This paper applies the interval neutrosophic set theory to express fuzzy formal concept. A new interval neutrosophic fuzzy concept lattice is proposed. Furthermore, interval-distance and interval-similarity measure are discussed. We can find some interval neutrosophic fuzzy concepts to meet particular similarity range given by users. The result of this paper may enhance the flexibility of extracting knowledge and expand the capacity of knowledge.
GanterB. and WilleR., Formal concept analysis: Mathematical foundations, Springer-Verlag, Berlin Heidelberg, 1999.
2.
SinghP.K. and Aswani KumarC., and GaniA., A comprehensive survey on formal concept analysis, its research trends and applications, International Journal of Applied Mathematics and Computer Science26(2) (2016), 495–516.
3.
SinghP.K., AswaniK.C. and LiJ.H., Knowledge representation using interval-valued fuzzy formal concept lattice, Soft Computing20(4) (2016), 1485–1502.
4.
SinghP.K., Three-way fuzzy concept lattice representation using neutrosophic set, International Journal of Machine Learning and Cybernetics (2016), 1–11.
5.
SamarandacheF., A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press, Rehoboth1999.
6.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
7.
TurksenI.B., Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems20(2) (1986), 191–210.
8.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986), 87–96.
9.
AtanassovK.T. and GargovG., Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31(3) (1989), 343–349.
10.
TongS.C., Interval number and fuzzy number linear programmings, Fuzzy Sets and Systems66(3) (1994), 301–306.
11.
WangH.B., SmarandacheF., ZhangY.Q. and SunderramanR., Interval neutrosophic sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, AZ, 2005.
12.
AroraM., BiswasR. and PandyU.S., Neutrosophic relational database decomposition, International Journal of Advanced Computer Science and Applications2(8) (2011), 121–125.
13.
AnsariA.Q., BiswasR. and AggarwalS., Proposal for applicability of neutrosophic set theory in medical AI, International Journal of Computer Applications27(5) (2011), 5–11.
14.
YeJ., Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, Journal of Intelligent and Fuzzy Systems26(1) (2014), 165–172.
15.
YeJ., Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, International Journal of General Systems42(4) (2014), 386–394.
16.
SahinR. and KarabacakM., A multi attribute decision making method based on inclusion measure for interval neutrosophic sets, International Journal of Engineering and Applied Sciences02(2) (2015), 13–15.
17.
YuS.M., WJ. and WJ.Q., An extended TODIM approach with intuitionistic linguistic numbers, International Transactions in Operational Research (2016). DOI: 10.1111/itor.12363
18.
WangJ.Q., etc., Multi-criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric operators, Neural Computing and Applications (2016). DOI: 10.1007/s00521-016-2747-0
19.
PengH.G., ZhangH.Y. and WangJ.Q., Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems, Neural Computing and Applications (2016). DOI: 10.1007/s00521-016-2702-0
20.
LiangR.X., WangJ.Q. and LiL., Multi-criteria group decision making method based on interdependent inputs of single valued trapezoidal neutrosohpic information, Neural Computing and Applications (2016). DOI: 10.1007/s00521-016-2672-2
21.
TianZ.P., WangJ., WangJ.Q. and ZhangH.Y., Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development, Group and Negotiation (2016). DOI: 10.1007/s10726-016-9479-5
22.
PengJ., WangJ. and YangW., A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems, International Journal of Systems Science48(2) (2016), 425–435.
23.
ZhangH.Y., JiP., WangJ.Q. and ChenX.H., A novel decision support model for satisfactory restaurants utilizing social information: A case study of TripAdvisor.com, Tourism Management59 (2017), 281–297.
24.
WuX.H., WangJ.Q., PengJ. and ChenX.H., Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems, International Journal of Fuzzy Systems18(6) (2016), 1104–1116.
25.
GuoY.H. and ChengH.D., New neutrosophic approach to image segmentation, Pattern Recognition42(5) (2009), 587–595.
26.
ZhangM., ZhangL. and ChengH.D., A neutrosophic approach to image segmentation based on watershed method, Signal Processing90(5) (2010), 1510–1517.
27.
TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems12 (1997), 153–166.
28.
WeiG.W., Hesitant Fuzzy prioritized operators and their application to multiple attribute group decision making, Knowledge-Based Systems31 (2012), 176–182.
29.
WeiG.W., AlsaadiF.E., HayatT. and AlsaediA., Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making, Iranian Journal of Fuzzy Systems13(4) (2016), 1–16.
30.
LinR., ZhaoX.F., WangH.J. and WeiG.W., Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27 (2014), 49–63.
31.
LinR., ZhaoX.F. and WeiG.W., Models for selecting an ERP system with hesitant fuzzy linguistic information, Journal of Intelligent and Fuzzy Systems26(5) (2014), 2155–2165.
32.
XuF., XingZ.Y. and YinH.D., Attribute reductions and concept lattices in interval-valued intuitionistic fuzzy rough set theory: Construction and properties, Journal of Intelligent and Fuzzy Systems30(2) (2016), 1231–1242.
33.
WeiG.W., Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, International Journal of Machine Learning and Cybernetics7(6) (2016), 1093–1114.
34.
LiD.F. and ChengC.T., New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Letters23 (2002), 221–225.
35.
YeJ., Multicriteria group decision-making method using the distance-based similarity measures between intuitionistic trapezoidal fuzzy numbers, International Journal of General Systems41(7) (2012), 729–739.
36.
LiuX.C., Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems52(3) (1994), 305–318.
