Vague multigraphs

Abstract

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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References

  1. Akram M, Chen W, Shum KP (2013) Some properties of vague graphs. Southeast Asian Bull Math 37:307–324

    MathSciNet  MATH  Google Scholar 

  2. Akram M, Feng F, Sarwar S, Jun YB (2014) Certain types of vague graphs. Univ Politeh Buchar Sci Bull Ser A 67:141–154

    MathSciNet  MATH  Google Scholar 

  3. Akram M, Gani N, Saeid A Borumand (2014) Vague hypergraphs. J Intell Fuzzy Syst 26:647–653

    MathSciNet  MATH  Google Scholar 

  4. Akram M, Sarwar M, Borzooei RA (2018) A novel decision-making approach based on hypergraphs in intuitionistic fuzzy environment. J Intell Fuzzy Syst 35:1905–1922

    Article  Google Scholar 

  5. Baowen L, Peizhuang W, Xihui L, Yong S (1988) Fuzzy bags and relations with set-valued statistics. Comput Math Appl 15(10):811–818

    MathSciNet  Article  Google Scholar 

  6. Bhattacharya P (1987) Some ramarks on fuzzy graphs. Pattern Recognit Lett 6:297–302

    Article  Google Scholar 

  7. Blizard WD (1988) Multiset theory. Notre Dame J Form Log 30(1):36–66

    MathSciNet  Article  Google Scholar 

  8. Borzooei RA, Rashmanlou H (2015) Degree of vertices in vague graphs. J Appl Math Inform 33(50):545–557

    MathSciNet  Article  Google Scholar 

  9. Borzooei RA, Rashmanlou H (2015) Dominating in vague graph and its applications. J Intell Fuzzy Syst 29:1933–1940

    Article  Google Scholar 

  10. Diestel R (2017) Graph theory, 5th edn. Springer, Berlin

    Google Scholar 

  11. Gau WL, Buherer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23:610–614

    Article  Google Scholar 

  12. Gani AN, Latha SR (2012) On irregular fuzzy graphs. Appl Math Sci 6:517–523

    MathSciNet  MATH  Google Scholar 

  13. Pramanik T, Samanta S, Pal M (2016) Interval-valued fuzzy planar graphs. Int J Mach Learn Cybern 7(4):653–664

    Article  Google Scholar 

  14. Samanta S, Pal M (2013) Concept of fuzzy planar graphs. Proceedings of science and information conference, London, 5–7, 557–563

  15. Maheswari NRS, Sekar C (2015) Semi neighbourly irregular graphs. Int J Comb Graph Theory Appl 5(2):135–144

    Google Scholar 

  16. Ramakrishna N (2009) Vague graphs. Int J Comput Cognit 7:51–58

    Google Scholar 

  17. Rashmanlou H, Borzooei RA (2015) Product vague graphs and its applications. J Intell Fuzzy Syst 30(1):371–382

    Article  Google Scholar 

  18. Rosenfeld A (1975) Fuzzy graphs, fuzzy sets and their applications. Academic Press, Cambridge, pp 77–95

    Google Scholar 

  19. Yager RR (1986) On the theory of bags. Int. Syst. 13:23–37

    MathSciNet  Article  Google Scholar 

  20. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

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Acknowledgements

This study was funded by Shahid Beheshti University.

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Correspondence to R. A. Borzooei.

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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

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Keywords

  • Vague graph
  • Vague multiset
  • Vague multigraph
  • Planarity of vague multigraph