On a new picture fuzzy correlation coefficient with its applications to pattern recognition and identification of an investment sector

Picture fuzzy set is an efficient tool to realize the content of vagueness and uncertainty specifically in circumstances that could not be easily handled by intuitionistic fuzzy sets such as human voting, personnel selection, medical diagnosis, etc. In human voting, a voter can either vote in favor or vote against or presses “none of the above” button or refuse from voting. In personnel selection, the results of selection could be divided into four categories: true positive, false positive, true negative, and false negative. In medical diagnosis, the symptoms headache and temperature have neutral effect on the diseases’ chest problem and stomach problem. So, for these type of situations, the picture fuzzy sets are playing a vital significance. The correlation coefficient of picture fuzzy sets is a versatile measure to determine the association of two picture fuzzy sets and it has numerous implications in interdisciplinary studies like pattern recognition, decision making, clustering, diagnostic problems, etc. In this paper, we introduce a new correlation coefficient for picture fuzzy sets with some of its properties. This correlation coefficient is better than the existing correlation coefficients and other such measures in the picture fuzzy theory because it expresses the association between two picture fuzzy sets along with the nature of the association (positive or negative). Further, we examine the improvisation of the proposed picture fuzzy correlation coefficient over some existing picture fuzzy correlation measures in view of its application in pattern recognition. Finally, we utilize the proposed picture fuzzy correlation coefficient for determining an appropriate investment sector in the global economic slowdown.