There are two very usful methods for solving MAGDM problems, called TOPSIS method and Choquet integral method. Because of the ability of Choquet integral method in managing of interaction criteria, we combined it with TOPSIS method to use from their benefits. First, we will introduce a new method for computing the distance between IT2FNs. Then, we proposed a hybrid method based on TOPSIS and Choquet integral in fuzzy type-2 environment. Numerical examples are considered to illustrate the proposed methods.
AshtianiB., HaghighiradF. and MontazerG.A., Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets, Appl Soft Comput9 (2009), 457–461.
2.
BebcakovaI., HolecekP. and TalasovaJ., On the application of the Choquet integral to multiple criteria evaluation, Acta Polytechnica Hungarica8(3) (2011).
3.
BoranF.E., GencS., KurtM. and AkayD., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with a TOPSIS method, Expert Syst Appl36 (2009), 11363–11368.
4.
BustinceH., FernandezJ., MesiarR. and KalickaJ., Discrete interval valued Choquet integrals, 6th International Summer School on Aggregation Operatores, AGOP, 2011.
5.
ChenC.T., Extensions of the TOPSIS for group decision making under fuzzy environment, Fuzzy Sets Syst114 (2000), 1–9.
6.
ChakrabortyC. and ChakrabortyD., A theoretical development on a fuzzy distance measure for fuzzy numbers, Mathematical and Computer Modelling43(3-4) (2006), 254–261.
7.
ChengC.H., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems95(3) (1998), 307–317.
8.
ChenS.M., YangM.W., LeeL.W. and YangS.W., Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets, Expert Systems with Applications39 (2012), 5295–5308.
9.
ChenS.M. and LeeL.W., Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method, Expert Systems with Applications37 (2010), 2790–2798.
10.
ChenS.M. and HngJ.A., Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets and the TOPSIS method, Expert Systems with Applications37 (2010), 2790–2798.
11.
GrabischM. and LabreucheC., A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid, Annals of Operation Research175(1) (2010), 247–286.
12.
GrabischM. and RoubensM., Application of the Choquet integral in multi criteria decision making, Fuzzy Measures and Integrals Theory and Application (2000), 348–374.
13.
GrzegorzewskiP., Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric, Fuzzy Sets and Systems148(2) (2004), 319–328.
14.
GuhaD. and ChakrabortyD., A Theoretical development of distance measure for intuitionistic fuzzy numbers, International Journal of Mathematics and Mathematical Sciences25 (2010).
15.
GuhaD. and ChakrabortyD., A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers, Applied Soft Computing Journal10(1) (2010), 90–99.
16.
HuangG.S., LiuY.S. and WangX.D., Some new distances between intuitionistic fuzzy sets, in Proceedings of the International Conference on Machine Learning and Cybernetics (ICMLC 05), Guangzhou, China, 2005, pp. 2478–2482.
HwangC.L. and YoonK., Multiple attribute decision making: Methods and Applications, Springer, Berlin, 1981.
19.
HamrawiH., CouplandS. and JohnR., A novel alpha-cut representation for type-2 fuzzy sets, In 6th IEEE World Congress on Computational Intelligence, 2010, pp. 1–8.
20.
KarnikN.N. and MendelJ.M., Centroid of a type-2 fuzzy set, Information Sciences132 (2001), 195–220.
21.
KeikhaA. and NehiH.M., Fuzzified Choquet integral and its applications in MADM: A review and a new method, International Journal of Fuzzy Systems (2015). DOI: 10.1007/s40815-015-0037-0
22.
KeikhaA. and NehiH.M., Multi Attribute Decision Making Problems with Interval Type-2 Fuzzy Numbers Information and Choquet Integral, Submitted.
23.
LiC., ZhangG., YiJ. and WangM., Uncertainty degree and modeling of interval type-2 fuzzy sets: Definition, method and application, Computers and Mathematics with Applications66 (2013), 1822–1835.
24.
MendelJ.M. and WuD., Cardinality, Fuzziness, Variance and Skewness of Interval Type-2 Fuzzy Sets,, Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007).
25.
MendelJ.M. and JohnR.I., Interval Type-2 fuzzy logic systems made simple, IEEE Transaction on Fuzzy Systems14(6) (2006).
26.
MendelJ.M. and WuH., New results about the centroid of an interval type-2 fuzzy set including the centroid of a fuzzy granule, Information Sciences177 (2007), 360–377.
27.
MendelJ.M., LiuF. and ZhaiD., α-plane representation for type-2 fuzzy sets: Theory and applications, IEEE Transactions on Fuzzy Systems17 (2009), 1189–1207.
28.
MendelJ.M. and JohnR.I.B., Type-2 fuzzy sets made simple, IEEE Transaction on Fuzzy Systems10(2) (2002).
29.
MizumotoM. and TanakaK., Some properties of fuzzy sets of type-2, Information and Control31 (1976), 312–340.
30.
NasabF.G. and MalkhalifehM.R., Extension of TOPSIS for group decision making based on the type-2 fuzzy positive and negative ideal solutions, Int J Industrial Mathematics2(3) (2010), 199–213.
31.
RutkowskiL., Computational Intelligence Methods and Techniques, Copyright for the English edition 2008, Springer-VerlagBerlin Heidelberg.
32.
SadeghianA., MendelJ.M. and TahayoriH., Advances in type-2 fuzzy sets and systems theory and applications, Springer Science, Business MediaNew York, 2013.
33.
SakawaM., Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, New York, 1993.
34.
SangX., LiuX. and CaiM., A distance based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers, 2014 IEEE International Conference on Fuzzy Systems (FUZZIEEE), Beijing, China, 2014.
35.
SzmidtE. and KacprzykJ., Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems114 (2000), 505–518.
36.
TakacZ., Intersection and union of type-2 fuzzy sets and connection to (α1, α2)-double cuts, Proc EUSFLAT-LFA, 2011, 1052–1059.
37.
TakacZ., On some properties of α-Planes of type-2 fuzzy sets, Kybernetika49(1) (2013), 149–163.
38.
TranL. and DucksteinL., Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets and Systems130(3) (2002), 331–341.
39.
TzengG.H. and HuangJ.J., Multiple Attribute Decision Making Methods and Application, CRC, 2011.
40.
VoxmanW., Some remarks on distances between fuzzy numbers, Fuzzy Sets and Systems100(1-3) (1998), 353–365.
41.
WangZ., LeungK.S., WongM.L., FangJ. and XuK., Nonlinear nonnegative multi regressions based on Choquet integrals, International Journal of Approximation Reasoning25 (2000), 71–87.
42.
WangW. and XinX., Distance measure between intuitionistic fuzzy sets, Pattern Recognition Letters26(13) (2005), 2063–2069.
43.
HungW.L. and YangM.S., Similarity measures of intuitionistic fuzzy sets based on Lp metric, International Journal of Approximate Reasoning46(1) (2007), 120–136.
44.
WuD. and MendelJ.M., A vector similarity measure for interval type2 fuzzy sets and type-1 fuzzy sets, submitted to Information Sciences, 2006.
45.
WuD. and MendelJ.M., Uncertainty measures for interval type-2 fuzzy sets, Information Sciences177 (2007), 5378–5393.
46.
WuH.J., SuY.L. and LeeS.J., A fast method for computing the centroid of a type-2 fuzzy set, IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics42(3) (2002).
47.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
48.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-1, Inform Sci8 (1975), 199–249.
49.
ZhaiD. and MendelJ.M., Uncertainty measures for general Type-2 fuzzy sets, Information Sciences181 (2011), 503–518.
