Complex Picture Fuzzy N-Soft Sets and Their Decision Making Algorithm

Abstract We establish in this manuscript a new model complex picture fuzzy N-soft sets (CPFN-SSs) which is the fusion of complex picture fuzzy sets (CPFSs) along with N-soft sets (N-SSs) and a novel definition of CPFSs which is a mixture of complex fuzzy sets (CFSs) and picture fuzzy sets (PFSs). In CPFN-SS notions of N-SSs, fuzzy N-SSs (FN-SSs), intuitionistic FN-SSs (IFN-SSs), picture FN-SSs (PFN-SSs) complex FN-SSs (CFN-SS), complex IFN-SSs (CIFN-SSs) are generalized. We also talk about few basic operations on CPFN-SSs with the assistance of examples. Additionally, we establish two kinds of union (extended and restricted) and intersection (extended and restricted) of CPFN-SSs and illustrate them through examples. We also establish a complement of CPFN-SSs along with an example. Furthermore, we define an algorithm to solve the data in the environment of CPFN-SSs, and then we represent two real-world applications (performance assessment of e-waste recycling program and predication about the champions of FIFA world cup 2022 through audience poll) of our established model in decision-making (DM) to show the advantages and usefulness of the CPFN-SSs. In the end, we represent a comparison of our established model with some existing methods which shows that our established model is more general than existing ones.