A New Operation on Soft Sets: Extended Difference of Soft Sets

Year 2019, Issue: 27, 33 - 42, 01.03.2019

Aslıhan Sezgin , Shahzad Ahmad Adnan Mehmood

https://izlik.org/JA73MR23NJ

Abstract

Soft Set Theory, which has been considered as an adequate mathematical device, was proposed by Molodtsov to deal with ambiguities and uncertainties. Several operations on soft sets were defined in many soft set papers. This study is based on the paper "On operations of Soft Sets" by Sezgin and Atag\"{u}n [Comput. Math. Appl. 61 (2011) 1457-1467]. In this paper, we define a new operation on soft sets, called extended difference and investigate its relationship between extended difference and restricted difference and some other operations of soft sets.

Keywords

Soft sets , Restricted union , Extended union , Restricted intersection , Extended intersection , Restricted difference , Extended difference

References

• [1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59 (2010) 3458-3463.
• [2] H. Aktaş, N. Çağman, Soft sets and soft groups, Inform. Sci. 177 (2007) 2726-2735.
• [3] M. I. Ali, F. Feng, X. Liu, W. K. Min, On some new operations in soft set theory, Comput. Math. Appl. 57 (9) (2009) 1547-1553.
• [4] N. Çağman and S. Enginoğlu, Soft matrix theory and its decision making, Comput. Math. Appl. 59 (2010) 3308-3314.
• [5] N. Cağman and S. Enginoğlu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010) 848-855.
• [6] F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008) 2621-2628.
• [7] Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178 (2008) 2466-2475.
• [8] P. K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555-562.
• [9] P. K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
• [10] D. Molodtsov, Soft set theory-¯rst results, Comput. Math. Appl. 37 (1999) 19-31.
• [11] D. Pei, D. Miao, From soft sets to information systems, In: Proceedings of Granular Computing (Eds: X. Hu, Q. Liu, A. Skowron, T.Y. Lin, R.R. Yager, B. Zhang) IEEE (2) 2005 617-621.
• [12] A. Sezgin, A.O. AtagÄun, On operations of soft sets, Comput. Math. Appl. 61 (2011) 1457-1467.
• [13] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci. 172 (2005) 1-40.