Soft Computing

pp 1–12

# A new correlation coefficient of the Pythagorean fuzzy sets and its applications

Methodologies and Application

## Abstract

In this paper, we propose a new correlation coefficient between Pythagorean 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. In probability and statistical theory, the correlation coefficient indicates the strength of the linear correlation between two random variables. The correlation coefficient is equal to one in the case of a linear correlation and − 1 in the case of a linear inverse correlation. Other values in the range (− 1, 1) indicate the degree of linear dependence between variables. The closer the coefficient is to − 1 and 1, the stronger the correlation between variables. 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, and the value of this correlation coefficient is in [− 1, 1]. We also commented on the linear relationship between fuzzy sets affecting their correlation coefficients through examples to show the usefulness in the proposed new measure. Then, we develop this direction to build correlation coefficients between the interval-valued intuitionistic fuzzy sets and apply it in the pattern recognition problem.

## Keywords

Pythagorean fuzzy set Interval-valued Pythagorean fuzzy set Variance Covariance Correlation coefficient

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