Soft Ideals of a Soft Lattice

E.K.R.Nagarajan; P.Geetha

doi:https://doi.org/10.14445/22315373/IJMTT-V8P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 8 | Number 2 | Year 2014 | Article Id. IJMTT-V8P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V8P515

Soft Ideals of a Soft Lattice

E.K.R.Nagarajan, P.Geetha

Abstract

soft set theory was introduced by Molodtsov in 1999 as a mathematical tool for dealing with problems that contain uncertainty. Faruk Karaaslan et al.[6] defined the concept of soft lattices, modular soft lattices and distributive soft lattices over a collection of soft sets. In this paper, we define the concept of soft ideals and soft filters over a collection of soft sets, study their related properties and illustrate them with some examples. We also define the maximum and minimum conditions in soft lattice. In addition, we characterize soft modularity and soft distributivity of soft lattices of soft ideals.

Keywords

Soft lattices, soft filters , distributive soft lattices, modular soft lattices, soft lattice of soft ideals.

References

[1] Cagman N., and Enginoglu S., Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207/2 (2010), 848-855.
[2] Davey B.A., and Priestley H.A. Introduction to lattices and order, Cambridge University Press, India, 2009.
[3] Gabor Szasz, Introduction to Lattice Theory, Academic Press, New York and London, 1963.
[4] George Gratzer, General Lattice Theory, Second edition, Birkhauser verlag, Boston, 1998.
[5] Irfan Ali M., Feng Feng, Xiaoyan Liu, Won Keun Min and Shabir M., On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553.
[6] Karaaslan F., Cagman N., and Enginoglu S., Soft Lattices, J. New. Res. Sci. 1 (2012),5-17 .
[7] Li F., Soft Lattices, Glob. J. Sci. Front. Res.10/4 (2010), 56-58.
[8] Maji P.K., Biswas R., and Roy A.R. Soft set theory, Comput. Math. Appl. 45 (2003), 555-562.
[9] Molodtsov D.A., Soft set theory-First Results, Comput. Math. Appl.37 (1999), 19-31.
[10] Nagarajan E.K.R., and Meenambigai G., An Application of Soft Sets to Soft Lattices, Kragujevac J. Math. 35/1 (2011), 75-87.
[11] Nagarajan E.K.R., and Geetha P., Characterization Theorems for Modular and Distributive Soft Lattices, J. Innov. Res. in Sci. Eng. and Tech. 2/11 (2013), 6019-6031.
[12] Serife Yilmaz and osman Kazanchi., Soft Lattices(Ideals,Filters) Related to Fuzzy Point, U.P.B.Sci. Bull., Series A. 75/3 (2013), 75-90.

Citation :

E.K.R.Nagarajan, P.Geetha, "Soft Ideals of a Soft Lattice," International Journal of Mathematics Trends and Technology (IJMTT), vol. 8, no. 2, pp. 112-119, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V8P515