Bipolar neutrosophic with Dombi-Heronian mean operators for multi-criteria decision-making applications

Aggregation operators (AOs) play a crucial role in multi-criteria decision-making (MCDM) by providing methods to combine multiple evaluations into a single representative value. Dombi operations, based on Dombi t-norms and t-conorms, offer flexible parameters to address varying degrees of uncertainty and aggregation requirements. At the same time, the bipolar neutrosophic set (BNS) enhances decision-making by capturing positive, negative, and indeterminate information, making it particularly effective under uncertain or incomplete data. However, existing Dombi-based operators within the BNS framework do not consider interrelationships between input arguments. To address this limitation, this study introduces a novel aggregation operator known as the bipolar neutrosophic Dombi-based improved generalized weighted Heronian mean (BND-IGWHM), which combines Dombi operations, the Heronian mean, and BNS. Furthermore, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is employed to analyze cause-and-effect relationships in complex decision problems.Recognizing its limitations in capturing interdependencies among arguments, we propose a DEMATEL method enhanced with the BND-IGWHM operator, offering a more comprehensive decision-making methodology. To demonstrate the applicability and effectiveness of the proposed operators, we integrate them into multi-criteria decision-making (MCDM) processes using both a score-based ranking method and a Decision-Making Trial and Evaluation Laboratory (DEMATEL)-based method. A comparative analysis is then performed to evaluate the performance of the proposed BND-IGWHM-DEMATEL method against existing aggregation methods. The results demonstrate that the DEMATEL-based method employing the BND-IGWHM operator offers greater flexibility and improved aggregation accuracy, leading to more effective decision-making in uncertain and bipolar environments.