| Summary: | Social networks (SNs) and many other industrial types of networks, structured by many nodes and relationships between nodes, have become an integral part of our daily lives. A binary-state network (BN) is often used to model structures and applications of SNs and other networks. The BN reliability is the probability that a BN functions continuously, i.e., that there is always a path between a specific pair of nodes. This metric is a popular index for designing, managing, controlling, and evaluating networks. The traditional BN reliability assumes that the network is activity-on-arc, and the reliability of each arc is known in advance. However, this is not always the case. Functioning components operate in different environments; moreover, a network might have newly installed components. Hence, the reliability of these components is not always known. To resolve the aforementioned problems, in which the reliability of some components of a network is uncertain, we introduce the fuzzy concept for the analysis of these components and propose a new algorithm to solve this uncertainty-component activity-on-node BN reliability problem. The time complexity of the proposed algorithm is analyzed, and the superior performance of the algorithm is demonstrated through examples.
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