•The weights of decision makers play important role in group AHP.•Weights of decision makers can be determined using the symmetric projection method.•The symmetric projection method promotes the homogeneity of the decision makers.•Group weights in AHP can be determined with Symmetric Projection Group Approach.•Symmetric Projection Group Approach was evaluated using four evaluation measures. The complexity of the socio-economic environment requires the involvement of a group of decision makers in the decision-making process. They can contribute the diversity of knowledge and experience that allow all the important aspects of the decision-making problem to be taken into account. In the aggregation process, the weights of the decision makers play an important role. In this paper we have focused on the group analytic hierarchy process (AHP). We emphasized the homogeneity of the opinions of the decision makers as the basis for determining the importance weights of the decision makers. We reviewed the projection method and its upgrades for determining decision makers weights and demonstrated with examples that they are not suitable for application in AHP. We proposed a new symmetric projection method that eliminates the imperfections of the previous projection methods. We proposed a Symmetric Projection Group Approach (SPGA) to derive group weights in AHP. To validate the SPGA, we selected four evaluation measures. The evaluation of the examples shows that the SPGA achieves good evaluation results compared to the other methods for deriving decision makers weights and is suitable for real-world applications.