Year 2016 ,
Volume: 13 Issue: 1, - , 01.05.2016
A. Erami
,
A. Hasankhani
A. Borumand Saeid
References
[1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, (2010), 3458-3463.
[2] D. Afkhami Taba, A. Hasankhani, M. Bolurian, Soft nexuses, Comput. Math. Appl., 64(6), (2012), 1812-1821.
[3] H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 177, (2007), 2726-2735.
[4] A. Ali, M. Aslam, A. Fahmi, Soft Loops, U.P.B. Sci. Bull. Series A, 76(2), (2014), 159-168.
[5] N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl., 59, (2010), 3308-
3314.
[6] C. C. Chang, Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88, (1958), 467-490.
[7] R. L. O. Cignoli, I. M. L. D’Ottavianoand D. Mundici, AlgebraicFoundationsofMany-ValuedReasoning,Kluwer
Academic, Dordrecht, Boston, (2000).
[8] F. Citak, N. Cagman, J. Zhan, Soft K-INT-Ideals of Semirings, preprint.
[9] A. DiNola, P. Flondor, I. Leustean, MV-modules, J. of Algebra, 267, (2003), 21-40.
[10] A. Erami, A. Hasankhani, Soft Vectorial MV -algebras, Indian J. of Science and Technology, 7(9), (2014), 1428- 1436.
[11] B. A. Ersoy, S. Onar, B. Davvaz, K. Hila, Structure of idealistic fuzzy soft Γ-near-ring, U.P.B. Sci. Bull. Series A, 77(3), (2015), 15-28.
[12] F. Feng, Y. B. Jun, X. Z. Zhao, Soft semirings, Comput. Math. Appl., 56, (2008), 2621-2628.
[13] F. Forouzesh, E. Eslami, A. Borumand Saeid, On prime A-ideals in MV-modules, U.P.B. Sci. Bull. Series A,
76(3), (2014), 181-198.
[14] A. R. Hadipour, A. Borumand Saeid, Fuzzy soft BF-algebra, Indian J. of Science and Technology, 6(3), 4199-
4204.
[15] K. Hila, T. Vougiouklis, K. Naka, On the structure of soft m-ary semihypergroups, U.P.B. Sci. Bull. Series A, 76(4), (2014), 91-106.
[16] Y. B. Jun, K. J. Lee, E. H. Roh, IntersectionalsoftBCK/BCI-ideals,AnnalsofFuzzyMathematicsandInformatics, 4(1), (2012), 1-7.
[17] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56, (2008), 1408-1413.
[18] Y. B. Jun, S. Z. Song, Filters of BE-algebras associated with uni-soft set theory, Applied Mathematical Sciences,
9(84), (2015), 4155-4164.
[19] O. Kazanci, S. Yilmaz, S. Yamak, Soft set and soft BCH-Algebras, Hacettepe J. of Mathematics and Statistics,
39(2), (2010), 205-217.
[20] M. Khan, F. Ilyas, M. Gulistan, S. Anis, A study of fuzzy soft AG-groupoids, Annals of Fuzzy Mathematics and
Informatics, 9(4), (2015), 621-638.
[21] P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Comput. Math. Appl., 45, (2003), 555-562.
[22] P. K. Maji, A. R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl., 44, (2002),
1077-1083.
[23] D. Molodtsov, Soft Set Theory: First Results, Comput. Math. Appl., 37, (1999), 19-31.
[24] M. M. K. Rao, Fuzzy soft Γ-semiring and fuzzy soft k-ideal over Γ-semiring, Annals of Fuzzy Mathematics and
Informatics, 9(2), (2015), 341-354.
[25] D. Noje, B. Bede, Vectorial MV-algebras, Soft computing, 7, (2003), 258-262.
[26] D. Pei and D. Miao, From soft sets to information systems, Proceedings of Granular Computing, IEEE, 2, (2005),
617-621.
[27] Q. M. Sun, Z.L. Zhang, J. Liu, Soft sets and soft modules, Lecture Notes in Computer Science, 5009, (2008),
403-409.
[28] S. Yamak, O. Kazanci, B. Davvaz, Soft hyperstructure, Comput. Math. Appl., 62, (2011), 797-803.
[29] J. Zhan, W. A. Dudek, Soft MTL-Algebras based on Fuzzy Sets, U.P.B. Sci. Bull Series A, 74(2), (2012), 41-56.
[30] Z. Zhu, Soft Sets, Soft BL-algebras and Soft Logic System BL, Sciverse Science direct, Procedia Engineering,
15, (2011), 3531-3535.
MV-Modules in View of soft Set Theory
Year 2016 ,
Volume: 13 Issue: 1, - , 01.05.2016
A. Erami
,
A. Hasankhani
A. Borumand Saeid
Abstract
In this paper, the concept of a soft MV -module is introduced and some examples are provided.
