The complex interval-valued Atanassov intuitionistic fuzzy set theory is an advanced modification of traditional fuzzy information that combines elements of both interval-valued fuzzy information and Atanassov intuitionistic fuzzy set theory, and incorporates complex numbers. Additionally, aggregating a finite number of alternatives into a singleton set is very important, where the Hamy mean operator and prioritized aggregation operator are much more suitable and flexible for depicting such kinds of problems. Our main goal of this manuscript was to analyze the Dombi operational laws based on complex interval-valued Atanassov intuitionistic fuzzy numbers. Further, the prioritized Hamy mean operators based on Dombi operational laws for complex interval-valued Atanassov intuitionistic fuzzy values, called the complex interval-valued Atanassov intuitionistic fuzzy Dombi Hamy mean operator, complex interval-valued Atanassov intuitionistic fuzzy weighted Dombi prioritized Hamy mean operator, complex interval-valued Atanassov intuitionistic fuzzy Dombi Dual Hamy mean operator, and complex interval-valued Atanassov intuitionistic fuzzy weighted Dombi Dual prioritized Hamy mean operator, were proposed. Some dominant and flexible properties of the evaluated operators were also examined. Further, in some multi-attribute decision-making problems, biased conclusions may be produced due to the deficiency of consideration for many relationships between the criteria of decision-making. Therefore, to evaluate the proficiency and reliability of the proposed operators, the multi-attribute decision-making technique based on derived operators for complex interval-valued Atanassov intuitionistic fuzzy values was developed. Finally, the proposed method with some prevailing techniques was compared to show its advantages and benefits.