The single-valued neutrosophic set (SVNS) is an extension of the fuzzy set and intuitionistic fuzzy set. This is a useful tool to deal with uncertain and inconsistent information. In the information theory, the distance measure, entropy measure and similarity measures have an important role. Several entropy measures of SVNSs have been proposed and applied in many real problems. But they have some restriction in practice and in the academic study. The similarity measures induced from entropy were studied and gave interesting results. In this paper, we introduce a new entropy measure concept based on the SVNS, which overcomes the restriction of existing entropy measures. At the same time, we also investigate some similarity measures which are induced from new entropy measures and apply them to propose the multi-criteria decision making (MCDM) model in selecting the supplier.
BroumiS. and SmarandacheF., Several similarity measures of SVNS sets, SVNS Sets and Systems1(1) (2013), 54–62.
5.
BurilloP. and BustinceH., Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems78(3) (1996), 305–316.
6.
ChiP. and LiuP., An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set, Neutrosophic Sets and Systems1(1) (2013), 63–70.
7.
CuiW.H. and YeJ., Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets, Entropy20(11) (2018), 844–855.
8.
CuiW. and YeJ., Improved symmetry measures of simplified neutrosophic sets and their decision-making method based on a sine entropy weight model, Symmetry10(6) (2018), 225–236.
9.
DinhN.V., ThaoN.X., ChauN.M., Some dissimilarity measures of picture fuzzy set, the 10th Fundamental and Applied IT Research (FAIR’ 2017) (2017), 104–109.
10.
FanJ. and XieW., Distance measure and induced fuzzy entropy, Fuzzy Sets and Systems104(2) (1999), 305–314.
11.
HuangH.L., New Distance Measure of Single-Valued SVNS Sets and Its Application, International Journal of Intelligent Systems31(10) (2016), 1021–1032.
12.
JoshiR., KumarS., GuptaD. and KaurH., A Jensen-α-Norm Dissimilarity Measure for Intuitionistic Fuzzy Sets and Its Applications in Multiple Attribute Decision Making, International Journal of Fuzzy Systems20(4) (2018), 1188–1202.
13.
KharalA., A SVNS multi-criteria decision making method, New Mathematics and Natural Computation10(02) (2014), 143–162.
14.
LiangX., WeiC. and XiaM., New entropy, similarity measure of intuitionistic fuzzy sets and their applications in group decision making, International Journal of Computational Intelligence Systems6(5) (2013), 987–1001.
15.
LiuP., ChuY., LiY. and ChenY., Some Generalized SVNS Number Hamacher Aggregation Operators and Their Application to Group Decision Making, International Journal of Fuzzy Systems16(2) (2014), 242–255.
16.
MajumdarP. and SamantaS.K., On similarity and entropy of SVNS sets, Journal of Intelligent & Fuzzy Systems26(3) (2014), 1245–1252.
17.
NguyenX.T. and GargH., Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process, Complex & Intelligent Systems5(2) (2019), 217–228.
18.
PengJ.J., WangJ.Q., ZhangH.Y. and ChenX.H., An outranking approach for multi-criteria decision-making problems with simplified SVNS sets, Appl Soft Comput25 (2014), 336–346.
19.
PengX., YuanH. and YangY., Pythagorean fuzzy information measures and their applications, International Journal of Intelligent Systems32(10) (2017), 991–1029.
20.
QinZ., LiX. and JiX., Portfolio selection based on fuzzy cross-entropy, Journal of Computational and Applied mathematics228(1) (2009), 139–149.
21.
SmarandacheF., Neutrosophy, SVNS Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, (1998), http://fs.gallup.unm.edu/eBook-Neutrosophics6.pdf (edition online).
22.
SmarandacheF., Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Spherical Fuzzy Set, and q-Rung Orthopair Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited), Journal of New Theory (29) (2019), 1–31.
23.
SzmidtE. and KacprzykJ., Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems118(3) (2001), 467–477.
24.
ThaoN.X., CuongB.C. and SmarandacheF., Rough standard neutrosophic sets: an application on standard neutrosophic information systems, Neutrosophic Sets and Systems14(1) (2016), 80–92.
25.
ThaoN.X., SonL.H., CuongB.C., AliM. and LanL.H., Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis. In: BhatejaV, NguyenB., NguyenN., SatapathyS., LeDN. (eds) Information Systems Design and Intelligent Applications. Advances in Intelligent Systems and Computing672 (2018), 834–842.
26.
ThaoN.X. and SmarandacheF., Divergence Measure of Neutrosophic Sets and Applications, Neutrosophic Sets and Systems21 (2018), 142–152.
27.
ThaoN.X., AliM. and SmarandacheF., An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis, Journal of Intelligent & Fuzzy Systems36(1) (2019), 189–198.
28.
ThaoN.X. and SmarandacheF., A new fuzzy entropy on pythagorean fuzzy sets, Journal of Intelligent & Fuzzy Systems37(1) (2019), 1065–1074.
29.
ThaoN.X., AliM., NhungL.T., GianeyH.K. and SmarandacheF., A new multi-criteria decision making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets, Journal of Intelligent & Fuzzy Systems37(6) (2019), 7785–7796.
30.
ThaoN.X., Similarity measures of picture fuzzy sets based on entropy and their application in MCDM, Pattern Anal Applic (2019). https://doi.org/10.1007/s10044-019-00861-9.
31.
VermaR. and SharmaB., R-norm entropy on intuitionistic fuzzy sets, Journal of Intelligent & Fuzzy Systems28(1) (2015), 327–335.
32.
WangH., SmarandacheF., ZhangY. and SunderramanR., Single valued SVNS sets, Multisp Multistruct4 (2010), 410–413.
33.
WangJ.Q., YangY., LiL., Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators, Neural Computing and Applications 30(5) (2018), 1529–1547.
34.
WuH., YuanY., WeiL. and PeiL., On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making, Soft Computing22(22) (2018), 7367–7376.
35.
ThaoN.X., A new correlation coefficient of the intuitionistic fuzzy sets and its application, Journal of Intelligent & Fuzzy Systems35(2) (2018), 1959–1968.
36.
XuechengL., Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems52(3) (1992), 305–318.
37.
YeJ., Cosine similarity measures for intuitionistic fuzzy sets and their applications, Math Comput Modell53(1–2) (2011), 91–97.
38.
YeJ., Vector similarity measures of simplified SVNS sets and their application in multicriteria decision making, Int J Fuzzy Syst16(2) (2014a), 204–211.
39.
YeJ., Clustering methods using distance-based similarity measures of single-valued SVNS sets, J Intell Syst23(4) (2014b), 379–389.
40.
YeJ., Single valued SVNS cross-entropy for multi-criteria decision making problems, Applied Mathematical Modelling38(3) (2014c), 1170–1175.
41.
YeJ., Improved cosine similarity measures of simplified SVNS sets for medical diagnoses, Artificial Intelligence in Medicine63(3) (2015a), 171–179.
42.
YeJ., Improved cross entropy measures of single valued SVNS sets and interval SVNS sets and their multicriteria decision making methods, Cybernetics and Information Technologies15(4) (2015b), 13–26.
43.
YeJ. and FuJ., Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function, Computer Methods and Programs in Biomedicine123 (2016), 142–149.
44.
YeJ., Single-valued SVNS similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine, Soft Computing21(3) (2017), 817–825.
45.
YeJ. and CuiW., Exponential entropy for simplified neutrosophic sets and its application in decision making, Entropy20(5) (2018), 357–366.
46.
YeJ. and DuS., Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship, International Journal of Machine Learning and Cybernetics10(2) (2019), 347–355.
