This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on this view, we introduce a weighted geometric mean to aggregate heights during the addition of generalized Gaussian fuzzy numbers. We employ a reliability-aware ranking that jointly considers the core, height, and standard deviation of fuzzy edge costs to determine the shortest path, thereby capturing their central tendency, reliability, and variability while keeping Dijkstra-level complexity per relaxation. The method yields routes that are not only cost-efficient but also supported by highly reliable information. To assess robustness, we construct a crisp baseline from the ranking and conduct Monte Carlo alpha-cut sampling--drawing membership levels uniformly and then sampling within the induced intervals--to recompute path costs and quantify sensitivity via the mean percentage deviation and its standard deviation. Finally, a large-scale case study on the FAA air traffic network demonstrates that the proposed GGFN--SPP framework scales efficiently to real-world networks, balances cost and reliability through $α$--cut aggregation and risk-aware ranking, and exhibits stable performance under Monte Carlo simulations with subnormal fuzzy costs.

翻译：本文研究了有向图中的模糊最短路径问题，其中边成本被建模为具有高斯隶属函数的一般化模糊数。我们将高度解释为信息可靠性的指标。基于这一观点，我们引入加权几何均值来在一般化高斯模糊数加法过程中聚合高度。我们采用一种考虑可靠性的排序方法，该方法联合考虑模糊边成本的核心、高度和标准差，以确定最短路径，从而在保持每次松弛操作的Dijkstra级复杂度的同时，捕捉其中心趋势、可靠性和变异性。该方法生成的路径不仅成本高效，而且由高度可靠的信息支持。为了评估鲁棒性，我们从排序构建一个清晰基线，并进行蒙特卡洛α-截集采样——均匀抽取隶属度水平，然后在诱导区间内采样——以重新计算路径成本，并通过平均百分比偏差及其标准差来量化敏感性。最后，在FAA空中交通网络上的大规模案例研究表明，所提出的GGFN-SPP框架能够高效扩展到现实世界网络，通过α-截集聚合和风险感知排序平衡成本与可靠性，并在次正态模糊成本的蒙特卡洛模拟下表现出稳定的性能。