In this paper, we introduce two new operations on soft sets, called inverse production and characteristic production, by using Molodtsov’s definition of the soft sets. We prove that the set of all soft sets over a universe U is an abelian group under the each operations and called “the inverse group of soft sets” and “the characteristic group of soft sets”. We finally show that these groups are isomorphic.
AbdullahS., AslamM., KhanT.A. and NaeemM., A new type of fuzzy normal subgroups and fuzzy cosets, Journal of Intelligent and Fuzzy Systems25 (2013), 37–47.
2.
AcarU., KoyuncuF. and TanayB., Soft sets and soft rings, Comput Math Appl59 (2010), 3458–3463.
3.
AktaşH. and ÇağmanN, Soft sets and soft groups, Inform Sci177 (2007), 2726–2735.
4.
AliM.I., FengF., LiuX., MinW.K. and ShabirM., On some new operations in soft set theory, Comput Math Appl57(9) (2009), 1547–1553.
5.
AtagünA.O. and SezginA., Soft substructures of rings, fields and modules, Comput Math Appl61(3) (2011), 592–601.
6.
BabithaK.V. and SunilJ.J., Soft set relations and functions, Comput Math Appl60(7) (2010), 1840–1849.
7.
ÇağmanN. and EnginoğluS, Soft set theory and uni-int decision making, Eur J Oper Res207 (2010), 848–855.
8.
ÇağmanN. and EnginoğluS, Soft matrix theory and its decision making, Comput Math Appl59 (2010), 3308–3314.
9.
FengF., JunY.B. and ZhaoX., Soft semirings, Comput Math Appl56 (2008), 2621–2628.
10.
FengF., LiuX.Y., Leoreanu-FoteaV. and JunY.B., Soft sets and soft rough sets, Inform Sci181(6) (2011), 1125–1137.
11.
FengF., LiC.X., DavvazB. and Irfan AliM., Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput14 (2010), 899–911.
12.
HilaK. and AbdullahS., A study on intuitionistic fuzzy sets in Γ-semihypergroups, Journal of Intelligent and Fuzzy Systems26 (2014), 1695–1710.
13.
JunY.B., Soft BCK/BCI-algebras, Comput Math Appl56 (2008), 1408–1413.
14.
JunY.B. and ParkC.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform Sci178 (2008), 2466–2475.
15.
JunY.B., LeeK.J. and ZhanJ., Soft p-ideals of soft BCI-algebras, Comput Math Appl58 (2009), 2060–2068.
16.
KazanciO., YılmazŞ and YamakS, Soft sets and soft BCH-algebras, Hacet J Math Stat39(2) (2010), 205–217.
17.
MajiP.K., BiswasR. and RoyA.R., Soft set theory, Comput Math Appl45 (2003), 555–562.
18.
MajumdarP. and SamantaS.K., On soft mappings, Comput Math Appl60(9) (2010), 2666–2672.
19.
MolodtsovD., Soft set theory-first results, Comput Math Appl37 (1999), 19–31.
20.
SezginA., AtagünA.O. and AygünE., A note on soft near-rings and idealistic soft near-rings, Filomat25 (2011), 53–68.
21.
SezginA., AtagünA.O and ÇağmanN., Union soft substructures of near-rings and N-groups, Neural Comput and Applic21 (2012), 133–143.
22.
SezerA.S., A new approach to LA-semigroup theory via the soft sets, Journal of Intelligent and Fuzzy Systems26(5) (2014), 2483–2495.
23.
SezginA. and AtagünA.O., On operations of soft sets, Comput Math Appl61(5) (2011), 1457–1467.
24.
SezginA., AtagünA.O and ÇağmanN., Soft intersection nearrings with applications, Neural Comput and Applic21(1) (2012), 221–229.