Group decision making with incomplete intuitionistic fuzzy preference relations based on additive consistency

Due to complex circumstance, decision makers may have difficulty in offering complete intuitionistic fuzzy preference relations (IFPRs) in the decision making process, so that it will lead to loss of important information. By applying the existing additive consistency to estimate missing preference values, some obtained values may conflict with the defined domain. To address this issue, we present a new approach to group decision making (GDM) problems with incomplete IFPRs. Firstly, we introduce the concept of additive consistency for IFPRs. Then, two different conditions are provided in theorems, under these two conditions, missing preference values can be estimated such that they are expressible and consistent. Subsequently, for the incomplete IFPR which does not satisfy the conditions in two theorems, a new algorithm is put forward to revise the inconsistent preference values. Furthermore, based on the mean consensus index, the weights of decision makers can be determined in the process of GDM. Finally, an illustrative example is chosen to demonstrate the validity and practicality of the proposed method.