A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we applied the notion of vague sets to multigraphs and we introduce the concepts of vague multiset and Vague multigraph, which are two subclass of vague sets and vague graphs, respectively. Then we define the fundamental concepts of Vague multigraphs and get some related results. Moreover, by considering the notions of strength of edge, effective edge and effective vague multigraph, we investigate the planarity of a vague multigraph. Finally, we give an application for designing and modeling of streets in a city, by vague multigraphs.
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This study was funded by Shahid Beheshti University.
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Communicated by V. Loia.
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Baghernejad, M., Borzooei, R.A. Vague multigraphs. Soft Comput 23, 12607–12619 (2019). https://doi.org/10.1007/s00500-019-03814-w
- Vague graph
- Vague multiset
- Vague multigraph
- Planarity of vague multigraph