DOI QR코드

DOI QR Code

INTUITIONISTIC FUZZY WEAK CONGRUENCES ON A SEMIRING

  • Hur, Kul (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Jang, Su-Youn (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Lee, Keon-Chang (Department of Computer Science, Dongshin University)
  • Published : 2006.12.01

Abstract

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

Keywords

References

  1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96 https://doi.org/10.1016/S0165-0114(86)80034-3
  2. Baldev Banerjee and Dhiren Kr. Basnet, Intuitionistic fuzzy subrings and ideals, J. Fuzzy Math. 11(1) (2003), 139-155
  3. R. Biswas, Intuitionistic fuzzy subgroups, Mathematical Forum x(1989), 37-46
  4. S. Bourne and H. Zassenhaus, On semiradical of a semiring, Proc. Nat. Acad., 44(1958), 907-914
  5. H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems 78 (1996), 293-303 https://doi.org/10.1016/0165-0114(96)84610-0
  6. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88(1997), 81-89 https://doi.org/10.1016/S0165-0114(96)00076-0
  7. G. Deschrijver and E. E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems 136 (2003), 333-361 https://doi.org/10.1016/S0165-0114(02)00269-5
  8. T. K. Dutta and B. K. Biswas, Fuzzy congruence and quotient semiring of a semiring, The Journal of Fuzzy Mathematics 4(4) (1996), 737-748
  9. K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems 3(1) (2003), 72-77 https://doi.org/10.5391/IJFIS.2003.3.1.072
  10. K. Hur, H. W. Kang and H. K. Song, Intuitionistic fuzzy subgroups and subrings, Honam Mathematical J. 25(2) (2003), 19-41
  11. K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy subgroups and cosets, Honam Math. J, 26(1) (2004), 17-41
  12. K. Hur, J. H. Kim and J. H. Ryou, Intuitionistic fuzzy topological spaces, J. Korea Soc. Math. Educ. Ser. B : Pure Appl. Math. 11(3) (2004), 243-265
  13. K. Hur, K. J. Kim and H. K. Song, Intuitionistic fuzzy ideals and bi-ideals, Honam Math. J. 26(3) (2004), 309-330
  14. K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy normal subgroups and intuitionistic fuzzy cosets, Honam Math. J. 26(4) (2004), 559-587
  15. K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2) (2005), 163-181
  16. K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy congruences on a lattice, J. Appl. Math & Computing 18(12) (2005), 465-486
  17. K. Hur, S. Y. Jang and Y. B. Jun, Intuitionistic fuzzy congruences, Far East J. Math. Sci. 17(1) (2005), 1-29
  18. K. Hur, S. Y. Jang and K. C. Lee, Intuitionistic fuzzy weak congruence on a near-ring module, J. Korea Soc. Math. Educ. Ser. B : Pure Appl. Math. 13(3) (2006)
  19. N. Kuroki, Fuzzy congruence and fuzzy normal subgroups, Inform. Sci. 66(1992), 235-243 https://doi.org/10.1016/0020-0255(92)90095-P
  20. S. J. Lee and E. P. Lee, The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc. 37(1) (2000), 63-76
  21. V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems 41 (1991), 359-369 https://doi.org/10.1016/0165-0114(91)90138-G
  22. M. Samhan, Fuzzy congruences on semigroups, Inform. Sci. 74 (1993), 165-175 https://doi.org/10.1016/0020-0255(93)90132-6
  23. T. Yijia, Fuzzy congruences on a regular semigroup, Fuzzy sets and Systems 117 (2001), 447-453 https://doi.org/10.1016/S0165-0114(98)00275-9
  24. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X
  25. L. A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971), 177-200 https://doi.org/10.1016/S0020-0255(71)80005-1

Cited by

  1. Intuitionistic fuzzy k-ideals of a semiring vol.9, pp.2, 2009, https://doi.org/10.5391/IJFIS.2009.9.2.110