Considering all physical, biological, and social systems, fuzzy graph models serve the elemental processes of all-natural and artificial structures. As the indeterminate information is a necessary real-life problem, which is mostly uncertain, modeling those problems based on FG is highly demanding for an expert. Interval-valued intuitionistic fuzzy graph (IVIFG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which fuzzy graphs possibly will not succeed in bringing about satisfactory results. Also, IVIFGs are so useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The m-polar IVIFG is a novel concept of IVIFGs. Hence, in this paper, we introduce the notion of m-polar f-morphism on m-polar IVIFGs. The action of m-polar f-morphism on m-polar IVIFGs is studied. Some elegant theorems on weak and co-weak isomorphism are obtained. Likewise, we survey m-polar f-morphism on strong regular IVIFG and highly irregular m-polar IVIFG.
