Complex picture fuzzy N-soft sets and their decision-making algorithm

When a decision-maker gives such type of data like yes, no, abstain, or neutral along with 2-dimensional information in grading system, then the existing notions such as fuzzy N-soft set (FN-SS), intuitionistic FN-SS are not capable to handle such type of data. To handle such type of data and other problems we introduce the notion of complex picture fuzzy N-soft sets (CPFN-SS) which is the fusion of complex picture fuzzy sets (CPFSs) and N-soft sets (N-SS). CPFN-SS is a vital technique to handle tricky and unreliable information in real-life decision-making problems. We also introduce a novel definition of complex picture fuzzy soft sets which is a combination of complex fuzzy sets and picture fuzzy sets. In CPFN-SS notions of N-soft sets, fuzzy N-SSs, intuitionistic FN-SSs (IFN-SSs), picture FN-SSs complex FN-SSs, complex IFN-SSs are generalized. Furthermore, we describe some basic operations on CPFN-SSs such as complement, extended union, restricted union, extended intersection, and restricted intersection and illustrate them with the help of examples. After that, we define an algorithm to solve the data in the environment of CPFN-SSs. To show the advantages and usefulness of the proposed CPFN-SSs we represent two real-life applications, i.e., 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. In the end, we do a comparison of our established CPFN-SS with some existing methods which shows that CPFN-SS is more effective, better, and generalization of the existing ones.