Rough set theory initiated by Pawlak [16] and soft set theory initiated by Molodtsov [15] are strong mathematical tools for handling uncertain and vague information. In this study, we bring out some results of soft rough sets (-sets) and topological structure of soft rough sets. We define -open set, -closed set, -interior, -closure, -frontier, -neighbourhood and -limit point. Furthermore, we propose an algorithm to illustrate uncertainties in the multi-criteria group decision making (MCGDM) using -sets. We utilize another algorithm for modeling uncertainties in multi-criteria decision making (MCDM) using soft rough topology(-topology).
M.I.Ali, F.Feng, X.Y.Liu, W.K.Min and M.Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications57(2009), 1547–1553.
2.
M.I.Ali, A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing11(2011), 3329–3332.
3.
H.Aktas and N.Çaėman, Soft sets and soft group, Information Sciences177(13)(2007), 2726–2735.
4.
M.Y.Bakier, A.A.Allam and SH.S.Abd-Allah, Soft rough topology, Annals of Fuzzy Mathematics and Informatics11(2)(2016), 4–11.
5.
N.Çagman, S.Karataş and S.Enginoglu, Soft topology, Computers and Mathematics with Applications62(2011), 351–358.
6.
D.Chen, The parametrization reduction of soft sets and its applications, Computers and Mathematics with Applications49(2005), 757–763.
7.
F.Feng, C.Li, B.Davvaz and M.I.Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing14(2010), 899–911.
8.
F.Feng, X.Liu, V.L.Fotea and Y. B.Jun, Soft sets and Soft rough sets, Information Sciences181(2011), 1125–137.
9.
M.Kryskiewicz, Rough set approach to incomplete information systems, Information Sciences112(1998) 39–49.
10.
X.Ma, Q.Liu and J.Zhan, A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47(2017), 507–530.
11.
X.Ma, Q.Liu, J.Zhan, M.I.Ali and N.Mehmood, A survey of decision making methods based on two classes of hybrid soft set models, Artificial Intelligence Review, 49(4)(2018), 511–529.
12.
T.J.Mathew, E.Sherly and J.C.R.Alcantud, A multimodal adaptive approach on soft set based diagnostic risk prediction system, Journal of Intelligence and Fuzzy Systems34(3)(2018), 1609–1618.
13.
P.K.Maji, A.R.Roy and R.Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(8-9)(2002), 1077–1083.
14.
P.K.Maji, A.R.Roy and R.Biswas, Soft set theory, Computers and Mathematics with Applications, 45(4-5)(2003), 555–562.
15.
D.Molodtsov, Soft set theoty-first results, Computers and Mathematics with Applications, 37(4-5)(1999), 19–31.
16.
Z.Pawlak, Rough sets, International Journal of Information and Computer Science11(1982), 341–356.
17.
Z.Pawlak and A.Skowron, Rough sets: Some extensions, Information Sciences177(2007) 28–40.
18.
D.Pie and D.Miao, From soft sets to information system, Granular Computing, IEEE International Conference2(2005) 617–621.
19.
M.Riaz and K.Naeem, Measurable Soft Mappings, Punjab University Journal of mathematics48(2)(2016), 19–34.
20.
M.Riaz, K.Naeem and M.O.Ahmad, Novel Concepts of Soft Sets with Applications, Annals of Fuzzy Mathematics and Informatics13(2)(2017), 239–251.
21.
M.Riaz and Z.Fatima, Certain properties of soft metric spaces, Journal of Fuzzy Mathematics25(3)(2017), 543–560.
22.
M.Riaz and M.R.Hashmi, Certain applications of fuzzy parameterized fuzzy soft sets in decision-making problems, International Journal of Algebra and Statistics5(2)(2016), 135–146.
23.
M.Riaz and M.R.Hashmi, Fuzzy parameterized fuzzy soft topology with applications, Annals of Fuzzy Mathematics and Informatics13(5)(2017),593–613.
24.
M.Riaz and M.R.Hashmi, Fuzzy Parameterized Fuzzy Soft Compact Spaces with Decision-Making, Punjab University Journal of mathematics50(2)(2018),131–145.
25.
M.Riaz, M.R.Hashmi, Fixed points of fuzzy neutrosophic soft mapping with decision-making, Fixed point theory and applications7(2018), 1–10.
26.
M.Riaz, M. R.Hashmi and A.Farooq, Fuzzy Parameterized Fuzzy Soft Metric spaces, Journal of Mathematical Analysis9(2)(2018), 25–36.
27.
R.Roy and P.K.Maji, A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics203(2)(2007), 412–418.
28.
A.S.Salama, Some Topological Properies of Rough Sets with Tools for Data Mining, International Journal of Computer Science Issues8(3)(2011), 588–595.
29.
M.Shabir and M.Naz, On soft topological spaces, Computers and Mathematics with Applications61(2011), 1786–1799.
30.
M.L.Thivagar, C.Richard and N.R.Paul, Mathematical Innovations of a Modern Topology in Medical Events, International Journal of Information Science2(4)(2012), 33–36
31.
L.A.Zadeh, Fuzzy sets, Information and Control8(1965), 338–353.
32.
J.Zhan, Q.Liu and T.Herawan, A novel soft rough set: soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54(2017), 393–402.
33.
J.Zhan, M.I.Ali and N.Mehmood, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods,Applied Soft Computing56(2017), 446–457.
34.
J.Zhan and J.C.R.Alcantud, A novel type of soft rough covering and its application to multicriteria group decision making, Artificial Intelligence Review (2018), https://doi.org/10.1007/s10462-018-9617-3.
35.
L.Zhang, J.Zhan, Fuzzy soft β-covering based fuzzy rough sets and corresponding decision-making applications,International Journal of Machine Learning and Cybernatics (2018), https://doi/10.1007/s13042-018-0828-3.
36.
L.Zhang, J.Zhan, Novel classes of fuzzy soft;-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making, Soft Computing (2018), https://doi.org/10.1007/s00500-018-3470-9.
37.
L.Zhang, J.Zhan, Z.X.Xu, Covering-based generalized IF rough sets with applications to multi-attribute decision-making, Information Sciences478(2019), 275–302.
