New Kind of Vague Graphs with Novel Application
Zehui Shao, Saeed Kosari, Yongsheng Rao, Hossein Rashmanlou and F. Mofidnakhaei
The concepts of fuzzy graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, and image capturing. A vague graph, a generalization of a fuzzy graph, is more useful for decision making problems, social network models and computer network models. In this paper, we introduce the concept of vague neutrosophic graphs. We present the dominating and independent sets of vague neutrosophic graphs. Some properties of regular, totally regular, irregular, and totally irregular vague neutrosophic graphs are discussed. We develop the vague neutrosophic weighted average operator (𝐴ω) and vague neutrosophic weighted geometric operator (𝐺ω) to aggregate the vague neutrosophic information. Furthermore, we develop a vague neutrosophic multiple criteria decision making approach, in which the evaluation values of alternatives on the attributes take the form of vague neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method.
Keywords: Domination set, vague set, vague neutrosophic graph
Mathematics Subject Classification 2000: 03C72,05C99.