In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided, and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are, respectively, demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.