<p>Variable precision fuzzy rough sets exhibit strong fault-tolerant capability in handling uncertain information, and overlap functions are widely utilized to aggregate fuzzy information owing to their flexible computational characteristics. Therefore, it is of significant importance to integrate variable precision fuzzy rough sets with overlap functions. This paper explores overlap function-based VPFRS models from theoretical and practical perspectives. Specifically, we propose two types of new variable precision fuzzy rough sets based on overlap functions, and further discuss their basic properties as well as the relationships between them. From the perspective of application, we establish a PROMETHEE-TOPSIS method using one of the constructed variable precision fuzzy rough set models. In the method, we introduce a subjective-objective integrated weight method to compute comprehensive attribute weights. Besides, we adopt the method to evaluate the maternal health risk for pregnant women to demonstrate its practicality. What’s more, comparative and experimental analyses are conducted to validate its superiority and robustness. In summary, this study enriches the theoretical framework of variable precision fuzzy rough sets and offers a novel solution for addressing decision problems.</p>