Abstract
Interval-valued intuitionistic fuzzy graphs (IVIFGs) have many fields of work in other sciences, including psychology, life sciences, medicine, and social studies, and can help researchers with optimization and save time and money. A very important type of IVIFG is an m-polar IVIFG that can play a significant role in managing and finding effective people in a company or institution. It can also be used to achieve very important results in the field of psychological sciences and social relations. Hence, in this study, we presented the notion of m-polar h-morphism on m-polar IVIFGs. Some elegant theorems on weak isomorphism (WI) and co-weak isomorphism (CWI) are obtained. Likewise, we survey m-polar h-morphism on strong regular (SR) and highly irregular (HI) m-polar-IVIFGs. Management always plays an important role in an organization and can cause its growth and prosperity. But finding a strong leader is a very important issue that needs to be addressed. Therefore, in the last section, we have tried to express the application of the m-polar IVIFG in the management problem.