Representation of Soft Substructures of a Soft Semigroup by Products

Nistala V.E.S. Murthy¹ , Chundru Maheswari²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.172-181, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.172181

Online published on Apr 30, 2019

Copyright © Nistala V.E.S. Murthy, Chundru Maheswari . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, for any soft semigroup over a semigroup we construct a crisp semigroup in such way that the complete lattice of all soft substructures of the given soft semigroup is complete epimorphic to a complete lattice of certain substructures of the crisp semigroup and that the complete lattice of all regular soft substructures of the given soft semigroup is complete isomorphic to a complete lattice of certain substructures of the crisp semigroup.

Key-Words / Index Term :
(Extended) Soft (sub) semigroup, Associated product semigroup for a soft semigroup, factorizable subsemigroup (left ideal, right ideal, ideal, quasi-ideal, bi-ideal)

References :
[1] D. Molodtsov, “Soft set theory-first results”, Computers & Mathematics with Applications, Vol.37,pp.19-31, 1999.
[2] M.I. Ali, M. Shabir, K.P. Shum, “On Soft Ideals over Semigroups”, Southeast Asian Bulletin of Mathematics, Vol.34, pp.595-610, 2010.
[3] N.V.E.S. Murthy, Ch. Maheswari, “Representation of Soft Subsets by Products”, International Journal of Mathematics And its Applications, Vol.6, Issue.(2-A), pp.227-241, 2018.
[4] P.A. Grillet, “Semi groups: An Introduction to the Structure Theory”, Marcel Dekker, New York, 1995.
[5] N.V.E.S. Murthy and Ch. Maheswari, “A First Study of f-(Fuzzy) Soft -Algebras and their f-(Fuzzy) Soft -Subalgebras”, Global Journal of Pure and Applied Mathematics, Vol.13, Issue.6, pp.2503-2526, 2017.
[6] M.I. Ali, M. Shabir, “Comments on De Morgan`s law in fuzzy soft sets”, Jornal of Fuzzy Mathematics, Vol.18, pp.679-686, 2010.
[7] D. Pei, D. Miao, “From soft sets to information systems”, Proceedings of Granular Computing, IEEE International Conference 2, pp.617- 621, 2005.
[8] F. Feng, Y.B. Jun, X. Zhao, “Soft semi rings”, Computers & Mathematics with Applications, Vol.56, pp.2621-2628, 2008.
[9] N.V.E.S. Murthy, Ch. Maheswari, “A Note on 0-Adjoined Soft Semigroups” (Communicated).
[10] N.V.E.S. Murthy, Ch. Maheswari, “A Note on the Extensions of the Soft Substructures of a Soft Semigroup” (Communicated)
[11] H. Aktas, N. Cagman, “Soft sets and soft groups”, Information Sciences, Vol.177, pp.2726-2735, 2007.
[12] M.I. Ali, F. Feng, X. Liu, W.K. Min, M. Shabir, “On some new operations in soft set theory”, Computers & Mathematics with Applications, Vol.57, pp.1547-1553, 2009.
[13] J.M. Howie, “An Introduction to Semigroup Theory”, Academic Press, London, 1976.
[14] P.K. Maji, R. Biswas, A.R. Roy, “Soft set theory”, Computers & Mathematics with Applications, Vol.45, pp.555-562, 2003.
[15] G. Szasz, “An Introduction to Lattice Theory”, Academic Press, New York.
[16] L.A. Zadeh, “Fuzzy sets”, Information and Control, Vol.8, pp.338-353, 1965.
[17] S. Mohanambal, G. Jeyanthi, A. Pethalakshmi, “An Efficient Decision making in Crop cultivation using Soft Set Theory”, International Journal of Computer Sciences and Engineering, Vol.6,Special Issue.4, pp.86-92, 2018.