In this paper, the study of vague soft structures of modules is initiated by introducing the concepts of vague soft module, vague soft module homomorphism and vague soft exactness. In the meantime, some of their properties and structural characteristics are investigated and discussed. Thereafter, several illustrative examples are given.
AbdullahS. and AminN., Analysis of S-box image encryption based on generalized fuzzy soft expert set, Nonlinear Dynamics79(3) (2015), 1679–1692.
2.
AbdullahS., AyubS., HussainI., BedregalB. and KhanM.Y., Analyses of S-boxes based on interval valued intuitionistic fuzzy sets and image encryption, International Journal of Computational Intelligence Systems10 (2017), 851–865.
3.
AfshanQ., AbdullahS. and AslamM., Cubic soft expert sets and their application in decision making, Journal of Intelligent & Fuzzy Systems31(3) (2016), 1585–1596.
4.
MolodtsovD., Soft set theory-First results, Comput Math Appl37(4-5) (1999), 19–31.
5.
MajiP.K., RoyA.R. and BiswasR., An application of soft sets in a decision making problem, Comput Math Appl44 (2002), 1077–1083.
6.
ChenD., TsangE.C.C., YeungD.S. and WangX., The parameterization reduction of soft sets and its applications, Comput Math Appl49 (2005), 757–763.
7.
MajiP.K., BiswasR. and RoyA.R., Soft set theory, Comput Math Appl45 (2003), 555–562.
8.
KongZ., GaoL., WangL. and LiS., The normal parameter reduction of soft sets and its algoritm, Comput Math Appl56(1), 3029–3037.
9.
SunQ.-M., ZhangZ.-L., LiuJ.Soft sets and modules, In: GuoyinWang, Tian-ruiLi, Grzymala-BusseJerzy W., MiaoDuoqian, SkowronAndrzej, YaoYiyu, Eds. Rough sets and knowledge technology, RSKT, Proceedings, Springer, 2008, pp. 403–409.
10.
XiangD., Soft module theory, IEEE, 2013, 10th International Conference on Fuzzy Systems and Knowledge Discovery.
11.
ShahT. and MedhitS., Primary decomposition in a soft ring and soft module, Iranian Journal of Science & Technology38A3(Special issue-Mathematics) (2014), 311–320.
12.
ZouY. and XiaoZ., Data analysis approaches of soft sets under incomplete information, Knowl Based Syst21(8) (2008), 941–945.
13.
JiangY., LiuH., TangY. and ChenQ., Semantic decision making using ontology-based soft sets, Mathematical and Computer Modelling42(11) (2010), 1005–1009.
14.
EramiA., HassankhaniA. and SaeidA.B., MV- modules in view of soft set theory, Çankaya University Journal of Science and Engineering13(1) (2016), 1–15.
15.
GauW.L. and BuehrerD.J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics23(2) (1993), 610–614.
16.
BustinceH. and BurilloP., Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems79 (1996), 403–405.
17.
ChenS.M., Measures of similarity between vague sets and between elements, IEEE Transactions on Systems27(1) (1997), 153–158.
18.
ChenS.M., Analyzing fuzzy system reliability using vague set theory, Int J Applied Science Engineering1(1) (2003), 82–88.
19.
HongD.H. and ChoiC.H., Multicriteria fuzzy decision making problems based on vague set theory, Fuzzy Sets and Systems114 (2000), 103–113.
20.
XuW., MaJ., WangS. and HaoG., Vague soft sets and their properties, Comput Math Appl59(2) (2010), 787–794.
21.
AlhazaymehK. and HassanN., Possibility vague soft set and its application in decision making, Int J Pure and Applied Math77(4) (2012), 549–563.
22.
AlhazaymehK. and HassanN., Generalized vague soft set and its application, Int J Pure Appl Math77(3) (2012), 391–401.
23.
AlhazaymehK. and HassanN., Vague soft set relations and functions, J Intell Fuzzy Syst28(3) (2015), 1205–1212.
24.
AcarU., KoyuncuF. and TanayB., Soft sets and soft rings, Comput Math Appl59(11) (2010), 3458–3463.
