Some novel concepts of interval-valued picture fuzzy graphs with applications toward the Transmission Control Protocol and social networks - Shi, Xiaolong; Kosari, Saeed; Khan, Waheed Ahmad (Frontiers in Physics, 2023)
Transmission Control Protocol (TCP) usually involves incomplete and imperfect network states for which sophisticated analysis is needed. Fuzzy logic could be more helpful for the analysis of network state more accurately. Interval-valued picture fuzzy set being most generalized form of fuzzy set has more capacity to analyze network state more intelligently. In this manuscript, we present the concepts of interval-valued picture fuzzy graphs (IVPFGs) as an extension of interval-valued fuzzy graphs and picture fuzzy graphs. Since interval-valued picture fuzzy sets are the most advanced form of fuzzy sets, IVPFGs would be a more efficient tool for handling data containing uncertainties. Firstly, we give basic concepts like degree, order and size are discussed, followed by operations like union, intersection, Cartesian product, composition and the ring sum of IVPFGs. Then, we provide few relationship between the ring sum and edge deletion of IVPFGs. Special types of IVPFGs including complete-IVPFGs, regular-IVPFGs, complement-IVPFGs and strong-IVPFGs are introduced. Concepts such as the strength of arcs, path sequence, strength of the path and connectedness are explored in IVPFGs. Different types of strengths of connectedness are discussed based on specific types of arcs. We also provide few structural properties of IVPFGs through these arcs. Finally, we give a clue about the potential implementation of interval-valued picture fuzzy graphs, an extension of the fuzzy logic-based Transmission Control Protocol (TCP) and towards social networking.