Advertisement

Bipolar Fuzzy (Directed) Hypergraphs

Chapter
  • 177 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 390)

Abstract

In this chapter, we present the concept of bipolar fuzzy hypergraphs and directed hypergraphs. We describe certain operations on bipolar fuzzy directed hypergraphs, which include addition, multiplication, vertex-wise multiplication, and structural subtraction.

References

  1. 1.
    Akram, M.: Bipolar fuzzy graphs. Inf. Sci. 181, 5548–5564 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Akram, M.: Bipolar fuzzy graphs with applications. Knowl. Based Syst. 39, 1–8 (2013)CrossRefGoogle Scholar
  3. 3.
    Akram, M., Dudek, W.A., Sarwar, S.: Properties of bipolar fuzzy hypergraphs. Ital. J. Pure Appl. Math. 31, 141–160 (2013)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Akram, A., Luqman, A.: Certain concepts of bipolar fuzzy directed hypergraphs. Mathematics 5(1), 17 (2017)CrossRefGoogle Scholar
  5. 5.
    Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  6. 6.
    Chen, S.M.: Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. (Cybernetics) 27(4), 725–733 (1997)Google Scholar
  7. 7.
    Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discret. Appl. Math. 42, 177–201 (1993)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, 1. Masson, Paris (1977)Google Scholar
  9. 9.
    Lee, K.M.: Bipolar-valued fuzzy sets and their basic operations. In: Proceedings of the International Conference, Bangkok, Thailand, pp. 307–317 (2000)Google Scholar
  10. 10.
    Lee, K.-M.: Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets. J. Fuzzy Logic Intell. Syst. 14(2), 125–129 (2004)Google Scholar
  11. 11.
    Lee-kwang, H., Lee, K.-M.: Fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. 25(1), 196–201 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)zbMATHGoogle Scholar
  13. 13.
    Parvathi, R., Thilagavathi, S., Karunambigai, M.G.: Intuitionistic fuzzy hypergraphs. Cybern. Inf. Technol. 9(2), 46–53 (2009)MathSciNetGoogle Scholar
  14. 14.
    Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications, pp. 77–95. Academic Press, New York (1975)Google Scholar
  15. 15.
    Samanta, S., Pal, M.: Bipolar fuzzy hypergraphs. Int. J. Fuzzy Logic Syst. 2(1), 17–28 (2012)CrossRefGoogle Scholar
  16. 16.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  17. 17.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhang, W.R.: Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis. In: Proceedings of the IEEE Conference, pp. 305–309 (1994)Google Scholar
  19. 19.
    Zhang, W.R.: YinYang bipolar fuzzy sets. In: Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence, pp. 835–840 (1998)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsUniversity of the PunjabLahorePakistan

Personalised recommendations