Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NOVEL DECISION MAKING METHOD BASED ON DOMINATION IN m-POLAR FUZZY GRAPHS

  • Akram, Muhammad (Department of Mathematics University of the Punjab New Campus) ;
  • Waseem, Neha (Department of Mathematics University of the Punjab New Campus)
  • Received : 2016.12.31
  • Accepted : 2017.06.14
  • Published : 2017.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this research article, we introduce certain concepts, including domination, total domination, strong domination, weak domination, edge domination and total edge domination in m-polar fuzzy graphs. We describe these concepts by several examples. We investigate some related properties of certain dominations in m-polar fuzzy graphs. We also present a decision making method based on domination in m-polar fuzzy graphs.

Keywords

References

  1. M. Akram, Bipolar fuzzy graphs, Inform. Sci. 181 (2011), no. 24, 5548-5564. https://doi.org/10.1016/j.ins.2011.07.037
  2. M. Akram and A. Adeel, m-polar fuzzy labeling graphs with application, Math. Comput. Sci. 10 (2016), no. 3, 387-402. https://doi.org/10.1007/s11786-016-0277-x
  3. M. Akram and A. Adeel, Representation of labeling tree based on m-polar fuzzy sets, Ann. Fuzzy Math. Inform. 13 (2017), no. 2, 189-197.
  4. M. Akram and N. Waseem, Certain metrics in m-polar fuzzy graphs, New Math. Nat. Comput. 12 (2016), no. 2, 135-155. https://doi.org/10.1142/S1793005716500101
  5. M. Akram, N. Waseem, and W. A. Dudek, Certain types of edge m-polar fuzzy graphs, Iran. J. Fuzzy Syst. 14 (2017), no. 4, 1-25.
  6. M. Akram and H. R. Younas, Certain types of irregular m-polar fuzzy graphs, J. Appl. Math. Comput. 53 (2017), no. 1, 365-382. https://doi.org/10.1007/s12190-015-0972-9
  7. P. Bhattacharya, Some remarks on fuzzy graphs, Pattern. Recognit. Lett. 6 (1987), 297-302. https://doi.org/10.1016/0167-8655(87)90012-2
  8. J. Chen, S. Li, S. Ma, and X. Wang, m-polar fuzzy sets: An extension of bipolar fuzzy sets, Sci. World. J. 2014 (2014), Article Id 416530, 8 pp.
  9. E. J. Cockayne and S. T. Hedetnieme, Towards a theory of domination in graphs, Net- works 7 (1977), no. 3, 247-261.
  10. P. Debnath, Domination in interval-valued fuzzy graphs, Ann. Fuzzy Math. Inform. 6 (2013), no. 2, 363-370.
  11. A. Kauffman, Introduction to la Theorie des Sous-emsembles Flous, Masson et Cie 1 (1973).
  12. A. Nagoorgani and M. B. Ahamed, Strong and weak domination in fuzzy graphs, East Asian Math. J. 23 (2007), no. 1, 1-8.
  13. A. Nagoorgani and V. T. Chandrasekaran, Domination in fuzzy graph, Adv. Fuzzy Sets. Syst. 1 (2006), no. 1, 17-26.
  14. A. Nagoorgani and P. Vadivel, Fuzzy independent dominating set, Adv. Fuzzy Sets. Syst. 2 (2007), no. 1, 99-108.
  15. O. Ore, Theory of Graphs, American Mathematical Society, Colloquium Publications, 38, Providence, 1962.
  16. R. Paravathi and G. Thamizhendhi, Domination in intuitionistic fuzzy graphs, Four- teenth International Conference on IFSs, Sofia, 15-16 May 2010, 16 (2010), no. 2, 39-49.
  17. C. Y. Ponnappan, S. B. Ahamed, and P. Surulinathan, Edge domination in fuzzy graphs- New Approach, Int. J. IT. Engr. Appl. Sci. Res. 4 (2015), no. 1, 14-17.
  18. A. Rosenfeld, Fuzzy graphs, Fuzzy Sets Appl., 77-95, Academic Press, New York, 1975.
  19. P. Slater, S. Hedetniemi, and T. W. Haynes, Fundamentals of Domination in Graphs, CRC Press, 1998.
  20. A. Somasundram and S. Somasundram, Domination in fuzzy graphs-I, Pattern. Recog- nit. Lett. 19 (1998), 787-791. https://doi.org/10.1016/S0167-8655(98)00064-6
  21. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  22. L. A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971), no. 2, 177-200. https://doi.org/10.1016/S0020-0255(71)80005-1