In this paper, we propose a new correlation coefficient between intuitionistic fuzzy sets. We then use this new result to compute some examples through which we find that it benefits from such an outcome with some well-known results in the literature. As in statistics with real variables, we refer to variance and covariance between two intuitionistic fuzzy sets. Then, we determined the formula for calculating the correlation coefficient based on the variance and covariance of the intuitionistic fuzzy set, the value of this correlation coefficient is in [−1,1]. Then, we develop this direction to build correlation coefficients between the interval-valued intuitionistic fuzzy sets and apply it in the pattern recognition problem.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy sets and Systems20(1) (1986),87–96.
2.
AtanassovK., Springer, On Intuitionistic Fuzzy Sets TheorySpringer, Berlin, 2012.
3.
AtanassovK. and GargovG., Interval valued intuitionistic fuzzy sets, Fuzzy sets and systems31(3) (1989),343–349.
4.
BharatiS.K. and SinghS.R., Intuitionistic fuzzy optimization technique in agricultural production planning: A small farm holder perspective, International Journal of Computer Applications89(6) (2014),17–23.
5.
BustinceH. and BurilloP., Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy sets and systems74(2) (1995),237–244.
6.
ChiangD.A. and LinN.P., Correlation of fuzzy sets, Fuzzy Sets and Systems102(2) (1999),221–226.
7.
GerstenkornT. and MańkoJ., Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems44(1) (1991),39–43.
8.
HungW.L., Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems9(04) (2001),509–516.
9.
HungW.L. and WuJ.W., Correlation of intuitionistic fuzzy sets by centroid method, Information Sciences144(1) (2002),219–225.
10.
HwangC.M., YangM.S., HungW.L. and LeeM.G., A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition, Information Sciences189 (2012),93–109.
11.
LiJ. and ZengW., A new dissimilarity measure between intuitionistic fuzzy sets and its application in multiple attribute decision making, Journal of Intelligent & Fuzzy Systems29(4) (2015),1311–1320.
12.
LiuB., ShenY., MuL., ChenX. and ChenL., A new correlation measure of the intuitionistic fuzzy sets, Journal of Intelligent & Fuzzy Systems30(2) (2016),1019–1028.
13.
MitchellH.B., A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems19(5) (2004),483–490.
14.
ShidpourH., BernardA. and ShahrokhiM., A group decision-making method based on intuitionistic fuzzy set in the three dimensional concurrent engineering environment: A multi-Objective programming approach, Procedia CIRP7 (2013),533–538.
15.
SzmidtE. and KacprzykJ., Intuitionistic fuzzy sets in group decision making, Notes on IFS2(1) (1996),11–14.
16.
SzmidtE. and KacprzykJ., A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning, Lecture Notes in Artificial Intelligent (2007),109–121.
17.
BuhaeskuT., On the convexity of intuitionistic fuzzy sets, Itinerant Seminar of functional equations, approximation and convexity, Cluj-Napoca, 1988, pp, 137–143.
18.
XuZ., On correlation measures of intuitionistic fuzzy sets, Lecture Notes in Computer Science4224 (2006),16–24.
19.
XuZ., Choquet integrals of weighted intuitionistic fuzzy information, Information Sciences180(5) (2010),726–736.
20.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965),338–353.
21.
ZengW. and WangJ., Correlation coefficient of interval-valued intuitionistic fuzzy sets, pp, International Conference on Fuzzy Systems and Knowledge Discovery (FSKD) (2011),98–102.
22.
ZhouX., ZhaoR., YuF. and TianH., Intuitionistic fuzzy entropy clustering algorithm for infrared image segmentation, Journal of Intelligent & Fuzzy Systems30(3) (2016),1831–1840.
