Vague multigraphs

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 mul...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 23; no. 23; pp. 12607 - 12619
Main Authors Baghernejad, M., Borzooei, R. A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019
Springer Nature B.V
Subjects
Artificial Intelligence
Computational Intelligence
Control
Engineering
Fuzzy sets
Graph theory
Graphs
Mathematical Logic and Foundations
Mechatronics
Methodologies and Application
Robotics
Set theory
Vague multigraph
Vague graph
Planarity of vague multigraph
Vague multiset
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Summary: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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-019-03814-w