AUTHOR=Rao Yongsheng , Chen Ruxian , Kosari Saeed , Talebi A. A. , Mojahedfar Masome TITLE=A study on vague-valued hesitant fuzzy graph with application JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1007019 DOI=10.3389/fphy.2022.1007019 ISSN=2296-424X ABSTRACT=

The hesitant fuzzy graph (HFG) is one of the most powerful tools to find the strongest influential person in a network. Many problems of practical interest can be modeled and solved by using HFG algorithms. HFGs, belonging to the FG family, have good capabilities when faced with problems that cannot be expressed by FGs. The vague-valued hesitant fuzzy graph (VVHFG) is the generalization of the HFG. A VVHFG is a powerful and useful tool to find the influential person in various parts, such as meetings, conferences, and every group discussion. In this study, we introduce a new concept of the VVHFG. Our purpose is to develop a notion of the VVHFG and also to present some basic definitions, notations, remarks, and proofs related to VVHFGs. We propose a numerical method to find the most dominating person using our proposed work. Finally, an application of the VVHFG in decision-making has been introduced.