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In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach.