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Applied Computational Intelligence and Soft Computing
Volume 2016, Article ID 5859080, 13 pages
http://dx.doi.org/10.1155/2016/5859080
Research Article

Application of Bipolar Fuzzy Sets in Graph Structures

Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan

Received 27 November 2015; Revised 25 December 2015; Accepted 28 December 2015

Academic Editor: Baoding Liu

Copyright © 2016 Muhammad Akram and Rabia Akmal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Sampathkumar, “Generalized graph structures,” Bulletin of Kerala Mathematics Association, vol. 3, no. 2, pp. 65–123, 2006. View at Google Scholar · View at MathSciNet
  2. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at MathSciNet
  3. W.-R. Zhang, “(Yin) (Yang) bipolar fuzzy sets,” in Proceedings of the IEEE International Conference on Fuzzy Systems Proceedings and the IEEE World Congress on Computational Intelligence (FUZZ-IEEE '98), vol. 1, pp. 835–840, IEEE, Anchorage, Alaska, USA, May 1998. View at Publisher · View at Google Scholar
  4. A. Kauffman, Introduction a la Theorie des Sous-Emsembles Flous, vol. 1, Masson et Cie, 1973.
  5. A. Rosenfeld, “Fuzzy graphs,” in Fuzzy Sets and Their Applications, L. A. Zadeh, K. S. Fu, and M. Shimura, Eds., pp. 77–95, Academic Press, New York, NY, USA, 1975. View at Google Scholar
  6. P. Bhattacharya, “Some remarks on fuzzy graphs,” Pattern Recognition Letters, vol. 6, no. 5, pp. 297–302, 1987. View at Publisher · View at Google Scholar · View at Scopus
  7. J. N. Mordeson, P. S. Nair, and J. N. Mordeson, Fuzzy Graphs and Fuzzy Hypergraphs, Second Edition 2001, Physica, Heidelberg, Germany, 2nd edition, 1998.
  8. T. Dinesh, A study on graph structures, incidence algebras and their fuzzy analogues [Ph.D. thesis], Kannur University, Kannur, India, 2011.
  9. M. Akram, “Bipolar fuzzy graphs,” Information Sciences, vol. 181, no. 24, pp. 5548–5564, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Akram, “Bipolar fuzzy graphs with applications,” Knowledge-Based Systems, vol. 39, pp. 1–8, 2013. View at Publisher · View at Google Scholar
  11. M. Akram and W. A. Dudek, “Regular bipolar fuzzy graphs,” Neural Computing & Applications, vol. 21, no. 1, pp. 197–205, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Akram, S.-G. Li, and K. P. Shum, “Antipodal bipolar fuzzy graphs,” Italian Journal of Pure and Applied Mathematics, vol. 31, pp. 97–110, 2013. View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Akram, W. A. Dudek, and S. Sarwar, “Properties of bipolar fuzzy hypergraphs,” Italian Journal of Pure and Applied Mathematics, vol. 31, pp. 426–458, 2013. View at Google Scholar · View at MathSciNet · View at Scopus
  14. N. O. Al-Shehrie and M. Akram, “Bipolar fuzzy competition graphs,” Ars Combinatoria, vol. 121, pp. 385–402, 2015. View at Google Scholar
  15. K.-M. Lee, “Bipolar-valued fuzzy sets and their basic operations,” in Proceedings of the International Conference, pp. 307–317, Bangkok, Thailand, 2000.
  16. S. Mathew and M. S. Sunitha, “Node connectivity and arc connectivity of a fuzzy graph,” Information Sciences, vol. 180, no. 4, pp. 519–531, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. L. A. Zadeh, “Similarity relations and fuzzy orderings,” Information Sciences, vol. 3, no. 2, pp. 177–200, 1971. View at Google Scholar · View at MathSciNet
  18. W.-R. Zhang, “Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis,” in Proceedings of the Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technology Workshop on Neural Networks and Fuzzy Logic, Fuzzy Information Processing Society Biannual Conference, pp. 305–309, San Antonio, Tex, USA, December 2014. View at Publisher · View at Google Scholar