The fuzzy set has its own limitations due to the membership function only. The fuzzy set does not describe the negative aspects of an object. The Fermatean fuzzy set covers the negative aspects of an object. The complex Fermatean fuzzy set is the most effective tool for handling ambiguous and uncertain information. The aim of this research work is to develop new techniques for complex decision-making based on complex Fermatean fuzzy numbers. First, we construct different aggregation operators for complex Fermatean fuzzy numbers, using Einstein t-norms. We define a series of aggregation operators named complex Fermatean fuzzy Einstein weighted average aggregation (CFFEWAA), complex Fermatean fuzzy Einstein ordered weighted average aggregation (CFFEOWAA), and complex Fermatean fuzzy Einstein hybrid average aggregation (CFFEHAA). The fundamental properties of the proposed aggregation operators are discussed here. The proposed aggregation operators are applied to the decision-making technique with the help of the score functions. We also construct different algorithms based on different aggregation operators. The extended TOPSIS method is described for the decision-making problem. We apply the proposed extended TOPSIS method to MAGDM problem “selection of an English language instructor”. We also compare the proposed models with the existing models.