Imprecision is an important factor in any decision-making process. Different tools and approaches have been introduced to handle the imprecise environment of group decision-making. One of the latest tools in dealing with imprecision is Pythagorean fuzzy sets. These sets generalize intuitionistic fuzzy sets with a wider scope of applications, and, thus, the motivation for investigating into its resourcefulness in tackling career placements problem. In this paper, we explore the concept of Pythagorean fuzzy sets and deduce some theorems in connection to score and accuracy functions. Some properties of Pythagorean fuzzy sets are outlined. The idea of relation is established in Pythagorean fuzzy set setting called Pythagorean fuzzy relation with numerical illustrations to validate the developed relation. Finally, a decision-making approach of career placements on the basis of academic performance is presented using the proposed Pythagorean fuzzy relation called max-min-max composition to ascertain the suitability of careers to applicants. The approach adopted in this paper is suggestible to solve the other multi-criteria decision-making problems or multi-attribute decision-making problems, respectively.

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Intuitionistic fuzzy set is a significance soft computing tool for curbing fuzziness embedded in decisionmaking processes. To enhance the applicability of intuitionistic fuzzy sets in modelling practical real-life problems, various computing methods have been proposed like distance measures, similarity measures and correlation measures. This paper proposes an intuitionistic fuzzy statistical correlation algorithm with applications to pattern recognition and diagnostic processes. This novel method assesses the magnitude of relationship and indicates whether the intuitionistic fuzzy sets under consideration are correlated in either positive or negative sense. We substantiate the proposed technique with some theoretical results and numerically validate it to be superior in terms of accuracy and reliability in contrast to some hitherto techniques. Finally, we determine decision-making processes involving pattern recognition and diagnostic processes by using JAVA programming language to code the intuitionistic fuzzy statistical correlation measure.