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Novel Concepts in Picture Fuzzy Graphs with an Application
Chang Wan, Fei Deng, Shitao Li, Janusz Kacprzyk and Hossein Rashmanlou
Vague graphs (VGs) play an important role in various fields such as computer science, psychology, medicine, political science, etc. and are used to effectively and efficiently find proper people in an organization or social institution. Therefore, in this paper, for the first time, we define the concept of a vague picture fuzzy graph (VPFG) and examine its properties. Likewise, the concepts of a complete-VPFG and a strong-VPFGs are introduced. First, we present several kinds of operations to the VPFGs and then give various products of the VPFGs. New terms such as the order and size, path, busy value, neighborhood degree, isomorphism, and complement of the VPFG are defined. Finally, an application of the VPFG to find the most effective person in a hospital is shown.
Keywords: Vague set, vague graph, picture fuzzy graph, isomorphism, complement, neighborhood degree