Research Article

Year 2017,
Volume: 14 Issue: 1, - , 01.05.2017
### Abstract

### References

- [1] R. A. Borzoei, A. Hasankhani, M. M. Zahedi, On hyper K-algebra, Math. Japonica, 52, (2000), 113–121.
- [2] P. Corsini, V. Leoreanu, Applications of Hyperstructures Theory, Adv in Math, Kluwer Acad Publ, (2003).
- [3] S. Ghorbani, A. Hasankhani, E. Eslami, Hyper MV-algebras, Set-Valued Mathematics and Applications, 1, (2008),205–222.
- [4] S. Ghorbani, E. Eslami, A. Hasankhani, Uniform Topology and Spectral Topology on Hyper MV-algebras, Quasigroupsand Related Systems, 17, (2009), 39–54.
- [5] S. Ghorbani, M. Jafari, Semi Implication Homomorphisms on Lattice Implication Algebras, The 46th AnnualIranian Mathematics Conference, (2015), 70–73.
- [6] M. Konstantinidou, J. Mittas, An Introduction to the Theory of Hyperlattices. Math. Balkanica, 7, (1977), 187–193.
- [7] F. Marty, Sur une Generalization de la Notation de Group, 8th Congress Math Scandianaves, Stockholm, (1934),45–49.
- [8] J. Mittas, M. Konstantinidou, Introduction `a l’hyperal`ebre de Boole. Math. Balkanica, 6, (1976), 314–320.
- [9] D. Pei, A Survey of Fuzzy Implication Algebras and their Axiomatization, International Journal of ApproximateReasoning, 55, (2014), 1643–1658.
- [10] S. Rasouli, B. Davvaz, Lattices Derived from Hyperlattices,Communications in Algebra, 38, (2010), 2720–2737.
- [11] L. Torkzadeh, S. Ghorbani, Some Characterization of Hyper MV-algebras, J Mahani Math Research Center, 1,(2012), 147–161.
- [12] W. M. Wu, Fuzzy Implication Algebra, Fuzzy Syst. Math., 4(1), (1990), 56–64 (in Chinese).
- [13] Y. Xu, Lattice Implication Algebras, J. Southwest Jiaotong University, 28(1), (1993), 20–27.
- [14] Y. Xu, K. Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math., 2, (1993), 251–260.

Year 2017,
Volume: 14 Issue: 1, - , 01.05.2017
### Abstract

### Keywords

### References

In this paper, we introduce the concept of hyper lattice implication algebras which is established

by combining the concept of hyper lattices and hyper implication algebras. We give some important examples

of hyper lattice implication algebras and obtain some of their properties. Then, we characterize hyper lattice

implication algebras in which 1 is an implication scalar element. We prove that the implication reduction of

hyper lattice implication algebras is a regular commutative fuzzy implication algebra, if 1 is an implication

scalar element. Finally, we define the notion of isomorphisms between two hyper lattice implication algebras

and obtain all of the hyper lattice implication algebras of order 2.

Hyper lattice implication algebra implication scalar element fuzzy implication algebra isomorphism

- [1] R. A. Borzoei, A. Hasankhani, M. M. Zahedi, On hyper K-algebra, Math. Japonica, 52, (2000), 113–121.
- [2] P. Corsini, V. Leoreanu, Applications of Hyperstructures Theory, Adv in Math, Kluwer Acad Publ, (2003).
- [3] S. Ghorbani, A. Hasankhani, E. Eslami, Hyper MV-algebras, Set-Valued Mathematics and Applications, 1, (2008),205–222.
- [4] S. Ghorbani, E. Eslami, A. Hasankhani, Uniform Topology and Spectral Topology on Hyper MV-algebras, Quasigroupsand Related Systems, 17, (2009), 39–54.
- [5] S. Ghorbani, M. Jafari, Semi Implication Homomorphisms on Lattice Implication Algebras, The 46th AnnualIranian Mathematics Conference, (2015), 70–73.
- [6] M. Konstantinidou, J. Mittas, An Introduction to the Theory of Hyperlattices. Math. Balkanica, 7, (1977), 187–193.
- [7] F. Marty, Sur une Generalization de la Notation de Group, 8th Congress Math Scandianaves, Stockholm, (1934),45–49.
- [8] J. Mittas, M. Konstantinidou, Introduction `a l’hyperal`ebre de Boole. Math. Balkanica, 6, (1976), 314–320.
- [9] D. Pei, A Survey of Fuzzy Implication Algebras and their Axiomatization, International Journal of ApproximateReasoning, 55, (2014), 1643–1658.
- [10] S. Rasouli, B. Davvaz, Lattices Derived from Hyperlattices,Communications in Algebra, 38, (2010), 2720–2737.
- [11] L. Torkzadeh, S. Ghorbani, Some Characterization of Hyper MV-algebras, J Mahani Math Research Center, 1,(2012), 147–161.
- [12] W. M. Wu, Fuzzy Implication Algebra, Fuzzy Syst. Math., 4(1), (1990), 56–64 (in Chinese).
- [13] Y. Xu, Lattice Implication Algebras, J. Southwest Jiaotong University, 28(1), (1993), 20–27.
- [14] Y. Xu, K. Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math., 2, (1993), 251–260.

There are 14 citations in total.

Subjects | Engineering |
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Journal Section | Articles |

Authors | |

Publication Date | May 1, 2017 |

Published in Issue | Year 2017 Volume: 14 Issue: 1 |