Cloud service reliability assessment is a vital decision-making activity for companies and individuals. In this assessment, the evaluation information can be represented by multi-valued neutrosophic numbers (MVNNs). MVNNs are regarded as an integration of single-valued neutrosophic numbers (SVNNs) and hesitant fuzzy numbers (HFNs); therefore, considering the defects of entropy and crossentropy measures for SVNNs and HFNs, we first define a framework of entropy measures and a family of cross-entropy measures for MVNNs in this paper. Second, a novel extended VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method based on entropy and cross-entropy measures is developed to address the decision-making problems when information about criteria weights is absolutely unknown. Finally, we apply the proposed method to evaluate cloud service reliability; also, a sensitivity analysis and a comparative analysis are made to interpret the practicality and effectiveness of it. The results of analyses verify that the proposed method based on cross-entropy is much better than the methods using general distance measures.