Reliability of Social Networks on Activity-on-Node Binary-State with Uncertainty Environments

Abstract

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.

Keywords

• social networks (SNs)
• binary-state network (BN)
• network reliability
• uncertainty environments
• activity-on-node
• binary-addition-tree algorithm (BAT)