Cluster analysis is a dynamic technique used to uncover natural groupings within data, making complex relationships easier to understand. By identifying similarities and patterns, it helps reveal insights that might otherwise go unnoticed. Methods like K-means, hierarchical clustering, mean shift clustering, spectral clustering, and fuzzy c-means clustering are widely embraced for their ability to transform raw data into clear, actionable clusters, simplifying decision-making and enhancing data analysis. Classification of things is very important in our daily life because when we do classification, it makes the importance of things clear and their characteristics are known, and later, we can use them easily. We have classified cluster analysis techniques in this manuscript, and maybe someone else before us has classified cluster analysis techniques by applying some other fuzzy structure, but our approach is different and generalized from all of them. We develop a strong mathematical framework by employing the theory of hesitant bipolar complex fuzzy sets. The proposed framework of Dombi Prioritized aggregation operators has various facts and features to solve multiple tasks in one frame. The proposed framework effectively handles both the positive and negative aspects of any object simultaneously. Additionally, it is designed to address the inherent hesitancy associated with objects, offering a comprehensive and adaptable solution. This framework also provides an extra step for the collection of some extra fuzzy information. Keeping in mind all these characteristics, we have classified cluster analysis techniques using this framework. Moreover, we used the multi-attribute decision methodology with a hesitant bipolar complex fuzzy Dombi Prioritized framework for the classification of the best cluster analysis technique. The key findings and results are the development of some aggregation operators, such as hesitant bipolar complex fuzzy Dombi prioritized arithmetic aggregation operators; hesitant bipolar complex fuzzy Dombi prioritized weighted arithmetic aggregation operators; hesitant bipolar complex fuzzy Dombi prioritized geometric aggregation operators, and hesitant bipolar complex fuzzy Dombi prioritized weighted geometric aggregation operators. At the end of the manuscript, we make a valuable comparison between the proposed theory and existing theories.