Complex Cubic Fuzzy Einstein Averaging Aggregation Operators: Application to Decision-making Problems

Different complex fuzzy sets are reported in the literature as the generalizations of fuzzy sets. Complex cubic fuzzy sets are also among those complex fuzzy sets, extensions of cubic sets. The main task is using complex cubic fuzzy sets in decision-making problems, and we propose some aggregation operators. We introduce the concept of complex cubic fuzzy ordered and hybrid weighted averaging operators using Einstein’s sum, product, scalar, and exponential multiplication. We discuss some algebraic operations of complex cubic fuzzy sets (CCFS) and their structural properties. We develop three arithmetic averaging operators: complex cubic fuzzy Einstein weighted averaging (CCFEWA), complex cubic fuzzy Einstein ordered weighted averaging (CCFEOWA), and complex cubic fuzzy Einstein hybrid weighted averaging (CCFEHWA) operators. The CCFEHWA operator generalizes both the CCFEWA and CCFEOWA operators. We apply the CCFEHWA operator to multiple attribute decision-making with complex cubic fuzzy data. In the end, we discuss a numerical example with comparative analysis.