This paper presents a novel framework for evaluating the network reliability of stochastic flow networks (SFNs) by integrating fuzzy set theory to address the inherent uncertainty in lead time constraints. Traditional network reliability models typically assume deterministic lead times, which fail to capture the variability and imprecision encountered in real-world operational environments. To overcome this limitation, this research represents lead times as fuzzy numbers using triangular membership functions, thereby enabling a more realistic characterization of temporal uncertainty in network performance analysis. The proposed methodology employs α-cut operations at multiple confidence levels to transform fuzzy lead times into crisp intervals, generating both optimistic (bestcase) and pessimistic (worst-case) reliability scenarios for each α-level. By systematically evaluating the network across different confidence thresholds, the framework produces reliability intervals that reflect the full spectrum of uncertainty. Such SFNs serve as probabilistic models for analyzing system capacity. These fuzzy reliability results are subsequently converted into a single, actionable crisp value through the Center of Area (COA) defuzzification method, facilitating practical decision-making while preserving the richness of uncertainty information. The proposed approach offers significant advantages for network planning and resource allocation in contemporary infrastructure systems, including transportation, energy distribution, and communication networks, where operational parameters are subject to volatility and uncertainty. By acknowledging and quantifying inherent uncertainties while providing risk-aware insights through reliability intervals, this framework supports more robust and informed decision-making in dynamic operational environments.
Huang et al. (Wed,) studied this question.