V. Chinnadurai - Department of Mathematics, Annamalai University, Tamil Nadu, India.
A. Bobin - Department of Mathematics, Annamalai University, Tamil Nadu, India.

Considering today’s complexity, we may have to deal with numbers that are dependent, like those of positive, neutraland negative values and require multi- attributes function. Also,the most significant factor is to combine these numbers to generate a single real number. When decision-makers come across such an environment, the decisions are harder to make and decision makers cannot use the soft set theory, a single attribute function. To overcome this hindrance, we introduce the notion of picture fuzzy hypersoft set with technique of order of preference by similarity to ideal solution (TOPSIS) method. This eventually helps the decisionmaker to collect the data without any misconceptions. We presentsome properties of the correlation coefficient and aggregation operators on it. Also, we propose an algorithm for the TOPSIS method based on correlation coefficients to identify a suitable leader, who can bring changes to society in the socio-political context. Finally,we present a comparative study with existing studies to show the effectiveness of the proposed method.

Picture fuzzy set, Hypersoft set, TOPSIS, Correlation coefficient