Intuitionistic fuzzy set theory has become a powerful tool to describe uncertain or vague information. Bonferroni mean (BM) operator captures the interrelationship among aggregated arguments during the aggregation process. Recently, the partitioned Bonferroni mean (PBM) operator has been proposed with the assumption that the interrelationships do not always exist among all of the attributes. The work studies the PBM operator under the intuitionistic fuzzy environment. First, we propose a generalized intuitionistic fuzzy interaction partitioned Bonferroni mean (GIFIPBM) operator for aggregating intuitionistic fuzzy numbers with considering the interaction between membership function and nonmembership function. Some properties and special cases of the new aggregation operator are also investigated. In addition, the paper proposes the generalized intuitionistic fuzzy weighted interaction partitioned Bonferroni mean (GIFWIPBM) operator to consider the importance of each argument in the final aggregated result.