Analysis of Social Networks, Communication Networks and Shortest Path Problems in the Environment of Interval-Valued q-Rung Ortho Pair Fuzzy Graphs

The ideas of q-rung ortho pair fuzzy set (q-ROPFS) and interval-valued q-rung ortho pair fuzzy set (IVq-ROPFS) are two major recent developments in the field of fuzzy set theory. A q-ROPFS and IVq-ROPFS improved the limited structures of Pythagorean fuzzy set, intuitionistic fuzzy set as well as fuzzy set by improving the conditions that makes these concepts restricted. The goal of this research is to introduce a new notion of interval-valued q-rung ortho pair fuzzy graph (IVQ-ROPFG) and to study the related graphical terms such as subgraph, complement, degree of vertices and path etc. Each of the graphical concept is demonstrated with an example. Another valuable contribution of this manuscript is the modeling of some traffic networks, telephone networks and social networks using the concepts of IVQ-ROPFGs. First, the famous problem of finding a shortest path in a traffic network is studied using two different approaches. A study of social network describing the strength of co-authorship between different researchers from several countries is also established using the concept of IVq-ROPFGs. Finally, a telephone networking problem is demonstrated showing the calling ratios of incoming and outgoing calls among a group of people. Two engineering decision-making problems are also studied using some aggregation operators and the concepts of IVq-ROPFGs. Through comparative study, the advantages of working in the environment of IVq-ROPFG are specified.