RETRACTED: Hamacher Weighted Aggregation Operators Based on Picture Cubic Fuzzy Sets and Their Application to Group Decision-Making Problems (Retracted Article)

In this study, an extended version of intuitionistic cubic fuzzy Hamacher weighted aggregation operators is the primary objective of the expected study. We establish new concept, picture cubic fuzzy set, and utilize this new concept for ranking in decision analysis. Picture cubic fuzzy Hamacher weighted averaging operator, picture cubic fuzzy Hamacher order weighted averaging, and picture cubic fuzzy Hamacher hybrid averaging operator are developed on the basis of picture cubic fuzzy sets. Some unique cases and few suitable properties of these proposed operators are also examined. In addition, based on these expected operators, we are designing a new multicriteria group decision-making framework. The proposed aggregation operators can be used in the performance evaluation of energy projects and security systems and devices. We give an illustrative example for the selection of small hydropower plants locations as an implementation and appropriateness of the proposed algorithm. Finally, we perform a comparative review of the designed algorithm with intuitionistic cubic fuzzy Hamacher weighted averaging operators to expose the new algorithm efficiency, feasibility, and goodness.