First we give notion of integral of intuitionistic fuzzy set and introduce intuitionistic fuzzy implicator and intuitionistic fuzzy inclusion measure. Then we propose a new measure of similarity between two intuitionistic fuzzy sets based on intuitionistic fuzzy inclusion measure. Examples are given to illustrate our notion and the application of this new similarity measure in multi-criteria decision making.
AbreuR., ZoeteweijP. and van GemundA.J.C., An evaluation of similarity coefficients for software fault localization, 12th Pacific Rim International Symposium on Dependable Computing, 2006, pp. 39–46.
2.
AltschulS.F., MaddenT.L., SchäfferA.A., ZhangJ., ZhangZ., MillerW. and LipmanD.J., Gapped BLAST and PSI-BLAST: A new generation of protein database search programs, Nucleic Acids Research25(17) (1997), 3389–3402.
3.
AngellR.C., FreundG.E. and WillettP., Automatic spelling correction using a trigram similarity measure, Information Processing & Management19(4) (1983), 255–261.
4.
AshbyF.G., Towards a unified theory of similarity and recognition, Psychological Review95 (1988), 124–150.
5.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
6.
AtanassovK., Intuitionistic Fuzzy Sets, Theory and Applications, Heidelberg: Physica-Verlag, 1999.
7.
AtanassovK., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
8.
AtanassovK., PasiG. and YagerR., Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making, International Journal of Systems Science36(14) (2005), 859–868.
9.
AtanassovK., VassilevP. and TsvetkovR., Intuitionistic Fuzzy Sets, Measures and Integrals, “Prof. Marin Drinov” Academic Publishing House, Sofia, 2013.
10.
BanA., Intuitionistic Fuzzy Measures. Theory and Applications, Nova Science Publishers, New York, 2006.
11.
BandyopadhyayS. and SahaS., Unsupervised classification: Similarity Measures, Classical and Metaheuristic Approaches, and Applications, Springer, 2013.
12.
BegI. and AshrafS., Fuzzy similarity and measure of similarity with Lukasiewicz implicator, New Mathematics and Natural Computation4(2) (2008), 191–206.
13.
BegI. and AshrafS., Similarity measures for fuzzy sets, Applied Mathematics and Computation8(2) (2009), 192–202.
14.
BegI. and RashidT., TOPSIS for hesitant fuzzy linguistic term sets, International Journal of Intelligent Systems28(12) (2013), 1162–1171.
15.
BegI. and RashidT., Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS, OPSEARCH51(1) (2014), 98–129.
16.
BegI. and RashidT., Aggregation operators of interval-valued 2-tuple linguistic information, International Journal of Intelligent Systems29 (2014), 634–667.
17.
BellmanR.E. and ZadehL.A., Decision making in a fuzzy environment, Management Science17(4) (1970), 141–164.
18.
BoranF.E. and AkayD., A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition, Information Sciences255(10) (2014), 45–57.
19.
BoranF.E., GenS., KurtM. and AkayD., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications36 (2009), 11363–11368.
20.
BustinceH. and BurilloP., Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems78 (1996), 293–303.
21.
CornelisC. and KerreE., Inclusion measures in Intuitionistic fuzzy set theory, ECSQARU, LNAI2711 (2003), 345–356.
22.
CrossV.V. and SudkampT.A., Similarity and Compatibility in Fuzzy Set Theory, Physica-Verlag, Heidelberg, NY, 2002.
23.
DeS.K., BiswasR. and RoyA.R., An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems117 (2001), 209–213.
24.
DengfengL. and ChuntianC., New similarity measures of Intuitionistic fuzzy sets and applications to pattren recognition, Pattren Recognition Letters23(1-3) (2002), 221–225.
25.
DeschrijverG., CornelisC. and KerreE.E., On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems12(1) (2004), 45–61.
26.
DuboisD., The role of fuzzy sets in decision sciences: Old techniques and new directions, Fuzzy Sets and Systems184 (2011), 3–28.
