This paper presents three novel single-valued neutrosophic soft set (SVNSS) methods. First, we initiate a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory. Moreover, we develop the combined weights, which can show both the subjective information and the objective information. Later, we propose three algorithms to solve single-valued neutrosophic soft decision making problem by Evaluation based on Distance from Average Solution (EDAS), similarity measure and level soft set. Finally, the effectiveness and feasibility of approaches are demonstrated by a numerical example.
MolodtsovD.A., Soft set theory-first results, Computers and Mathematics with Applications37 (1999), 19–31.
2.
ZadehL.A., Fuzzy sets, Information Control8 (1965), 338–353.
3.
PawlakZ., Rough sets, International Journal of Computer and Information Sciences11 (1982), 341–356.
4.
GorzalzanyM.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems21 (1987), 1–17.
5.
MajiP.K., BiswasR. and RoyA.R., Fuzzy soft sets, Journal of Fuzzy Mathematics9 (2001), 589–602.
6.
AlcantudJ.C.R., A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set, Information Fusion29 (2016), 142–148.
7.
FengF., JunY.B., LiuX. and LiL., An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics234 (2010), 10–20.
8.
YangX.B., LinT.Y. and YangJ.Y., Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications58 (2009), 521–527.
9.
PengX.D. and YangY., Information measures for interval-valued fuzzy soft sets and their clustering algorithm, Journal of Computer Applications35 (2015), 2350–2354.
10.
PengX.D. and YangY., Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight, Applied Soft Computing. http://dx.doi.org/10.1016/j.asoc.2016.06.036
11.
PengX.D., YangY., SongJ.P. and JiangY., Pythagoren fuzzy soft set and its application, Computer Engineering41 (2015), 224–229.
12.
YangY., TanX. and MengC.C., The multi-fuzzy soft set and its application in decision making, Applied Mathematics Modelling37 (2013), 4915–4923.
13.
YangY., PengX.D., ChenH. and ZengL., A decision making approach based on bipolar multi-fuzzy soft set theory, Journal of Intelligent and Fuzzy Systems27 (2014), 1861–1872.
14.
WangF.Q., LiH.X. and ChenX.H., Hesitant fuzzy soft set and its applications in multicriteria decision making, Journal of Applied Mathematics2014 (2014), 1–10.
15.
TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems25 (2010), 529–539.
16.
PengX.D. and YangY., Interval-valued hesitant fuzzy soft sets and their application in decision making, Fundamenta Informaticae141 (2015), 71–93.
17.
SmarandacheF., Neutrosophy/Neutrosophic Probability, Set, and Logic. American Research Press, Rehoboth, NM, 1998.
18.
WangH., SmarandacheF., ZhangY.Q. and SunderramanR., Single valued neutrosophic sets, Multispace Multistruct4 (2010), 410–413.
19.
YeJ., Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, International Journal of General Systems42 (2013), 386–394.
20.
YeJ., Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27 (2014), 2453–2462.
21.
YeJ., Clustering methods using distance-based similarity measures of single-valued neutrosophic sets, Journal of Intelligent Systems23 (2014), 379–389.
22.
YeJ., Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment, Journal of Intelligent and Fuzzy Systems27 (2014), 2927–2935.
23.
PengX.D. and DaiJ.G., Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function, Neural Computing and Applications. doi:10.1007/s00521-016-2607-y
24.
BiswasP., PramanikS. and GiriB.C., TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Computing and Applications27 (2016), 727–737.
25.
SahinR. and KucukA., Subsethood measure for single valued neutrosophic sets, Journal of Intelligent and Fuzzy Systems29 (2015), 525–530.
26.
YangH.L., GuoZ.L., SheY.H. and LiaoX.W., On single valued neutrosophic relations, Journal of Intelligent and Fuzzy Systems30 (2016), 1045–1056.
27.
HuangH.L., New distance measure of single-valued neutrosophic sets and its application, International Journal of Intelligent Systems31 (2016), 1021–1032.
28.
LiuP.D., The aggregation operators based on archimedean t-Conorm and t-Norm for single-valued neutrosophic numbers and their application to decision making, International Journal of Fuzzy Systems. doi: 10.1007/s40815-016-0195-8
29.
WuX.H.,
WangJ.,
PengJ.J. and ChenX.H., Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decisionmaking problems, International Journal of Fuzzy Systems. doi: 10.1007/s40815-016-0180-2
30.
