Document Type: Research Paper


1 Department Of Mathematics, Islamic Azad University of Kerman, Kerman, Iran

2 Department Of Mathematics, Shahid Bahonar University Of Kerman, Kerman, Iran


In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper K-ideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between intuitionistic fuzzy (weak) dual hyper K-ideals and intuitionistic fuzzy (weak) hyper K-ideals. Finally, we define the notion of the product of two intuitionistic fuzzy (weak) dual hyper K-ideals and prove several Decomposition Theorems.


[1] K. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.

[2] R. A. Borzooei and M. M. Zahedi,Positive implicative hyper K-ideals, Scientiae Mathematicae

Japonicae,53(3) (2001), 525-533.

[3] R. A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun,On hyper K-algebras, Math.

Japon.,52(1) (2000), 113-121.

[4] P. Corsini and V. Leoreanu,Applications of hyper structure theory, Kluwer Academic Publishers,


[5] Y. Imai and K. Iseki,On axiom systems of propositional calculi, XIV Proc. Japan Academy,

42(1966), 19-22.

[6] K. Iseki and S. Tanaka,An introduction to the theory of BCK-algebras, Math. Japon, 23

(1978), 1-26.

[7] F. Marty,Sur une generalization de la notion de groups, 8th congress Math. Scandinaves,

Stockholm, (1934), 45-49.

[8] J. Meng and Y. B. Jun,BCK-algebras, Kyung Moonsa, Seoul, Korea, 1994.

[9] L. Torkzadeh and M. M. Zahedi,Dual positive implicative hyper K-ideals of type 4, J. Quasigroups

and Related Systems,9 (2002), 85-106.

[10] L. Torkzadeh and M. M. Zahedi,(Weak) dual hyper K-ideals , Soft Computing, to appear.

[11] L. Torkzadeh and M. M. Zahedi,(Anti) fuzzy dual positive implicative hyper K-ideals, Italian

Journal of Pure and Applied Mathematics,17 (2005), 69-82.

[12] L. Torkzadeh and M. M. Zahedi,Intuitionistic fuzzy commutative hyper K-ideals, J. Appl.

Math. & Computing, to appear.

[13] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338-353.