Korean J. Math. Vol. 26 No. 3 (2018) pp.503-517
DOI: https://doi.org/10.11568/kjm.2018.26.3.503

Lattice ordered soft near rings

Article Sidebar

PDF
Published: Sep 30, 2018
Keywords:
Near Rings, Soft Near Rings, Lattice Ordered Soft Near Rings, Lattice Ordered Soft Near Ring Homomorphism.
Mathematics Subject Classification:
03G25, 20D05.

Main Article Content

Tahir Mahmood
Department of Mathematics International Islamic University Islamad, Pakistan
Zia Ur Rehman
Department of Mathematics International Islamic University Islamad, Pakistan
Aslıhan Sezgin
Department of Elementary Education Amasya University Amasya, Turkey

Abstract

Keeping in view the expediency of soft sets in algebraic structures and as a mathematical approach to vagueness, in this paper the concept of lattice ordered soft near rings is introduced. Different properties of lattice ordered soft near rings by using some operations of soft sets are investigated. The concept of idealistic soft near rings with respect to lattice ordered soft near ring homomorphisms is deliberated.


Article Details

References

[1] H. Aktas and N. C. a ̆gman, Soft sets and soft groups, Inform. Sci. 177 (2007) 2726–2735. Google Scholar

[2] M. I. Ali, A note on soft sets, rough sets and fuzzy soft sets, Comput. Math. Appl. 11 (2011) 3329–3332. Google Scholar

[3] M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547–1553. Google Scholar

[4] M. I. Ali, T. Mahmood, M. M. Rehman and M. F. Aslam, On lattice ordered soft sets, Appl Soft Comput. 36 (2015) 499–505. Google Scholar

[5] M. Aslam and M. Qurashi, Some contributions to soft groups, Annals of Fuzzy Math. and Infor. 4 (2012) 177–195. Google Scholar

[6] A. O. Atagu ̈n and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011) 592–601. Google Scholar

[7] G. Birkhoff, Lattice theory, American Mathematical Socity (1967). Google Scholar

[8] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008) 2621–2628. Google Scholar

[9] F. Feng, C. Li, B. Davvaz and M. I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14 (2010) 899–911 Google Scholar

[10] F. Ta ̧sdemir, A. O. Atagu ̈n, H. Altndi ̧s, Different prime N-ideals and IFP N-ideals, Indian J. Pure Appl. Math. 44(4), 527–542, 2013. Google Scholar

[11] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413. Google Scholar

[12] G. J. Klir and T. A. Folger, Fuzzy sets, Uncertainty and Inform. Prentice-Hall 24 (1987) 141–160. Google Scholar

[13] X. Ma, Q. Liu, J. Zhan, A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review 47 (2017) 507–530. Google Scholar

[14] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555–562. Google Scholar

[15] P. K. Maji, A. R. Roy and R. Biswas, An Application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077–1083. Google Scholar

[16] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19–31. Google Scholar

[17] Z. Pawlak, Rough sets, Int. J. Inform. Comput. Sci. 11 (1982) 341–356. Google Scholar

[18] G. Pilz, Near-rings, N. Holl. Publ. Comp. Amst. New York-Oxford, 1983. Google Scholar

[19] A. Sezgin, A. O. Atagu ̈n and E. Ayg" un, A Note on soft near-rings and Idealistic soft near-rings, Comut. Math. Appl. 25 (2011) 53–68. Google Scholar

[20] A. Sezgin and A. O. Atagu ̈n, On operations of soft sets, Comput. Math. Appl. 61 (2011) 1457–1467. Google Scholar

[21] Q. M. Sun, Z. L. Zhang and J. Liu, Soft sets and soft modules, Lecture notes in Comput. Sci. 5009 (2008) 403–409. Google Scholar

[22] J. D. Yadav, Fuzzy soft near ring, MNK. Appl. 4 (2015) 94–101. Google Scholar

[23] C. F. Yang, A Note on soft set theory, Comput. Math. Appl. 56 (2008) 1899–1900. Google Scholar

[24] J. Zhan, Q. Liu and T. Herawan, A novel soft rough set: soft rough hemirings and its multicriteria group decision making, Applied Soft Computing 54 (2017) 393–402. Google Scholar

[25] J. Zhan, M. I. Ali and N. Mehmood, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing 56 (2017) 446–457. Google Scholar

[26] J. Zhan, Q. Liu and B. Davvaz, A new rough set theory: rough soft hemirings, Journal of Intelligent & Fuzzy Systems 28 (2015) 1687–1697. Google Scholar

[27] L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338–353. Google Scholar