Fundamentals of Picture Fuzzy Hypersoft Set with Application

Theory of picture fuzzy soft set and generalized picture fuzzy soft sets(GPFSS) extended to picture fuzzy hypersoft sets (PFHSS) and generalized picture fuzzy hypersoft set (GPFHSS) respectively handle the uncertainties and multi-attribute values in the material during evaluation. The main focus of this research work is to initiate and learn new operations, along with properties and examples of PFHSS and GPFHSS. Several basic operations PFHSS are defined and also prove De Morgans laws for PFHSS. Furthermore, we construct an algorithm using GPFHSS and a new expectation score function for the positive value of the score function that is useful for ranking different MADM problems. We conclude from this study the proposed outlook used to manipulate the uncertainties and multi-attribute values decision-making problems.