Consistency Comparison Analysis of Decision Making With Intuitionistic Fuzzy Preference Relations

To ensure the quality and progress of the project, it is very important to select the suitable construction enterprise. Intuitionistic fuzzy preference relations (IFPRs) are useful tools for showing the positive and negative judgments of decision makers. The main purpose of preference relations is to rank compared objects fully. Thus, the analysis of consistency is necessary to guarantee the reasonable ranking. However, the current concepts of consistency are inadequate to define the consistency of IFPRs, particularly for inconsistent and incomplete IFPRs. Therefore, the utilization of IFPRs in practical decision problems is restricted because inconsistent and/or incomplete IFPRs are usually encountered. To solve this issue, a new additive consistency concept for IFPRs is defined in this paper, which is unrelated to object labels and satisfies several reasonable properties. Considering inconsistent case, a mathematical model based method for getting additively consistent IFPRs is provided. A mathematical model for acquiring unknown judgments in IFPRs is established. A procedure for decision making with IFPRs is then given. Meanwhile, numerical examples about evaluating the construction company are offered to indicate the concrete application of the new results, and a comparative analysis is performed.