Contributions to the Theory of Soft Sets

Yıl 2014, Cilt: 3 Sayı: 4, 1 - 1, 01.04.2014

Naim Çağman

Öz

Molodtsov introduced the concept of soft set asa new mathematical tool for dealing with problems containinguncertainties. In the literature, different kinds of operations ofsoft sets are defined and used in theory and applications. Someresearchers showed that some of these definitions have a few gaps.In this paper, we make contributions to the theory of soft setsin which we first make some modifications to the operations ofsoft sets and fill in these gaps. Until now, to define soft setsand their properties, the authors have used different subsets ofthe parameters set for each soft set. Whereas, we use a singleparameter set for all of soft sets in our approach. We then comparethe definitions with those defined before

Anahtar Kelimeler

-

Kaynakça

• M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications 57 (2009) 1547-1553.
• N. C.a˘gman and S. Engino˘glu, Soft set theory and uni-int decision making, Euro- pean Journal of Operational Research 207/2 (2010) 848-855.
• P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (2003) 555-562.
• D.A. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications 37 (1999) 19-31.
• T. J. Neog, D.M. Sut, A New Approach to the Theory of Soft Sets, International Journal of Computer Applications 32/2 (2011) 0975-8887.
• D. Pei, D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T.Y. Lin, R.R. Yager, B. Zhang (Eds.), Proceedings of Granular Com- puting, vol. 2, pp. 617-621, 2005, IEEE.
• A. Sezgin, A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications 61 (2011) 1457-1467.
• Y. Xia, L. Zuhua, Some new operations of soft sets, Uncertainty Reasoning and Knowledge Engineering (URKE), 2nd International Conference, pp. 290 - 295, 14-15 Aug. 2012, IEEE.
• C.F. Yang, A note on ”Soft set theory” [Computers and Mathematics with Ap- plications 45 (2003) 555-562], Computers and Mathematics with Applications 56 (2008) 1899-1900.
• P. Zhu, Q. Wen, Operations on Soft Sets Revisited, Journal of Applied Mathemat
• ics 2013 (2013) 1-7.