal programming models to estimate the missing values in incomplete UMLFPRs are established. Considering group decision making, a consensus index is proposed, and an improving consensus method is provided. Furthermore, a method to group decision making with UMLFPRs is proposed, which can address the inconsistent and incomplete cases. Meanwhile, the associated numerical examples are offered to show the concrete application of the developed procedure.