A divergence measure plays an important part in distinguishing two probability distributions and drawing conclusions based on that discrimination. In this paper, we proposed the concept of divergence measure of picture fuzzy sets. We also built some formulas of the proposed divergence measure of picture fuzzy sets anddiscussed some basic properties of this measure.Based on the proposedmeasure, we developed a multi-criteria decision-making algorithm. Finally, we applied the proposed multi-criteria decision-making algorithm in the medical diagnosis problem and the classification problem.
AtanassovK.T., Intuitionistic Fuzzy Sets, Fuzzy set and systems20 (1986), 87–96.
2.
ChairaT.A.K., Ray, A new measure using intuitionistic fuzzy set theory and its application to edge detection, Applied Soft Computing8(2) (2007), 919–927.
3.
CuongB.C. and KreinovichV., Picture Fuzzy Sets-a new concept for computational intelligence problems, In: 3rd World Congress onInformation and Communication Technologies (WICT), Hanoi, Vietnam, IEEE CS, 2013, pp.1–6.
4.
CuongB.C. and HaiP., Some fuzzy logic operators for picture fuzzy sets, In: 7thKnowledge and Systems Engineering (KSE), Hochiminh, Vietnam, 2015, pp. 132–137.
5.
CuongB.C., NganR.T. and HaiB.D, An involutive picture fuzzy negator on picture fuzzy sets and some De Morgan triples, In: 7th Knowledge and Systems Engineering (KSE), Hochiminh, Vietnam, 2015, pp. 126–131
6.
DeS.K., BiswasR. and RoyA.R., An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy sets and Systems117(2) (2001), 209–213.
7.
DinhN.V., ThaoN.X. and ChauN.M., Distance and dissimilarity measure of picture fuzzy sets, In: 10th Fundamental and Applied IT Research (FAIR 2017), Danang, Vietnam, 2017, pp. 104–109.
8.
GargH., Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making, Arabian Journal for Science and Engineering42(12) (2017), 5275–5290.
9.
HungW.L. and YangM.S., On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition, Information sciences178(6) (2007), 1641–1650.
10.
KobzaV., JanišV. and MontesS., Divergence measures on hesitant fuzzy sets, Journal of Intelligent & Fuzzy Systems33(3) (2017), 1589–1601.
11.
KumarS.V.A., HarishB.S. and AradhyaV.M., A picture fuzzy clustering approach for brain tumor segmentation, In: 2ndCognitive Computing and Information Processing (CCIP), Mysore, India, 2016, pp. 1–6.
12.
JainK.C. and ChhabraP., New information inequalities on new generalized f-divergence and applications, Le Matematiche70(2) (2015), 271–281.
13.
LeN.T., Van NguyenD., NgocC.M. and NguyenT.X., New dissimilarity measures on picture fuzzy sets and applications, Journal of Computer Science and Cybernetics34(3) (2018), 219–231.
14.
LiuP. and LiH., Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making, Cognitive Computation9(4) (2017), 494–512.
15.
LiuP., LiuJ. and MerigóJ.M., Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making, Applied Soft Computing62 (2018), 395–422.
16.
LiuP., Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators, Computers & Industrial Engineering108 (2017), 199–212.
17.
LiuP. and WangP., Some q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making, International Journal of Intelligent Systems33(2) (2018), 259–280.
18.
LiuP. and ChenS.M., Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers, IEEE Transactions on Cybernetics47(9) (2017), 2514–2530.
19.
LiuP., ChenS.M. and LiuJ., Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators, Information Sciences411 (2017), 98–121.
20.
LiuP. and ChenS.M., Multiattribute Group Decision Making Based on Intuitionistic 2-Tuple Linguistic Information, Information Sciences430-431 (2018), 599–619.
21.
MishraA.R., KumariR. and SharmaD.K., Intuitionistic fuzzy divergence measure-based multi-criteria decision-making method, Neural Computing and Applications (2017), 1–16.
22.
MontesS., PalN.R. and JanišV., Divergence measures for intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems23(2) (2015), 444–456.
23.
MontesS., CousoI., GilP. and BertoluzzaC., Divergence measure between fuzzy sets, International Journal of Approximate Reasoning30(2) (2002), 91–105.
24.
NguyenX.T., Evaluating Water Reuse Applications under Uncertainty: A Novel Picture Fuzzy Multi Criteria Decision Making Medthod, International Journal of Information Engineering and Electronic Business10(6) (2018), 32–39.
25.
Ohlan, A new generalized fuzzy divergence measure and applications, Fuzzy Information and Engineering7(4) (2015), 507–523.
26.
