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

  • Received : 2013.02.12
  • Accepted : 2013.10.25
  • Published : 2013.12.25


We study the conditions under which a given interval-valued fuzzy subgroup of a given group can or can not be realized as a union of two interval-valued fuzzy proper subgroups. Moreover, we provide a simple necessary and su cient condition for the unio of an arbitrary family of interval-valued fuzzy subgroups to be an interval-valued fuzzy subgroup. Also we formulate the concept of interval-valued fuzzy subgroup generated by a given interval-valued fuzzy set by level subgroups. Furthermore we give characterizations of interval-valued fuzzy conjugate subgroups and interval-valued fuzzy characteristic subgroups by their level subgroups. Also we investigate the level subgroups of the homomorphic image of a given interval-valued fuzzy subgroup.


interval-valued fuzzy subgroup;level subgroup;interval-valued fuzzy conjugate subgroup;interval-valued fuzzy characteristic subgroup


  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.
  3. J. Y. Choi, S. R. Kim and K. Hur, Interval-valued smooth topological spaces, Honam Math. J. 32(4) (2010), 711-738.
  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.
  5. S. Y. Jang, K. Hur and P. K. Lim, Interval-valued fuzzy normal subgroups, IJFIS 12(3) (2012), 205-214.
  6. H. Kang, Interval-valued fuzzy subgroups and homomorphisms, Honam Math. J. 33(4) (2011), 499-518.
  7. H. Kang and K. Hur, Interval-valued fuzzy subgroups and rings, Honam Math. J. 32(4) (2010), 593-617.
  8. 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.
  9. K. C. Lee, K. Hur and P. K. Lim, Interval-valued fuzzy subgroups and level subgroups, To be Submitted.
  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.
  12. L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci 8 (1975), 199-249.

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  1. Lattices of Interval-Valued Fuzzy Subgroups vol.14, pp.2, 2014,