Then, different types of intersections and unions of the family of soft MV -modules are established. Moreover,
the notions of soft MV-submodules and soft MV -module homomorphisms are introduced and some of their
properties are studied.
References
[1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, (2010), 3458-3463.
[2] D. Afkhami Taba, A. Hasankhani, M. Bolurian, Soft nexuses, Comput. Math. Appl., 64(6), (2012), 1812-1821.
[3] H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 177, (2007), 2726-2735.
[4] A. Ali, M. Aslam, A. Fahmi, Soft Loops, U.P.B. Sci. Bull. Series A, 76(2), (2014), 159-168.
[5] N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl., 59, (2010), 3308-
3314.
[6] C. C. Chang, Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88, (1958), 467-490.
[7] R. L. O. Cignoli, I. M. L. D’Ottavianoand D. Mundici, AlgebraicFoundationsofMany-ValuedReasoning,Kluwer
Academic, Dordrecht, Boston, (2000).
[8] F. Citak, N. Cagman, J. Zhan, Soft K-INT-Ideals of Semirings, preprint.
[9] A. DiNola, P. Flondor, I. Leustean, MV-modules, J. of Algebra, 267, (2003), 21-40.
[10] A. Erami, A. Hasankhani, Soft Vectorial MV -algebras, Indian J. of Science and Technology, 7(9), (2014), 1428- 1436.
[11] B. A. Ersoy, S. Onar, B. Davvaz, K. Hila, Structure of idealistic fuzzy soft Γ-near-ring, U.P.B. Sci. Bull. Series A, 77(3), (2015), 15-28.
[12] F. Feng, Y. B. Jun, X. Z. Zhao, Soft semirings, Comput. Math. Appl., 56, (2008), 2621-2628.
[13] F. Forouzesh, E. Eslami, A. Borumand Saeid, On prime A-ideals in MV-modules, U.P.B. Sci. Bull. Series A,
76(3), (2014), 181-198.
[14] A. R. Hadipour, A. Borumand Saeid, Fuzzy soft BF-algebra, Indian J. of Science and Technology, 6(3), 4199-
4204.
[15] K. Hila, T. Vougiouklis, K. Naka, On the structure of soft m-ary semihypergroups, U.P.B. Sci. Bull. Series A, 76(4), (2014), 91-106.
[16] Y. B. Jun, K. J. Lee, E. H. Roh, IntersectionalsoftBCK/BCI-ideals,AnnalsofFuzzyMathematicsandInformatics, 4(1), (2012), 1-7.
[17] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56, (2008), 1408-1413.
[18] Y. B. Jun, S. Z. Song, Filters of BE-algebras associated with uni-soft set theory, Applied Mathematical Sciences,
9(84), (2015), 4155-4164.
[19] O. Kazanci, S. Yilmaz, S. Yamak, Soft set and soft BCH-Algebras, Hacettepe J. of Mathematics and Statistics,
39(2), (2010), 205-217.
[20] M. Khan, F. Ilyas, M. Gulistan, S. Anis, A study of fuzzy soft AG-groupoids, Annals of Fuzzy Mathematics and
Informatics, 9(4), (2015), 621-638.
[21] P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Comput. Math. Appl., 45, (2003), 555-562.
[22] P. K. Maji, A. R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl., 44, (2002),
1077-1083.
[23] D. Molodtsov, Soft Set Theory: First Results, Comput. Math. Appl., 37, (1999), 19-31.
[24] M. M. K. Rao, Fuzzy soft Γ-semiring and fuzzy soft k-ideal over Γ-semiring, Annals of Fuzzy Mathematics and
Informatics, 9(2), (2015), 341-354.
[25] D. Noje, B. Bede, Vectorial MV-algebras, Soft computing, 7, (2003), 258-262.
[26] D. Pei and D. Miao, From soft sets to information systems, Proceedings of Granular Computing, IEEE, 2, (2005),
617-621.
[27] Q. M. Sun, Z.L. Zhang, J. Liu, Soft sets and soft modules, Lecture Notes in Computer Science, 5009, (2008),
403-409.
[28] S. Yamak, O. Kazanci, B. Davvaz, Soft hyperstructure, Comput. Math. Appl., 62, (2011), 797-803.
[29] J. Zhan, W. A. Dudek, Soft MTL-Algebras based on Fuzzy Sets, U.P.B. Sci. Bull Series A, 74(2), (2012), 41-56.
[30] Z. Zhu, Soft Sets, Soft BL-algebras and Soft Logic System BL, Sciverse Science direct, Procedia Engineering,
15, (2011), 3531-3535.
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There are 30 citations in total.