Relationship Between Hyper MV -algebras and Hyperlattices

Borzooei, R. A.; Radfar, Akefe; Niazian, Sogol

doi:10.1515/awutm-2016-0016

Abstract

Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.

References

[1] R. A. Borzooei W. A. Dudek, A. Radfar and O. Zahiri, Some remarks on hyper MV -algebras, Journal of Intelligent and Fuzzy Systems, 27, (2014), 2997-300510.3233/IFS-141258
Search in Google Scholar Back to article
[2] R. A. Borzooei , A. Hasankhani, M. M. Zahedi and Y. B. Jun, On hyper K-algebra, J. Math. Japonica, 1, (2000), 113-121
Search in Google Scholar Back to article
[3] R. A. Borzooei and S. Niazian, Weak hyper residuated lattices, Quasigroups and Related Systems, 21, (2013), 29-42
Search in Google Scholar Back to article
[4] R. A. Borzooei and A. Radfar, Classification of hyper MV -algebras of order 3, Ratio Mathematica, 22, (2012), 3-12
Search in Google Scholar Back to article
[5] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88, (1958), 467-49010.1090/S0002-9947-1958-0094302-9
Search in Google Scholar Back to article
[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers, Dordrecht, 200310.1007/978-1-4757-3714-1
Search in Google Scholar Back to article
[7] Sh. Ghorbani E. Eslami and A. Hasankhani, On the category of hyper MV - algebras, Math. Log. Quart., 55, (2009), 21-3010.1002/malq.200710082
Search in Google Scholar Back to article
[8] Sh. Ghorbani E. Eslami and A. Hasankhani, Quotient hyper MV -algebras, Sci. Math. Japonica, 3, (2007), 371-386
Search in Google Scholar Back to article
[9] Sh. Ghorbani A. Hasankhani and E. Eslami, Hyper MV -algebras, Set-Valued Mathematics and Applications, 1, (2008), 205-222
Search in Google Scholar Back to article
[10] R. S. Grigolia, Algebraic analysis of Lukasiewicz-Tarski logical systems, In Wo- jocicki, R., Malinkowski, G.(eds) Selected papers on Lukasiewicz Sentential Calkuli, Osolineum, 1, (1977), 81-92
Search in Google Scholar Back to article
[11] X. Z. Guo and X. L. Xin, Hyperlattice, Pure and Applied Mayhematics, 20, (2004), 40-43
Search in Google Scholar Back to article
[12] Y. B. Jun M. S. Kang and H. S. Kim, Hyper MV -deductive systems of hyper MV -algebras, Commun. Korean Math. Soc., 20, (2010), 537-54510.4134/CKMS.2010.25.4.537
Search in Google Scholar Back to article
[13] Y. B. Jun M. S. Kang and H. S. Kim, New types of hyper MV -deductive systems in hyper MV -algebras, Math. Log. Quart, 56, (2010), 400-40510.1002/malq.200910011
Search in Google Scholar Back to article
[14] J. Lukasiewicz, On three-valued logic (Polish), Ruch Filozoficzny, 5, (1920), 160-171
Search in Google Scholar Back to article
[15] J. Lukasiewicz and A. Tarski, Unte suchungen uber den Assagenkalkul, C. R. Seances Soc. Sci. Letters Varsovie, 23, (1930), 30-50
Search in Google Scholar Back to article
[16] F. Marty, Sur une generalization de la notion de groups, 8th Congress Math. Scandinaves, Stockholm, (1934), 45-49
Search in Google Scholar Back to article
[17] E. Post, Introduction to a general theory of elementary propositions, Am. J. Math., 43, (1921), 163-18510.2307/2370324
Search in Google Scholar Back to article
[18] L. Torkzadeh and A. Ahadpanah, Hyper MV -ideals in hyper MV -algebras, Math. Log. Quart., 56(1), (2010), 51-6210.1002/malq.200810035
Search in Google Scholar Back to article
[19] M. Ward and R. P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc., 45, (1939), 335-35410.1090/S0002-9947-1939-1501995-3
Search in Google Scholar Back to article
[20] O. Zahiri R. A. Borzooei and M. Bakhshi, (Quotient) Hyper Residuated Lattices, Quasigroups and Related Systems, 20, (2012), 125-138
Search in Google Scholar Back to article

Relationship Between Hyper MV -algebras and Hyperlattices

Abstract

Paradigm

My account