Bipolar-Valued Complex Fuzzy Prioritized Weighted Dombi Aggregating Operators and Their Applications in Multi-Criteria Decision-Making Problems

Fuzzy set theory plays a crucial role in decision-making under uncertainty. However, traditional models struggle to represent both positive and negative dimensions of evaluations simultaneously. To address this limitation, bipolar-valued complex fuzzy sets (BVCFS) have been introduced, extending both bipolar fuzzy sets and complex fuzzy sets. In this study, we propose two new prioritized aggregation operators: the Bipolar-Valued Complex Fuzzy Prioritized Weighted Dombi Arithmetic Averaging (BVCFPrWDAA) Operator and the Bipolar-Valued Complex Fuzzy Prioritized Weighted Dombi Geometric Averaging (BVCFPrWDGA) Operator. These operators leverage Dombi t-norm and t-conorm functions, which provide a more flexible and accurate framework for multi-criteria decision-making (MCDM). We investigate the fundamental properties of these operators, including idempotency, monotonicity, and boundedness, to ensure their reliability in decision-making applications. Additionally, we introduce a novel score function to enhance the precision of alternative rankings. A decision-making algorithm is developed and applied to a real-world MCDM problem, which demonstrates the superior performance of the proposed methods compared to existing approaches. The comparative analysis highlights the advantages of our approach, showing that the BVCFPrWDAA operator yields a consistent ranking, while the BVCFPrWDGA operator enables a broader differentiation among alternatives.