27.
DuboisD., GottwaldS., HajekP., KacprzykJ. and PradeH., Terminological difficulties in fuzzy set theory— The case of “Intuitionistic Fuzzy Sets”, Fuzzy Sets and Systems156(3) (2005), 485–491.
28.
El-SayedM.A. and AboelwafaN., Study of face recognition approach based on similarity measures, International Journal of Computer Science Issues9(5) (2012), 133–139.
29.
FonckP., FodorJ. and RoubensM., An application of aggregation procedures to the definition of measures of similarity between fuzzy sets, Fuzzy Sets and Systems97 (1998), 67–74.
30.
FooteJ., A similarity measure for automatic audio classification, AAAI Technical Report SS-97-03, 1997.
31.
GowdaK.C. and DidayE., Symbolic clustering using a new similarity measure, IEEE Transactions on Systems, Man and Cybernetics22(2) (1992), 368–378.
32.
HerreraF. and MartinezL., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems8(6) (2000), 746–752.
33.
JarvisR.A. and PatrickE.A., Clustering using a similarity measure based on shared near neighbors, IEEE Transactions on Computers22(11) (1973), 1025–1034.
34.
KöhlerS., SchulzM.H., KrawitzP., BauerS., DölkenS., OttC.E., MundlosC., HornD., MundlosS. and RobinsonP.N., Clinical diagnostics in human genetics with semantic similarity searches in ontologies, The American Journal of Human Genetics85 (2009), 457–464.
35.
LeeS. and CrawfordM.M., Unsupervised multistage image classification using hierarchical clustering with a bayesian similarity measure, IEEE Transactions on Image Processing14(3) (2005), 312–320.
36.
LeeK. and ParkH., Modular PCA and probabilistic similarity measure for robust face recognition, International Journal of Multimedia and Ubiquitous Engineering7(2) (2012), 497–502.
37.
LiD-F, Multi attribute decision making models and methods using intuitionistic fuzzy sets, Journal of Computer and System Sciences70 (2005), 73–85.
38.
LiB. and HeW., The structures of intuitionistic fuzzy equivalence relations, Information Sciences278 (2014), 883–899.
39.
LiD.F., WangY.C., LiuS. and ShanF., Fractional programming methodology for multi-attribute group decision making using IFS, Applied Soft Computing8(1) (2008), 219–225.
40.
MartinezL. and HerreraF., An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges, Information Sciences207(1) (2012), 1–18.
41.
MundaG., A conflict analysis approach for illuminating distributional issues in sustainability policy, European Journal of Operational Research194 (2009), 307–322.
42.
NguyenH.T. and WalkerE.A., Fuzzy logic (Third Edition) CRC Press, 2006.
43.
PapakostasG.A., HatzimichailidisA.G. and KaburlasosV.G., Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view, Pattern Recognition Letters34(14) (2013), 1609–1622.
44.
ShiY., GasseB.V. and KerreE., The role a fuzzy implication plays in a multi-criteria decision algorithm, International Journal of General Systems42(1) (2013), 111–120.
45.
WangW.J., New similarity measures on fuzzy sets and on el10 I. Beg and T. Rashid, Intuitionistic fuzzy similarity measure: Theory and applications ements, Fuzzy Sets and Systems85 (1997), 305–309.
46.
XuZ., ChenJ. and WuJ., Clustering algorithm for intuitionistic fuzzy sets, Information Sciences178 (2008), 3775–3790.
47.
XuZ. and XiaM., Distance and similarity measure for hesitant fuzzy sets, Information Sciences181(1) (2011), 2128–2138.
48.
ZadehL.A., Similarity relations and fuzzy orderings, Information Sciences3(2) (1971), 177–200.
49.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–356.
50.
ZwickR., CarlsteinE. and BudescoD.V., Measures of similarity amongst fuzzy concepts: A comparative analysis, International Journal of Approximate Reasoning1 (1987), 221–242.
