Soft hypergraph for modeling global interactions via social media networks

Soft set theory is a map of a set of parameters to the subsets of a universe which can be utilized to parametrically model the uncertainty. On the other hand, Graph (hypergraph) theory is used to simplify some practical problems. Inspired by these concepts, the notion of "soft hypergraph" is developed as the generalization of both soft graph and hypergraph for important application in social media networking. Based on the structure of soft hypergraph, various techniques and operations are provided including soft sub-hypergraph, extended union, extended intersection, cartesian product and complement with elucidatory examples. As per the current global spread of COVID, most of the national and international interactions and social affairs have been virtually conducted via social media networks, such as Skype, Microsoft Teams, WhatsApp, Telegram, Zoom, Instagram, WeChat, etc. For the purpose of Intelligent management of network systems, we use the "generalized soft hypergraph" to model the global e-communication networking of individuals in online platforms.