The recent boom of economic activities has escalated the demand for oil that eventually will affect itsprices. However, oil prices are difficult to predict because most of the factors affecting oil prices are vagueand intangible. The challenges in predicting oil prices urgently require a novel approach where issues relatedto multiple-factors, uncertainty, and periodicity can be addressed. The authors propose the single-valuedneutrosophic relations based decision-making method inspired by the three memberships of neutrosophic sets, andamplitude and periodicity of complex numbers. The proposed method is applied to the case of oil prices where sixfactors affecting oil prices and six benchmarks measuring oil prices are employed. This new method combineswith complex neutrosophic numbers and algebraic relations, and can suggest the most influential factor that affectsoil prices. Considering the periodicity of 24 months, computation results verify the global economic rate as themost influential factor that affects the prices of oil. The main contribution of this study is the development ofa neutrosophic relations-based decision-making method to suggest the most influential factor that affects oil prices.The result provides evidence on the feasibility of the proposed method in suggesting the influential factors that affectoil prices. © 2020 CAAI Transactions on Intelligence Technology. All rights reserved.