Soft Sequences in Real Analysis


  • Abdulsattar Abdullah hamad
  • V. Amarendra Babu
  • . .





limit superior, limit inferior, soft sequences, Soft set, soft real numbers


In This work is an attempt to present new class of limit soft sequence in the real analysis it is called ( limit inferior of soft sequence " and limit superior of soft sequence) respectively are introduced and given result an example with two new definitions and studied some of the properties of them are investigated.



[1] Hac Aktas and Naim Cagman, (2007), Soft sets and soft groups, Informations Sciences,177, 2726-2735.

[2] Atanassov K., Intuitionistic fuzzy sets, (1986), Fuzzy Sets and Systems, 20, 87-96.

[3] Dubois D. and Prade H., (2008), Gradual elements in a fuzzy set, Soft Comput, 12, 165-175.

[4] Fortin J., Dubois D. and Prade H., (2008), Gradual numbers and their applications to fuzzy interval analysis, IEEE Transaction of Fuzzy Systems, 16 (2), 388-402.

[5] Klir G. J. and Yuan B., “Fuzzy sets and fuzzy logic, Theory and applicationsâ€, Prentice-Hall of India Pvt.Ltd., (1997).

[6] Maji P. K., Biswas R. and Roy A. R., (2003), On soft set theory, Computers Math. Applic., 45, 555-562.

[7] Maji P. K, Biswas R. and Roy A. R., (2001), Fuzzy soft sets, The Journal of fuzzy Math., 9 (3), 589-602.

[8] Majumdar P. and Samanta S. K., (2008), Similarity measure of soft sets, World Scientific Publishing Compa Vol. 4, No.1, 1-12.

[9] Molodtsov D., (1999), Soft set theory-first results, Computers Math. Applic, 37 (4/5), 19-31.

[10] Pawlak Z., Rough sets, (1982), International Journal of Information and Computer Sciences, 11, 341-356.

[11] Zadeh L.A., Fuzzy sets, (1965), Infor. And Control, 8, 338-353.

[12] Karadogan A, (2008)Application of fuzzy set theory in the selection of underground mining method, Journal of the southern African institute of mining and metallurgy, vol. 108, pp. 73-79

[13] Atagun A.O. and Sezgin A, (2011), Soft substructures of rings, fields and modules, Computers and Mathematics with applications 61, 592-601.

[14] Sezgin A. and Atagun A. O. , (2011), On Operation of soft sets, Computers and Mathematics with applications 61, 1457- 1467

[15] Kharal A . and Ahmad B, (2010), Mappings on soft classes, Inf. Sci ., INS-D-08-1231 by ESS, pp. 1-11

[16] Chen D., Tsang E. C. C., Yeung D. S. and Wang X, (2005), The .parameterization reduction of soft sets and its application, Comp. Math. with appl. 45, 757-763.

[17] Sut D.K.. (2012),An Application of Fuzzy Soft Relation in Decision Making Problems, Int. Journal of Mathematics Trends and Technology,Vol.3 Issue 2. 201-205

[18] Feng F., Jun Y . B. and Zhao X.. (2008), Soft semi rings, Computers Math . Applic. 56, 2621-262.

[19] Prade H. and Dubois D, “Fuzzy Sets and Systems: Theory and Applicationsâ€, Academic Press, London, 1980.

[20] Zimmerman H.J, “Fuzzy Set Theory and Its Applicationsâ€, Kluwer Academic, Boston, MA, 1996.

[21] ktas H.A and Cagman N.. (2007), Soft sets and Soft groups, Information Sciences 177, 2726-2735

[22] Yang H.and Guo Z.. (2011), Kernels and closures of soft set relations, and soft set relation mappings, Comp. Math. Appl. 651-662

[23] Ghosh J., Dinda B. and. Samanta T. K, (2011), Fuzzy Soft Rings and Fuzzy Soft Ideals, Int. J. Pure Appl. SCI. Technol., 2(2), pp. 66-74.

[24] Zhou J., Li Y. and Yin Y, (2011), Intuitionistic fuzzy soft set semigroups, Mathematics Aeterna, vol. 1, No. 03, 173-183.

[25] Atanassov K.. (1994), Operators over interval valued intuitionistic fuzzy sets, fuzzy sets and systems, 64, 159-174

[26] Babitha K.V. and Sunil J.J. (2011), Soft sets relations and functions, Computers Math. Applic 60 , 1840- 1849.

[27] Gong K., Xiao Z. and Zhang X. (2010), The bijective soft set with its operations, Computers and Math. Appl. 60, 2270- 2278.

[28] Qin K.and Hon Z.. (2010), On soft equality . Computers Math . Appl . 234, 1347 -1355.

[29] Irfan Ali M., Feng F., Liu X., Min W. K. and Shabir M, (2009), On some new operations in soft set theory, Comp. and Math . With appl. 57, 1547- 1553

[30] Ozturk M.A . and Inan E.. (2011), Soft Γ - rings and idealistic soft Γ – rings, annals of fuzzy Mathematics and informatics volume 1, no. 1, pp. 71-80.

[31] Mushrif M.M., Sengu pta S, and Ray A. K., (2006),Texture Classification Using A Novel, Soft Set Theory Based Classification Algorithm, LNCS 3851,pp. 246-254 2006

[32] Cagman N., Citak F., and Enginogiu S.. (2011),FP-soft set theory and its applications , annals of fuzy math.infom.vol. 2,no.2,pp.219-226

[33] Cagman N., Citakand F., Enginoglu S, (2010), fuzzy parameterized fuzzy soft set theory and its applications, journal of Turkish fuzzy systems association.,pp.21-35.

[34] Hassan R.N., Tantawy O.A, (2016), Soft Real Analysis, journal of progressive Research in Mathematics.vol 8,issue 1, 65-69

[35] Das S., samanta S.k., (2012), soft real sets, soft real numbers and their properties, Journal of fuzzy mathematics vol.20,N0.3, 551

[36] Maji P.K., ROY AR.and Biswas. R, (2002), An application of soft set in a decision making problem computers and mathematics with application 44(8/9),1077-1083.

[37] Mane maran (2011), .on fuzzy soft groups Int, journal of comp.Applications , vol.15,no7, 38

[38] Alkhazaleh.A.salleh and hassan N., (2011), Soft maltiset theory, Applied mathematical sciences, vol.5,No72 ,3561-3573.2011.

[39] Herawan T., Ghazali R.and Deris M.M.D (2010), Soft set theoretic approach for dimensionality reduction , Information journal of Database theory and Application vol.3 , No.2,47-60

[40] Xu W. (2010), Vague soft sets and their properties, Computers and mathematics with applications 59 , 787-794,.

[41] Ge X .and yan S., (2011), Investigation on some operation of soft sets . word academy of science,eng. And tech . 75, 1113 – 1116.

[42] Jun Y.B., Kimand H.S, Park C.H (2011), Positive implicative ideals of BCK-algabras based on soft set theory, Bull.malays .math.sci-soc. 34 (2),345-354

[43] Jun Y.B., Lee K.J.and Park C.H.. (2008), Soft set theory applied to commutative ideals in BCK-Algabras J.Appl.math.and informatics, vol.26 , no,3-4,pp 707-720.

[44] Pawlak Z., Hard And soft sets, proceeding of the international Eworkshop on Rough sets and knowledge Discovery, Banff,1993

View Full Article:

How to Cite

Abdullah hamad, A., Amarendra Babu, V., & ., . (2018). Soft Sequences in Real Analysis. International Journal of Engineering & Technology, 7(4.19), 32–35.
Received 2018-11-28
Accepted 2018-11-28
Published 2018-11-27