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=Volume 10 - 2022

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 infuential person in a network. Many problems of
practical interest can be modeled and solved by using HFG
algorithms. HFGs, belonging to the FGs family, have good
capabilities when faced with problems that cannot be expressed by
FGs. Vague-valued hesitant fuzzy graph (VVHFG) is the generalization
of HFG. A VVHFG is a powerful and useful tool to find the
influential person in various parts, as meetings, conferences and
every group discussion. In this paper, we introduce a new concept of
VVHFG. Our purpose is to develop a notion of 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 VVHFG in decision making has been introduced.