Vendor-managed inventory (VMI) is a supply chain coordination improvement system. Due to the vendor's responsibility for the replenishment decision, demand forecasting and quick response for retailers' demand fluctuations are crucial in a VMI system. Our study focuses on order prediction of the VMI for FMCG companies, which is multicriteria decision-making entailing to consider various quantitative and qualitative criteria in the fuzzy decision-making process. The interval-valued intuitionistic fuzzy set (IVIFS) is applied to solve ambiguity, vagueness, and subjectivity in human judgments. With real sales data, sales conditions, and objective expert opinions, the proposed method showed logical and reliable results. The study also presented that the proposed methodology improves the company's supply chain performance while preventing excessive stocks and customer backorders with equalization of the alternatives.