<p>The complex bipolar fuzzy sets fundamentally expand upon bipolar fuzzy sets and complex fuzzy set, and demonstrate efficacy in dealing with two-dimensional uncertainty, specifically where amplitude and phase information are both relevant. However, existing aggregation operators within the complex bipolar fuzzy environment generally fail to provide ample flexibility and generalization to accommodate broader range of decision-making scenarios. To overcome this deficiency, this research puts forward four novel aggregation operators based on Dombi operations: Complex bipolar Dombi fuzzy weighted arithmetic aggregation operator, Complex bipolar Dombi fuzzy weighted geometric aggregation operator, Complex bipolar Dombi fuzzy ordered weighted arithmetic aggregation operator, and Complex bipolar Dombi fuzzy ordered weighted geometric aggregation operator. These operators incorporate operational parameters to enhance adaptability and accuracy in aggregation processes. In this research, we propose the mathematical formulation and fundamental properties of these operators within the complex bipolar fuzzy framework. To demonstrate the usefulness of the proposed method, a case study involving the selection of a buffalo with the objective of profit maximization and the best possible return on investment is presented. The outcomes confirm that the suggested operators offer enhanced flexibility and efficiency over existing aggregation methods. The comparative study additionally demonstrates their distinct advantages, making them valuable tools for complex bipolar fuzzy decision-making applications.</p>