Indian Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access

Fuzzy Point Hyper BCK-algebras


Affiliations
1 Dept. of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran, Islamic Republic of
2 Dept. of Mathematics, Islamic Azad university, Kerman Branch, Kerman, Iran, Islamic Republic of
 

By using the concept of fuzzy points, we generalize the notion of hyper BCK-algebra and the notions of fuzzy point hyper BCK-(sub) algebras, fuzzy point (weak, strong) hyper BCK-ideals, quasi hyper BCK-(sub) algebras and quasi (weak, strong) hyper BCK-ideals are introduced. The relationship between these notions are stated and proved. Finally, we study the condition QH on quasi hyper BCK-algebras.

Keywords

Hyper BCK-algebra, (Quasi, Fuzzy Point) Hyper BCK-algebra, (quasi, Fuzzy Point) Hyper BCK-ideal
User

  • Akram M and Zhan, Jianming (2006) On sensible fuzzy ideals of BCK-algebras with respect to a t-conorm. Int. J. Math. Math. Sci. Vol. 2006, Article ID: 35930, page 1-12.

  • Borzooei R. A and Bakhshi M (2002) Some results on Hyper BCK–algebras. Quasigroups & Related Systems. 11, 9-24.

  • Borzooei R. A and Harizavi H (2003) On decomposable Hyper BCK–algebras. Quasigroups & Related Systems. 13 (2), 193-202.

  • Borzooei R. A and Zahedi M. M (2002) Fuzzy structures on hyper K–algebras. Int. J. of Uncertainly, Fuzziness & Knowledge-Based Systems. 10 (1), 77-93.

  • Imai Y and Iseki K (1969) On axiom systems of propositional calculi. XIV Proc. Japan Acad. 42, 19-22.

  • Jun Y. B and Xin X. L (2001) Fuzzy hyper BCK-ideals of hyper BCK-algebras. Scientiae Mathematicae Japonicae. 53 (2), 353-360.

  • Jun Y. B, Xin X. L, Roh E. H and Zahedi M. M (2000) Strong hyper BCK-ideals of hyper BCK-algebras. Math. Japon. 51 (3), 493-498.

  • Jun Y. B, Zahedi M. M, Xin X. L and Borzooei RA (2000) On hyper BCK-algebras, Italian J. Pure & Applied Math. No.8, 127-136.

  • Marty F (1934) Sur une generalisation de La notion de groupe. 8th Congress Math. Scandinaves, Stockholm, 45-49.

  • Zadeh L. A (1965) Fuzzy sets. Inform. & Control. 8, 338-353.


Abstract Views: 404

PDF Views: 99




  • Fuzzy Point Hyper BCK-algebras

Abstract Views: 404  |  PDF Views: 99

Authors

A. Borumand Saeid
Dept. of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran, Islamic Republic of
L. Torkzadeh
Dept. of Mathematics, Islamic Azad university, Kerman Branch, Kerman, Iran, Islamic Republic of

Abstract


By using the concept of fuzzy points, we generalize the notion of hyper BCK-algebra and the notions of fuzzy point hyper BCK-(sub) algebras, fuzzy point (weak, strong) hyper BCK-ideals, quasi hyper BCK-(sub) algebras and quasi (weak, strong) hyper BCK-ideals are introduced. The relationship between these notions are stated and proved. Finally, we study the condition QH on quasi hyper BCK-algebras.

Keywords


Hyper BCK-algebra, (Quasi, Fuzzy Point) Hyper BCK-algebra, (quasi, Fuzzy Point) Hyper BCK-ideal

References





DOI: https://doi.org/10.17485/ijst%2F2010%2Fv3i5%2F29746