Cold-chain vaccine distribution often suffers from limited visibility and high supply chain risks due to uncertain demand, dynamic environments, and operational constraints. These challenges make it difficult to ensure timely delivery, maintain product integrity, and control operational costs, highlighting the need for a structured approach to address these uncertainties and improve overall system performance. In response to this need, this research investigates the integration of Supply Chain Visibility (SCV) and Supply Chain Risk (SCR) in cold-chain vaccine distribution using a fuzzy multi-objective decision-making framework. Real-world data from Bangladesh, including demand, capacity, and operational constraints were utilized to validate the proposed research. Based on this datasheet, a multi-objective integer programming model was developed to simultaneously maximize SCV, minimize SCR, and reduce overall cost. The model uses fuzzy triangular numbers to capture uncertainties in demand, visibility, and risk. Furthermore, a Genetic Algorithm (GA) is employed to find optimized solutions. The obtained results demonstrate that, enhancing visibility while mitigating supply chain risks significantly improves operational performance, with SCV increased by 21%, SCR reduced by 2%, and the optimal cost decreased by BDT 175 million. Overall, this research offers a practical decision support tool for efficient cold-chain vaccine distribution in developing countries.