ParkashO. and KumarR., Modified fuzzy divergence measure and its applications to medical diagnosis and MCDM, Risk and Decision Analysis6(3) (2017), 231–237.
27.
SinghP., Correlation coefficients for picture fuzzy sets, Journal of Intelligent & Fuzzy Systems28(2) (2015), 591–604.
28.
SmarandacheF. and NeutrosophicNeutrosophy., Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.unm.edu/eBook-Neutrosophics6.pdf (edition online).
29.
SonL.H., DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets, Expert Systems with Applications42(1) (2015), 51–66.
30.
SonL.H., Generalized picture distance measure and applications to picture fuzzy clustering, Applied Soft Computing46(C) (2016), 284–295.
31.
SonL.H., Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures, Fuzzy Optimization and Decision Making16(3) (2017), 359–378.
32.
SrivastavaS. and Maheshwari, Decision making in medical investigations using new divergence measures for intuitionistic fuzzy sets, Iranian Journal of Fuzzy Systems13(1) (2016), 25–44.
33.
ThaoN.X., CuongB.C., AliM. and LanL.H., Fuzzy equivalence on standard and rough neutrosophic sets and applications to clustering analysis, In: Information Systems Design and Intelligent Applications, Springer-Singapore, 2018, pp. 834–842.
34.
ThaoN.X. and DinhN.V., Rough picture fuzzy set and picture fuzzy topologies, Journal of Computer Science and Cybernetics31(3) (2015), 245–253.
35.
ThaoN.X. and SmarandacheF.A., A new fuzzy entropy on pythagorean fuzzy sets, Journal of Intelligent & Fuzzy Systems37(1) (2019), 1065–1074.
36.
ThaoN.X. and DuongT.T.T., Selecting target market by similar measures in interval intuitionistic fuzzy set, Technological and Economic Development of Economy (2019), 1–17 (accepted).
37.
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.
38.
ThongP.H., A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality, Knowledge-Based Systems109 (2016), 48–60.
39.
ThongP.H. and SonL.H., Picture fuzzy clustering for complex data, Engineering Applications of Artificial Intelligence56 (2016), 121–130.
40.
ThongP.H., Picture fuzzy clustering: a new computational intelligence method, Soft computing20(9) (2016), 3549–3562.
41.
Van DinhN., ThaoN.X. and ChauN.M., On the picture fuzzy database: theories and application, J Sci & Devel13(6) (2015), 1028–1035.
42.
Van DinhN. and ThaoN.X., Some measures of picture fuzzy sets and their application, Journal of Science and Technology: Issue on Information and Communications Technology3(2) (2017), 35–40.
43.
VermaR. and SharmaB.D., On generalized intuitionistic fuzzy divergence (relative information) and their properties, Journal of Uncertain Systems6(4) (2012), 308–320.
44.
VermaR. and MaheshwariS., A new measure of divergence with its application to multi-criteria decision making under fuzzy environment, Neural Computing and Applications28(8) (2017), 2335–2350.
45.
WangC.Y., ZhouX.Q., TuH.N. and TaoS.D., Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making, Ital. J. Pure Appl. Math37 (2017), 477–492.
46.
WeiG., Picture fuzzy aggregation operators and their application to multiple attribute decision making, Journal of Intelligent & Fuzzy Systems33(2) (2017), 713–724.
47.
WeiG., Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics and Management17(4) (2016), 491–502.
48.
WeiG., Some similarity measures for picture fuzzy sets and their applications, Iranian Journal of Fuzzy Systems15(1) (2018), 77–89.
49.
Xuan ThaoN., A new correlation coefficient of the intuitionistic fuzzy sets and its application, Journal of Intelligent & Fuzzy Systems35(2) (2018), 1959–1968.
50.
ZadehL.A., Fuzzy sets, Information and control8(3) (1965), 338–353.
51.
ZhanJ. and AlcantudJ.C.R., A novel type of soft rough covering and its application to multi criteria group decision making, Artificial Intelligence Review (2018), 1–30.
52.
ZhanJ. and AlcantudJ.C.R., A survey of parameter reduction of soft sets and corresponding algorithms, Artificial Intelligence Review (2018), 1–34.
53.
Zhan, SunB. and AlcantudJ.C.R., Covering based multigranulation (I, T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences476 (2019), 290–318.
54.
ZhangJ. and Zhan XuZ.X., Covering-based generalized IF rough sets with applications to multi-attribute decision-making, Information Sciences478 (2019), 275–302.
55.
Zhang, ZhanJ., WuW.Z. and AlcantudJ.C.R., Fuzzy β-covering based (I, T)-fuzzy rough set models and applications to multi-attribute decision-making, Computers & Industrial Engineering128 (2019), 605–621.
