International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

INTUITIONISTIC FUZZY NORMAL SUBGROUP AND INTUITIONISTIC FUZZY ⊙-CONGRUENCES

  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Tecchnology Institute, Wonkwang University) ;
  • Kim, So-Ra (Division of Mathematics and Informational Statistics, and Nanoscale Science and Tecchnology Institute, Wonkwang University) ;
  • Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Tecchnology Institute, Wonkwang University)
  • Published : 2009.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

We unite the two con concepts - normality We unite the two con concepts - normality and congruence - in an intuitionistic fuzzy subgroup setting. In particular, we prove that every intuitionistic fuzzy congruence determines an intuitionistic fuzzy subgroup. Conversely, given an intuitionistic fuzzy normal subgroup, we can associate an intuitionistic fuzzy congruence. The association between intuitionistic fuzzy normal sbgroups and intuitionistic fuzzy congruences is bijective and unigue. This leads to a new concept of cosets and a corresponding concept of guotient.

Keywords

References

  1. K. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets and Systems pp.87-96, 1986 https://doi.org/10.1016/S0165-0114(86)80034-3
  2. Baldev Banerjee & Dhien Kr. Basnet: Intuitionistic fuzzy subrings and ideals. J. Fuzzy Math. 11(1) pp.139-155,2003
  3. R. Biswas: Intuitionistic fuzzy subgroups. Mathematical Forum $\chi$ pp.37-46,1989
  4. H. Bustince & P. Burillo: Structures on intuitionistic fuzzy relations. Fuzzy Sets and Systems pp.293-303,1996 https://doi.org/10.1016/0165-0114(96)84610-0
  5. D. Cokcr: An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systerns 88 pp.81-89,1997 https://doi.org/10.1016/S0165-0114(96)00076-0
  6. D. Cokcr & A. Haydar Es: On fuzzy compactness in intuitionistic fuzzy topo logical spaces. J. Fuzzy Math. 3 pp.899-909,1995
  7. G. Deschrijver & E. E. Kerre: On the composition ofintuitionistic fuzzy relations. Fuzzy Sets and Systems 136 pp.333-361,2003 https://doi.org/10.1016/S0165-0114(02)00269-5
  8. T. K. Dutta & B. K. Biswas: On fuzzy congruence of a near-ring module. Fuzzy Sets and Systems 112 pp.343-348,2004 https://doi.org/10.1016/S0165-0114(97)00411-9
  9. H. Gurcay, D. Coker & A. Haydar Es: On fuzzy continuity in intuitionistic fuzzy topo-logical spaces. J. Fuzzy Math. 5pp.365-378,1997
  10. K. Hur, S. Y. jang & H. W. Kang: Intuitionistic fuzzy subgroupoids. International journal of Fuzzy Logic and Intelligent Systems 3(1) pp.72-77,2003 https://doi.org/10.5391/IJFIS.2003.3.1.072
  11. K. Hur, H. W. Kang & H. K. Song: Intuitionistic fuzzy subgroups and subrings. Honam Mathematical J. 25(2) pp.19-41,2003
  12. K. Hur, S. Y. Jang & H. W. Kang: Intuitionistic fuzzy subgroups and cosets. Honam Math. J. 26(1 )pp.17-41 ,2004
  13. K. Hur, J. H. Kim & J. H. Ryou: Intuitionistic fuzzy topological spaces. J. Korea Soc. Math Educ. Ser. B : Pure Appl. Math. 11(3) pp.243-265, 2004
  14. K. Hur, Y. B. Jun and J. H. Ryou: Intuitionistic fuzzy topological groups. Honam Math J. 26(2) pp.163-192,2004
  15. K. Hur, S. Y. Jang & H. W. Kang: Intuitionistic fuzzy normal subgroups and intuitionistic fuzzy cosets. Honam Math. J. 26(4) pp.559-587,2004
  16. K. Hur, S. Y. Jang & H. W. Kang: Intuitionistic fuzzy equivalence relations. Honam Math. J. 27(2) pp.163-181,2005
  17. K. Hur, S. Y. Jang & H. W. Kang: Intuitionistic fuzzy congruences on a lattice. J. Appl. Math. Cornputing 18(1-2) pp.465-486, 2005
  18. K. Hur, S. Y. Jang & Y. B. Jun: Intuitionistic fuzzy congruemces. Far East J. Math. Sci., 17(1) pp.1-29,2005
  19. K. Hur, S. Y. Jang & H. W. Kang: The lattice of intuitionistic fuzzy congr'uences. International Mathernatical Forum, 1(5) pp.211-236,2006
  20. K. Hur, S. Y. Jang & K. C. Lee: Intuitionistic fuzzy weak congruence on a near-ring module, J. Korea Soc. Math. Educ. Ser B: Pure Appl. Math, 13(3) pp.167-187,2006
  21. K. Hur, S. Y. Jang & K. C. Lee:: Intuitionistic fuzzy weak congruenceson a semiring, International Journal of Fuzzy Logic and Intelligent Systems, 6(4)pp.321-330,2006 https://doi.org/10.5391/IJFIS.2006.6.4.321
  22. S. J. Lee & E. P. Lee: The category of intuitionistic fuzzy topological spaces. Bull. Korean Math. Soc. 37(1) pp.63-76,2000
  23. L. A. Zadeh: Fuzzy sets. Inform. and Control 8 pp.338-353,1965 https://doi.org/10.1016/S0019-9958(65)90241-X