In this note first we define the notions of intuitionistic
fuzzy dual positive implicative hyper K-ideals of types
1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we
give some classifications about these notions according to the
level subsets. Also by given some examples we show that these
notions are not equivalent, however we prove some theorems
which show that there are some relationships between these
notions. Finally we define the notions of product and antiproduct
of two fuzzy subsets and then give some theorems
about the relationships between the intuitionistic fuzzy dual
positive implicative hyper K-ideal of types 1,2,3,4 and their
(anti-)products, in particular we give a main decomposition
theorem.
[1] K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, No.
1 (1986) 87-96.
[2] R.A. Borzooei and M.M. Zahedi, "Positive Implicative hyper K-ideals,"
Scientiae Mathematicae Japonicae, Vol. 53, No. 3 (2001), 525-533.
[3] R.A. Borzooei, A. Hasankhani, M.M. Zahedi and Y.B. Jun, "On hyper
K-algebras" Math. Japon. Vol. 52, No. 1 (2000), 113-121.
[4] Y. Imai and K. Iseki, "On axiom systems of propositional calculi" XIV
Proc. Japan Academy, 42 (1966), 19-22.
[5] K. Iseki and S. Tanaka, "An introduction to the theory of BCK-algebras",
Math. Japon, 23 (1978), 1-26.
[6] F. Marty, "Sur une generalization de la notion de groups", 8th congress
Math. Scandinaves, Stockholm, (1934), 45-49.
[7] J. Meng and Y.B. Jun, "BCK-algebras", Kyung Moonsa, Seoul, Korea,
(1994).
[8] L. Torkzadeh and M.M. Zahedi, "Dual Positive Implicative Hyper KIdeals
of Type 3", J. Quasigroups and Related Systems, 9(2002), 85-106.
[9] L. Torkzadeh and M.M. Zahedi, "Dual Positive Implicative Hyper KIdeals
of Type 1", Submitted.
[10] L. A. Zadeh, "Fuzzy sets", Information and Control, 8 (1965) 338-353.
[1] K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, No.
1 (1986) 87-96.
[2] R.A. Borzooei and M.M. Zahedi, "Positive Implicative hyper K-ideals,"
Scientiae Mathematicae Japonicae, Vol. 53, No. 3 (2001), 525-533.
[3] R.A. Borzooei, A. Hasankhani, M.M. Zahedi and Y.B. Jun, "On hyper
K-algebras" Math. Japon. Vol. 52, No. 1 (2000), 113-121.
[4] Y. Imai and K. Iseki, "On axiom systems of propositional calculi" XIV
Proc. Japan Academy, 42 (1966), 19-22.
[5] K. Iseki and S. Tanaka, "An introduction to the theory of BCK-algebras",
Math. Japon, 23 (1978), 1-26.
[6] F. Marty, "Sur une generalization de la notion de groups", 8th congress
Math. Scandinaves, Stockholm, (1934), 45-49.
[7] J. Meng and Y.B. Jun, "BCK-algebras", Kyung Moonsa, Seoul, Korea,
(1994).
[8] L. Torkzadeh and M.M. Zahedi, "Dual Positive Implicative Hyper KIdeals
of Type 3", J. Quasigroups and Related Systems, 9(2002), 85-106.
[9] L. Torkzadeh and M.M. Zahedi, "Dual Positive Implicative Hyper KIdeals
of Type 1", Submitted.
[10] L. A. Zadeh, "Fuzzy sets", Information and Control, 8 (1965) 338-353.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64108", author = "M.M. Zahedi and L. Torkzadeh", title = "Intuitionistic Fuzzy Dual Positive Implicative Hyper K- Ideals", abstract = "In this note first we define the notions of intuitionistic
fuzzy dual positive implicative hyper K-ideals of types
1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we
give some classifications about these notions according to the
level subsets. Also by given some examples we show that these
notions are not equivalent, however we prove some theorems
which show that there are some relationships between these
notions. Finally we define the notions of product and antiproduct
of two fuzzy subsets and then give some theorems
about the relationships between the intuitionistic fuzzy dual
positive implicative hyper K-ideal of types 1,2,3,4 and their
(anti-)products, in particular we give a main decomposition
theorem.", keywords = "hyper K-algebra, intuitionistic fuzzy dual positive implicative hyper K-ideal.", volume = "1", number = "5", pages = "255-4", }