Some novel concepts of interval-valued picture fuzzy graphs with applications toward the Transmission Control Protocol and social networks

Abstract

The Transmission Control Protocol 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. The interval-valued picture fuzzy set being the most generalized form of fuzzy set has more capacity to analyze the 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. First, basic concepts such as degree, order, and size are discussed, followed by operations such as union, intersection, Cartesian product, composition, and the ring sum of IVPFGs. Then, we provide a few relationships 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 a few structural properties of IVPFGs through these arcs. Finally, we give a clue about the potential implementation of IVPFGs, an extension of the fuzzy logic-based Transmission Control Protocol and toward social networking.