Interval valuedm-polar fuzzy planar graph and its application

In this article, a new idea of interval-valuedm-polar fuzzy (IVmPF) graph is introduced and investigated some of it's properties. Here, IVmPF multiset, interval-valuedm-polar fuzzy (IVmPF) multi graph are presented. IVmPF planar value of an interval-valuedm-polar fuzzy (IVmPF) planar graph along with degree of planarity value is also introduced to measure the planarity value of an interval-valuedm-polar fuzzy (IVmPF) graph. Some related terms like complete IVmPF graph, strong IVmPF graph, strong edges, faces of IVmPF planar graph are presented. In this paper, IVmPF dual graph is also described which is closely related to IVmPF planar graph. Some important properties are studied on IVmPF dual graph. Lastly, a real life application on IVmPF planar graph has been discussed to show its practicability.

Automated summary

This article introduces the concept and properties of interval-valued m-polar fuzzy (IVmPF) graph, including IVmPF multiset, IVmPF multi graph, the planarity value of IVmPF planar graph, and IVmPF dual graph. It also studies some important properties of IVmPF dual graph and discusses a real-life application of IVmPF planar graph.