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The Floyd-Warshall algorithm is commonly used to determine the shortest path between any two nodes in a network and is extensively used to solve the Shortest Path Problem (SPP) in areas such as road transportation, logistics, and computer networks. While it performs effectively with precise (crisp) edge weights, challenges arise when the edge weights are ambiguous or uncertain. Additionally, although each edge can be influenced by multiple criteria, most existing studies typically consider only a single criterion when assigning weights. To address this limitation, this study presents a modified version of the classical Floyd-Warshall algorithm for All-Pairs Shortest Paths (APSP), capable of managing networks with uncertain parameters by representing edge weights as single-valued neutrosophic numbers (SVNNs). The proposed SVNN Floyd-Warshall algorithm calculates the minimum possible weights for all node pairs, with each edge weighted using SVNNs. Furthermore, it supports multi-criteria decision-making by allowing up to n different criteria for each edge. A computer network routing example is provided to demonstrate the effectiveness of the proposed method. The results show that the SVNFW algorithm performs effectively in uncertain environments and offers more flexible and robust solutions compared to traditional methods. Its ability to handle both uncertainty and multi-criteria evaluation makes it well suited for dynamic, real-world applications. Future research is recommended to examine the algorithm’s scalability in large-scale networks and to explore its integration with real-time data for adaptive routing solutions.