Article Preview
TopIntroduction
One of the most broadly applied indices in statistics is Karl Pearson’s correlation coefficient. Generally, in statistical theory, the correlation coefficient measures a linear relationship between two variables. Correlation coefficient is an important measure in data analysis and classification for their wide application in real world such as decision making, pattern recognition, market prediction, medical diagnosis and other real word problems concerning political, legal, economics, financial, social, educational etc systems. In the context of statistical theory, observations should be described by certain probability distributions. However, in real world application, the observations are sometimes described using linguistic terms such as excellent, good, bad or approximately known, rather than known with certainty i.e. observations may be fuzzy. It becomes challenge for researchers to measure the correlation coefficient between two random variables involving fuzziness. The concept of correlation coefficient has been extended to fuzzy observations. In many research papers, crisp correlation coefficients calculated for fuzzy observations (Bustince & Burillo, 1995; Chiang & Lin, 1999; Gerstenkorn & Manko, 1991; Hong & Hwang, 1995; Yu, 1995). On the other hand, some researchers have been proposed various methods to calculate fuzzy correlation coefficient for fuzzy observations by using fuzzy sets (Liu & Kao; 2002; Hong, 2006).
Attanassov (1983) generalized the concept of fuzzy set to intuitionistic fuzzy sets (IFS) to incorporate hesitation or uncertainty in the membership degrees of any object in fuzzy set. In fuzzy set, the degree of acceptance is considered only but IFS is characterized by a membership function (acceptance) and a non-membership function (rejection) so that the sum of both values is less than one (Attanassov, 1986). Presently intuitionistic fuzzy sets are being studied and used in different fields of Science and Engineering. Among the works on these sets, (Kumar & Yadav, 2011, 2012; Li, 2010, 2014; Li & Liu, 2015; Wan & Li, 2015; Yang, Li & Lai, 2016a; Yang, Fei & Li, 2016b; Park & Kwun, 2009) can be mentioned. Therefore, it is expected that intuitionistic fuzzy sets could be used to simulate any activities and processes requiring human expertise and knowledge, which are inevitably imprecise or not totally reliable