Int-Soft Ideals of Pseudo MV-Algebras

Young Bae Jun; Seok-Zun Song; Hashem Bordbar

doi:10.18778/0138-0680.47.1.01

Authors

Young Bae Jun Department of Mathematics Education Gyeongsang National University, Jinju 52828, Korea
Seok-Zun Song Department of Mathematics, Jeju National University, Jeju 690-756, Korea
Hashem Bordbar Department of Mathematics, Shahid Beheshti University, Tehran, Iran

DOI:

https://doi.org/10.18778/0138-0680.47.1.01

Keywords:

int-soft ideal, implicative int-soft ideal

Abstract

The notion of (implicative) int-soft ideal in a pseudo MV -algebra is introduced, and related properties are investigated. Conditions for a soft set to be an int-soft ideal are provided. Characterizations of (implicative) int-soft ideal are considered. The extension property for implicative int-soft ideal is established.

References

[1] H.Bordbar, S. S.Ahn, M.M. Zahedi and Y.B. Jun, Semiring structures based on meet and plus ideals in lower BCK-semilattices, Journal of Computational Analysis and Applications, Vol. 23, No. 5 (2017), pp. 945–954.
Google Scholar

[2] H. Bordbar, R. A. Borzooei, Y. B. Jun, Uni-soft commutative ideals and closed uni-soft ideals in BCI-algebras, New Mathematics and Natural Computation, Vol. 14, No. 2 (2018), pp. 235–247.
Google Scholar

[3] H. Bordbar, H. Harizavi and Y. B. Jun, Uni-soft ideals in coresiduated lattices, Sigma Journal of Engineering and Natural Sciences, Vol. 9, No. 1 (2018), pp. 69–75.
Google Scholar

[4] H. Bordbar, M. Novak, I. Cristea, Properties of reduced meet ideals in lower BCK-semilattices, APLIMAT 2018, pp. 97–109.
Google Scholar

[5] H. Bordbar and M. M. Zahedi, A Finite type Closure Operations on BCK-algebras, Applied Mathematics & Information Sciences Letters, Vol. 4, No. 2 (2016), pp. 1–9.
Google Scholar

[6] H. Bordbar and M. M. Zahedi, Semi-prime Closure Operations on BCK-algebra, Communications of the Korean Mathematical Society Vol. 30, No. 4 (2015), pp. 385–402.
Google Scholar

[7] H. Bordbar, M. M. Zahedi, S. S. Ahn and Y. B. Jun, Weak closure operations on ideals of BCK-algebras, Journal of Computational Analysis and Applications, Vol. 23, No. 2 (2017), pp. 51–64.
Google Scholar

[8] H.Bordbar, M.M. Zahedi and Y.B. Jun, Relative annihilators in lower BCK-semilattices, Mathematical Sciences Letters, Vol. 6, No. 2 (2017), pp. 1–7.
Google Scholar

[9] N. Çağman, F. Çitak and S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2010), pp. 848–855.
Google Scholar

[10] A. Dvurečenskij, On pseudo MV-algebras, Soft Computing 5 (2001), pp. 347–354.
Google Scholar

[11] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), pp. 301–327.
Google Scholar

[12] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Commentationes Mathematicae (Prace Matematyczne) Vol. 47, No. 1 (2007), pp. 31–46.
Google Scholar

[13] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras, Multiple-Valued Logic Vol. 6, No. 1–2 (2001), pp. 95–135.
Google Scholar

[14] Y. B. Jun, S. S. Ahn and K. J. Lee, Classes of int-soft filters in residuated lattices, The Scientific World Journal, Vol. 2014, Article ID 595160, 12 pp.
Google Scholar

[15] Y. B. Jun, K. J. Lee and M. S. Kang, Intersectional soft sets and applications to BCK/BCI-algebras, Communications of the Korean Mathematical Society Vol. 28, No. 1 (2013), pp. 11–24.
Google Scholar

[16] Y. B. Jun, K. J. Lee and E. H. Roh, Intersectional soft BCK/BCI-ideals, Annals of Fuzzy Mathematics and Informatics, Vol. 4, No. 1 (2012), pp. 1–7.
Google Scholar

[17] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences 178 (2008), pp. 2466–2475.
Google Scholar

[18] D. Molodtsov, Soft set theory - First results, Computers & Mathematics with Applications 37 (1999), pp. 19–31.
Google Scholar

[19] J. Rachunek, A non-commutative generalization of MV-algebras, Czechoslovak Mathematical Journal, Vol. 52(127), No. 2 (2002), pp. 255–273.
Google Scholar

[20] A. Walendziak, On implicative ideals of pseudo MV-algebras, Scientiae Mathematicae Japonicae, Vol. 62, No. 2 (2005), pp. 281–287.
Google Scholar