New energy vehicles (NEVs) are the main direction for the development of the global automobile industry. Evaluating and analyzing the competitiveness of new energy vehicle enterprises (NEVEs) is of great significance for promoting their development. In order to explore the current situation of NEVEs in Henan Province, this paper firstly constructs a competitiveness evaluation index system for NEVEs, comprising both quantitative and qualitative indexes. Then, a new definition of consistency, the consistency measure level, and corresponding improvement methods for interval multiplicative preference relations (IMPRs) are proposed. On this basis, fuzzy group decision-making models with IMPRs are constructed to deal with the ambiguity and uncertainty of the decision information, where consistency and consensus are both considered. In our case study, decision results are derived using Lingo 11.0 software. The results of this paper show that the degree of specialization has the greatest impact on the competitiveness of NEVEs, and some NEVEs are deficient in this regard. Related suggestions based on expert evaluation results are also provided. In addition, a comparison with other consistency improvement methods of IMPRs reveals that the methods proposed utilize the original information provided to decision-makers to the utmost degree.