Browse > Article
http://dx.doi.org/10.5391/IJFIS.2006.6.4.321

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)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.6, no.4, 2006 , pp. 321-330 More about this Journal
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
semiring; (intuitionistic fuzzy weak) congruence; (intuitionistic fuzzy) ideal; (intuitionistic fuzzy) k-ideal; intuitionistic fuzzy quotient semiring;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Baldev Banerjee and Dhiren Kr. Basnet, Intuitionistic fuzzy subrings and ideals, J. Fuzzy Math. 11(1) (2003), 139-155
2 S. Bourne and H. Zassenhaus, On semiradical of a semiring, Proc. Nat. Acad., 44(1958), 907-914
3 D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88(1997), 81-89   DOI   ScienceOn
4 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
5 K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2) (2005), 163-181
6 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)
7 N. Kuroki, Fuzzy congruence and fuzzy normal subgroups, Inform. Sci. 66(1992), 235-243   DOI   ScienceOn
8 L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353   DOI
9 L. A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971), 177-200   DOI   ScienceOn
10 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
11 T. Yijia, Fuzzy congruences on a regular semigroup, Fuzzy sets and Systems 117 (2001), 447-453   DOI   ScienceOn
12 K. Hur, S. Y. Jang and Y. B. Jun, Intuitionistic fuzzy congruences, Far East J. Math. Sci. 17(1) (2005), 1-29
13 S. J. Lee and E. P. Lee, The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc. 37(1) (2000), 63-76
14 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   DOI   ScienceOn
15 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   과학기술학회마을
16 M. Samhan, Fuzzy congruences on semigroups, Inform. Sci. 74 (1993), 165-175   DOI   ScienceOn
17 K. Hur, H. W. Kang and H. K. Song, Intuitionistic fuzzy subgroups and subrings, Honam Mathematical J. 25(2) (2003), 19-41
18 K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy congruences on a lattice, J. Appl. Math & Computing 18(12) (2005), 465-486
19 R. Biswas, Intuitionistic fuzzy subgroups, Mathematical Forum x(1989), 37-46
20 G. Deschrijver and E. E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems 136 (2003), 333-361   DOI   ScienceOn
21 K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96   DOI   ScienceOn
22 H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems 78 (1996), 293-303   DOI   ScienceOn
23 K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic fuzzy subgroups and cosets, Honam Math. J, 26(1) (2004), 17-41
24 K. Hur, K. J. Kim and H. K. Song, Intuitionistic fuzzy ideals and bi-ideals, Honam Math. J. 26(3) (2004), 309-330
25 V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems 41 (1991), 359-369   DOI   ScienceOn