The Aggregation operators (AOs) play an essential part in decision-making, particularly when there are other things to consider. The current study’s objective is to construct AOs and operational rules within an intuitionistic fuzzy Z-number (\(\textrm{IFZN}\)) framework. In order to accomplish this, we create special operational laws that give an acceptable or equitable solution for \(\textrm{IFZNs}\) through the use of the idea of proportionate distribution. In this article, we are introduced to \(\textrm{IFZNs}\) based on fairly operators which is probably a new concept in fuzzy theory. The proposed study aims to provide a set of weighted AOs using \(\textrm{IFZNs}\). In this research, we looked at fairly operators for the \(\textrm{IFZNs}\). Additionally, multi-attribute group decision-making challenges are resolved by applying the suggested fairness operators for the \(\textrm{IFZNs}\). With numerical examples of group decision-making difficulties, we present the proposed models. Likewise, a fairly multi-criteria decision-making (MCDM) technique is established by using recommended reasonable AOs with assessments from numerous decision-makers (DMs) and partially weighting the data under \(\textrm{IFZNs}\). We assert that the new technique is far more accurate and efficient than the current model. Likewise, an extensive execution of the suggested methodology is furnished that demonstrates the efficient utilization of the assigned tasks. Furthermore, Grey Relational Analysis (GRA) is incorporated as a ranking validation mechanism to evaluate the relational closeness of alternatives under the proposed \(\textrm{IFZN}\) environment. Comparative analysis demonstrates that the proposed \(\textrm{IFZN}\) fairly aggregation framework provides reliable and consistent decision-making results under uncertain group assessment information.
