DOI QR코드

DOI QR Code

Fuzzy ideal graphs of a semigroup

  • Received : 2018.05.23
  • Accepted : 2018.08.18
  • Published : 2018.12.25

Abstract

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

Keywords

References

  1. M. Akram, Bipolar fuzzy graphs, Inform. Sci., 181 (24) (2011) 5548-5564. https://doi.org/10.1016/j.ins.2011.07.037
  2. M. Akram, Interval-valued fuzzy line graphs, Neural Computing and Applications 21 (2012) 145-150.
  3. M. Akram and W. A. Dudek, Interval-valued fuzzy graphs, Computers and Mathematics with Applications 61 (2) (2011) 289-299. https://doi.org/10.1016/j.camwa.2010.11.004
  4. M. Akram and B. Davvaz, Strong intuitionistic fuzzy graphs, Filomat 26 (1) (2012) 177-196. https://doi.org/10.2298/FIL1201177A
  5. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  6. P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letters 6 (5) (1987) 297-302. https://doi.org/10.1016/0167-8655(87)90012-2
  7. S. M. Hong, Y. B. Jun and J. Meng, Fuzzy interior ideals in semigroups, Indian J. Pure Appl. Math. 26 (9) (1995) 859-863.
  8. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London 1976.
  9. Y. B. Jun and C. Y. Lee, Fuzzy $\Gamma$-rings, Pusan kyongnan Math. J. 8 (1991) 163-170.
  10. A. Kauffman, Introduction a la Theorie des Sous-emsembles Flous 1 1973.
  11. N. Kuroki, On fuzzy semigroups, Inform. Sci. 53 (3) (1991) 203-236. https://doi.org/10.1016/0020-0255(91)90037-U
  12. J. N. Mordeson and C. S. Peng, Operations on fuzzy graphs, Inform. Sci. 79 (3-4) (1994) 159-170. https://doi.org/10.1016/0020-0255(94)90116-3
  13. J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy Semigroups of Studies in Fuzziness and Soft Computing, Springer, Berlin, Germany 131 2003.
  14. M. Murali Krishna Rao, Ideals in ordered $\Gamma$-semiring, Discussiones Mathematicae General Algebra and Applications 38 (2018) 47-68. https://doi.org/10.7151/dmgaa.1284
  15. M. Murali Krishna Rao, bi-interior Ideals in semigroups, Discussiones Mathematicae General Algebra and Applications 38 (2018) 69-78. https://doi.org/10.7151/dmgaa.1283
  16. M. Murali Krishna Rao, T-fuzzy ideals in ordered $\Gamma$-semirings, Ann. Fuzzy Math. Inform. 13 (2) (2017) 253-276. https://doi.org/10.30948/afmi.2017.13.2.253
  17. M. Murali Krishna Rao, Left bi-quasi ideals of semirings, Bull. Int. Math. Virtual Inst. 8 (1) (2018) 45-53.
  18. M. Murali Krishna Rao, Bi-quasi-ideals and fuzzy bi-quasi ideals of $\Gamma$-semigroups, Bull. Int. Math. Virtual Inst. 7 (2) (2017) 231-242.
  19. M. Murali Krishna Rao, B. Venkateswarlu and N.Rafi, Left bi-quasi-ideals of $\Gamma$-semirings, Asia Pacific Journal of Mathematics 4 (2) (2017) 144-153.
  20. M. Murali Krishna Rao, Fuzzy soft $\Gamma$-semiring and fuzzy soft k-ideal over $\Gamma$-semiring, Ann. Fuzzy Math. Inform. 9 (2) (2015) 12-25.
  21. Marapureddy Murali Krishna Rao, Fuzzy graph of semigroup, Bull. Int. Math. Virtual Inst. 8 (3) (2018) 439-448.
  22. A. Rosenfeld, Fuzzy groups, J. Math. Anal .Appl. 35 (1971) 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  23. A. Rosenfeld, Fuzzy graphs in Fuzzy Sets and Their Applications, Academic Press, New York, NY, USA (1975) 77-95.
  24. M. S. Sunitha and A. V. Kumar, Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics 33 (9) (2002) 1451-1464.
  25. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X