Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.
AllahviranlooT. and FirozjaM.A., Ranking of fuzzy numbers by a new metric, Soft Computing14(7) (2010), 773–782.
2.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
3.
AtanassovK. and GargovG., Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31(3) (1989), 343–349.
4.
ChenS.J. and HwangC.L., Fuzzy Multiple Attribute Decision Making, Springer-Verlag, Berlin, Heidelberg, New York, 1992.
5.
DeP.K. and DasD., Ranking of trapezoidal intuitionistic fuzzy numbers, In Proceedings of IEEE ISDA2012, pp. 184–188.
6.
GrzegorzewskiP., Distances between intuitionistic fuzzy sets and/or interval valued fuzzy sets based on the Hausdorff metric, Fuzzy Sets and System148 (2004), 319–328.
7.
HuangG.S., LiuY.S. and WangX.D., Some new distances between intutionistic fuzzy sets, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, 2005, pp. 18–21.
8.
HungW.L. and YangM.S., Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance, Pattern Recognition Letters25 (2004), 1603–1611.
9.
NayagamV. Lakshmana Gomathi and VenkateshwariG., Ranking of intuitionistic fuzzy numbers, In Proceedings of the IEEE International Conference on Fuzzy Systems(IEEE FUZZ2008), pp. 1971–1974.
10.
LiD.F., A ratio ranking method of triangular intutionistic fuzzy numbers and its aaplication to madm problems, Computer and Mathematics with Applications60 (2010), 1557–1570.
11.
LiD.F., NanJ.X. and ZhangM.J., A ranking rethod of triangular intuitionistic fuzzy numbers and application to decision making, International Journal of Computational Intelligence Systems3(5) (2010), 522–530.
12.
MitchellH.B., Ranking intuitionistic fuzzy numbers, International Journal of Uncertainty Fuzziness and Knowledge Based Systems12(3) (2004), 377–386.
13.
SzmidtE. and KacprzykJ., On measuring distances between intuitionistic fuzzy sets, Notes IFS3 (1997), 1–13.
14.
SzmidtE. and KacprzykJ., Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems114 (1997), 505–518.
15.
WanS.P. and LiD.F., Possibility mean and variance based method for multi-attribute decision making with triangular intuitionistic fuzzy numbers, Journal of Intelligent and Fuzzy Systems24(4) (2013), 743–754.
16.
WanS.P., Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Mathematical Modelling37 (2013), 4112–4126.
17.
WangJ.Q., Overview on fuzzy multi-criteria decision making approach, Control Decision23 (2008), 601–606.
18.
WangJ.Q. and ZhangZ., Multi-criteria decision making with incomplete certain information based on intuitionistic fuzzy number, Control Decision24 (2009), 226–230.
19.
WangL.L., LiD.F. and ZhangS.S., Mathematical programming methodology for multi-attribute decision making using interval-valued intuitionistic fuzzy sets, Journal of Intelligent and Fuzzy Systems24(4) (2013), 755–763.
20.
WangX.F., WangJ.Q. and YangW.E., Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators, Journal of Intelligent and Fuzzy Systems26(1) (2014), 115–125.
21.
WeiG.W., Some arithmetic aggregation operators with intuitionistic trapezoidal fuzzy numbers and their application to group decision making, Journals of Computers5 (2010), 345–351.
22.
WuJ. and CaoQ., Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers, Applied Mathematical Modelling37 (2013), 318–327.
23.
XuZ. and ChenJ., On geometric aggregation over interval-valued intuitionistic fuzzy information, In Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery2 (2007), 466–471.
24.
XuZ.S., Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision22(2) (2007), 215–219.
25.
XuZ.S. and YagerR.R., Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems35 (2006), 417–433.
26.
YeJ., Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Systems with Applications36 (2009), 6899–6902.
27.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–356.