Characterizations of (∈, ∈ ∨ q) -interval valued fuzzy H-ideals in BCK-algebras
Keywords:
BCK-algebra, (∈, ∈ ∨ q) -interval valued fuzzy H-ideal, ∈ ∨ q) -interval valued fuzzy H-ideal.Abstract
In this paper, we define the concepts of (∈, ∈ ∨ q) -interval valued fuzzy H-ideals and(∈, ∈ ∨ q) -interval valued fuzzy H-ideals in BCK-algebras and investigated some of theirrelated properties. Some characterizations of these generalized interval valued fuzzy H-idealare derived.References
Bhakat, S. K. 2000. (∈, ∈ ∨ q) -fuzzy normal, quasinormal and maximal subgroups. Fuzzy Sets and Systems 112: 299-312.
Bhakat, S. K. & Das, P. 1996. (∈, ∈ ∨ q) -fuzzy subgroups. Fuzzy Sets and Systems 80: 359-368.
Biswas, R. 1994. Rosenfeld’s fuzzy subgroups with interval valued membership functions. Fuzzy Sets and System 63: 87-90.
Davvaz, B. 2006. (∈, ∈ ∨ q) -fuzzy subnear-rings and ideals. Soft Computing 10: 206-211.
Davvaz, B. & Corsini, P. 2007. Redefined fuzzy Hv-submodules and many valued implications. Information Sciences 177: 865-875.
Deschrijver, G. 2007. Arithmetic operators in interval valued fuzzy theory. Information Sciences 177: 2906-2924.
Gorzalczany, M. B. 1987. A method of inference in approximate reasoning based on interval valued fuzzy sets. Fuzzy Sets and System 21: 1-17.
Imai, Y. & Iseki, K. 1966. On axiom system of proposition calculi XIV. Proceeding of the Japan Academy 42: 19-22.
Iseki, K. 1980. On BCI-algebras. Mathematics Seminar Notes 8: 125-130.
Iseki, K. & Tanaka, S. 1978. An introduction to the theory of BCK-algebra. Mathematica Japonica 23: 1-26.
Jun, Y. B. 2000. Interval-valued fuzzy subalgebras/ideals in BCK-algebras. Scientiae Mathematicae 3: 435-444.
Jun, Y. B. 2001. Interval-valued fuzzy ideals in BCI-algebras. The Journal of fuzzy Mathematics 9(4): 807-814.
Jun, Y. B. 2004. On (α, β)-fuzzy ideals of BCK/BCI-algebras. Scientiae Mathematicae Japonicae 60: 613-617.
Jun, Y. B. 2005. On (α, β)-fuzzy subalgebras of BCK/BCI-algebras. Bulletin of the Korean Mathematical Society 42: 703-711.
Khalid, H. M. & Ahmad, B. 1999. Fuzzy H-ideals in BCI-algebras. Fuzzy Sets and Systems 101: 153-158.
Ma, X., Zhan, J., Davvaz, B. & Jun, Y. B. 2008. Some kinds of (∈, ∈ ∨ q) -interval valued fuzzy ideals of BCI-algebras. Information Sciences 178: 3738-3754.
Ma, X., Zhan, J. & Jun, Y. B. 2009. Some types of (∈, ∈ ∨ q) -interval valued fuzzy ideals of BCIalgebras. Iranian Journal of fuzzy Systems 6: 53-63.
Meng, J. 1994. On ideals in BCK-algebras. Mathematica Japonica 40: 143-154.
Meng, J. & Jun, Y. B. 1994. BCK-algebras. Kyung Moon Sa Co., Seoul, Korean.
Mostafa, S. M. 1997. Fuzzy implicative ideals of BCK-algebras. Fuzzy Sets and Systems 87: 361-368.
Pu, P. M. & Liu, Y. M. 1980. Fuzzy topology I: neighourhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Applications 76:571-599.
Rosenfeld, A. 1971. Fuzzy groups. Journal of Mathematical Analysis and Applications 35: 512-517.
Xi, O. G. 1991. Fuzzy BCK-algebra. Mathematica Japonica 36: 935-942.
Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8: 338-353.
Zadeh, L. A. 1975. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences 8: 199-249.
Zhan, J., Davvaz, B. & Shum, K. P. 2008. A new view of fuzzy hypernear-rings. Information Sciences 178: 425-438.
Zhan, J & Tan, Z. 2003. Characterizations of doubt fuzzy H-ideals in BCK-algebras. Soochow Journal of Mathematics 29(3): 293-298.
Zhan, J & Tan, Z. 2005. Fuzzy H-ideals in BCK-algebras. Southeast Asian Bulletin of Mathematics 29(6): 1165-1173.
