  Various networks such as cloud computing, water/gas/electricity networks,
wireless sensor networks, transportation networks, and 4G/5G networks, have
become an integral part of our daily lives. A binary-state network (BN) is
often used to model network structures and applications. The BN reliability is
the probability that a BN functions continuously; that is, that there is always
a simple path connected 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 reliability of each arc is
known in advance. However, this is not always the case. Functioning components
operate under 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 are uncertain, we introduce the fuzzy concept for the
analysis of these components, and propose a new algorithm to solve this
uncertainty-component BN reliability problem. The time complexity of the
proposed algorithm is analyzed, and the superior performance of the algorithm
is demonstrated through examples.
