DOI QR코드

DOI QR Code

INTERVAL-VALUED FUZZY SUBGROUPS AND LEVEL SUBGROUPS

Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki

  • Received : 2013.07.22
  • Accepted : 2013.07.29
  • Published : 2013.09.25

Abstract

We introduce the concept of level subgroups of an interval-valued fuzzy subgroup and study some of its properties. These level subgroups in turn play an important role in the characterization of all interval-valued fuzzy subgroup of a prime cyclic group.

Keywords

interval-valued fuzzy set;interval-valued fuzzy subgroup;level subgroup

References

  1. R. Biswas, Rosenfeld's fuzzy subgroups with interval-valued membership functions, Fuzzy set and systems 63 (1995), 87-90.
  2. M. Cheong and K. Hur, Interval-valued fuzzy ideals and bi-ideals of a semi-group, IJFIS 11 (2011), 259-266. https://doi.org/10.5391/IJFIS.2011.11.4.259
  3. J. Y. Choi, S. R. Kim and K. Hur, Interval-valued smooth topological spaces, Honam Math. J. 32(4) (2010), 711-738. https://doi.org/10.5831/HMJ.2010.32.4.711
  4. M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and Systems 21 (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
  5. S. Y. Jang, K. Hur and P. K. Lim, Interval-valued fuzzy normal subgroups, IJFIS 12(3) (2012), 205-214. https://doi.org/10.5391/IJFIS.2012.12.3.205
  6. Y. B. Jun, J. J. Bae, S. H. Cho and C. S. Kim, Interval-valued fuzzy strong semi-openness and interval-valued fuzzy strong semi-continuity, Honam Math. J. 28(3) (2006), 417-431.
  7. H. Kang, Interval-valued fuzzy subgroups and homomorphisms, Honam Math. J. 33(4) (2011), 499-518. https://doi.org/10.5831/HMJ.2011.33.4.499
  8. H. Kang and K.Hur, Interval-valued fuzzy subgroups and rings, Honam Math. J. 32(4) (2010), 593-617. https://doi.org/10.5831/HMJ.2010.32.4.593
  9. K. C. Lee, H. Kang and K.Hur, Interval-valued fuzzy generalized bi-ideals of a semigroup, Honam Math. J. 33(4) (2011), 603-611. https://doi.org/10.5831/HMJ.2011.33.4.603
  10. T.K.Mondal and S.K.Samanta, Topology of interval-valued fuzzy sets, Indian J. Pure Appl. Math. 30(1) (1999), 20-38.
  11. L.A.Zadeh, Fuzzy sets, Inform and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  12. L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci 8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5

Cited by

  1. ON INTERVAL-VALUED FUZZY LATTICES vol.37, pp.2, 2015, https://doi.org/10.5831/HMJ.2015.37.2.187

Acknowledgement

Supported by : Wonkwang University