Vague soft near-rings

Document Type : Research Paper

Authors

1 Department of Mathematics, Shivaji University, P.O.Box 416004,Kolhapur, India

2 Department of Mathematics , Sadguru Ghadage Maharaj College, Karad, P.O.Box 415124, Karad, India

Abstract

Soft set theory, proposed by Molodstov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0,1]. Such a set is characterized by a truth membership function and a false membership function. In this paper we introduce and study the concept of vague soft near-rings, vague soft ideals of near-rings. Also, we derive some properties of vague soft near-rings and vague soft ideals of near-rings.

Keywords


[1] Ashhan Sezgin, AkinOsman Atagun, and EminAygun, A Note Soft Rings and Idealistic Soft Near-Rings, Filomat, 25:1 (2011), 53–68.
[2] B. Pazar Varol, A. Aygunoglu and H. Aygun, On Fuzzy Soft Rings Journal of Hyperstructures, 2 (2012), 1–15.
[3] D.Molodtsov, Soft Set Theory-First Results, Computers Math. Applic., 37 (4/5) (1999),19–31.
[4] Ganeshsree Selvachandran and Abdul Razak Salleh, Vague Soft ring and Vague Soft Ideal, International Journal of Algebra 6 (2012), 557–572.
[5] Ganeshsree Selvachandran and Abdul Razak Salleh, Vague Soft Hypergroups and vague soft Hypergroup Homomorphism, Advances in Fuzzy Mathematics 6 (2014), Article ID-758637,.
[6] Jayant Ghosh, Bisvas Dinda and T.K.Sumanta, Fuzzy Soft Ring and Fuzzy Soft Ideals, Int. J. Pure Appl. Sci. Tecnhnol., 2 (2011), 66–74.
[7] J. D. P. Meldrum, Near-Rings and their Links with Groups, Pitman, London 1985.
[8] J. D. Yadav, Fuzzy Soft Near Rings, International Journal of Latest Research in Science and Technology, 4(6),(2015)94–101,.
[9] L. A. Zadeh, Fuzzy Sets, Information And Control, 8 (1965), 338–353.
[10] Manoj Borah, Tridiv Jyoti Neog, and Dusmanta Kumar Sut, A Study on Some Operations on Fuzzy Soft Sets, International Journal of Modern Engineering Re-search, 2(2) (2012), 219–225.
[11] P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Computers and Mathe-matics with Appilcation1hs,45(2003),555–562.
[12] Pilz Gunter, Near-Rings, North-Holland, Amsterdam 1983.
[13] Wei Xu, Jain Ma, Shouyang Wang, and Gang Hao, Vague Soft Sets and their Properties, Computers and Mathematics with Applications 59 (2010), 787–794.
[14] W. l. Gau and D. J. Buehrer, Vague Sets, IEEE Transactions on System, Man and Cybernetics, 23(2) (1993), 610–640.
[15] Y. Celik, C. Ekiz, and Sultan Yamak, A new View on Soft Rings, Hacettepe Journal of Mathematics and Statistics, 40(2) (2011), 273–286.