BroumiS., TaleaM., BakaliA. and SmarandacheF., Single valued neutrosophic graphs, Journal of New Theory10 (2016), 86–101.
31.
BroumiS., BakaliA., TaleaM. and SmarandacheF., Isolated single valued neutrosophic graphs, Neutrosophic Sets and Systems11 (2016), 74–78.
32.
BroumiS., TaleaM., SmarandacheF. and BakaliA., Single valued neutrosophic graphs: Degree, order and size, IEEE World Congress on Computational Intelligence (2016), 2444–2451.
33.
BroumiS., TaleaM., BakaliA. and SmarandacheF., On bipolar single valued neutrosophic graphs, Journal of New Theory11 (2016), 84–102.
34.
BroumiS., SmarandacheF., TaleaM. and BakaliA., An introduction to bipolar single valued neutrosophic graph theory, Applied Mechanics and Materials841 (2016), 184–191.
35.
PengJ.J., WangJ.Q. and YangW.E., A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems, International Journal of Systems Science. doi: 10.1080/00207721.2016.1218975
36.
PengJ.J., WangJ.Q. and WuX., An extension of the ELECTRE approach with multi-valued neutrosophic information, Neural Computing and Applications. doi: 10.1007/s00521-016-2411-8
37.
JiP., ZhangH.Y. and WangJ.Q., A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection, Neural Computing and Applications. doi: 10.1007/s00521-016-2436-z
38.
TianZ.P., WangJ., WangJ.Q. and ZhangH.Y., An improved MULTIMOORA approach for multi- criteria decision-making based on interdependent inputs of simplified neutrosophic linguistic information, Neural Computing and Applications. doi: 10.1007/s00521-016-2378-5
39.
TianZ.P., WangJ., WangJ.Q. and ZhangH.Y., Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development, Group Decision and Negotiation. doi: 10.1007/s10726-016-9479-5
40.
TianZ.P., WangJ., ZhangH.Y. and WangJ.Q., Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment, International Journal of Machine Learning and Cybernetics. doi: 10.1007/s13042-016-0552-9
41.
MajiP.K., Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics5 (2013), 157–168.
42.
ŞahinR. and
KüçükA., On similarity and entropy of neutrosophic soft sets, Journal of Intelligent and Fuzzy Systems27 (2014), 2417–2430.
43.
MukherjeeA. and SarkarS., Several similarity measures of neutrosophic soft sets and its application in real life problems, Annals of Pure and Applied Mathematics7 (2014), 1–6.
44.
DeliI. and BroumiS., Neutrosophic soft matrices and NSM decision making, Journal of Intelligent and Fuzzy Systems28 (2015), 2233–2241.
45.
AlkhazalehS., Time-neutrosophic soft set and its applications, Journal of Intelligent and Fuzzy Systems30 (2016), 1087–1098.
46.
Al-QuranA. and HassanN., Neutrosophic vague soft expert set theory, Journal of Intelligent and Fuzzy Systems30 (2016), 3691–3702.
47.
GhorabaeeM.K., ZavadskasE.K., OlfatL. and TurskisZ., Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS), Informatica26 (2015), 435–451.
48.
OpricovicS. and TzengG.H., Compromise solution by MCDMmethods: A comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research156 (2004), 445–455.
49.
GhorabaeeM.K., ZavadskasE.K., AmiriM. and TurskisZ., Extended EDAS method for fuzzy multi-criteria decisionmaking: An application to supplier selection, International Journal of Computers Communications and Control11 (2016), 358–371.
50.
LiuS.F., DangY.G. and FangZ.G., Grey systems theory and its applications, Science Press, Beijing, 2000.
51.
PengJ.J., WangJ.Q., WangJ., ZhangH.Y. and ChenX.H., Simplified neutrosophic sets and their applications in multicriteria group decision-making problems, International Journal of Systems Science47 (2016), 2342–2358.
52.
SmarandacheF., Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics. Pons Editions, Brussels, Belgium, 2016.
53.
MajiP.K., A neutrosophic soft set approach to a decision making problem, Annals of Fuzzy Mathematics and Informatics3 (2012), 313–319.
54.
KaraaslanF., Neutrosophic soft sets with applications in decision making, International Journal of Information Science and Intelligent System4 (2015), 1–20.
55.
DeliI. and BroumiS., Neutrosophic soft relations and some properties, Annals of Fuzzy Mathematics and Informatics9 (2015), 169–182.
