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This paper extends the notion of Pythagorean fuzzy sets and Fermatean fuzzy sets to 3,4-quasirung fuzzy sets (3,. In 3,4-QFSs, the sum of the cube of the membership degree and fourth power of nonmembership degree is less than or equal to 1. Therefore, the 3,4-QFSs can express imprecise information more flexibly and elaborately due to its broader space. Here, we define the score function and accuracy function for the ranking of 3,4-QFSs. Also, we develop complementary functions and some operational rules for the 3,4-QFSs. Then, based on the defined operational rules, we propose 3,4-quasirung fuzzy weighted averaging (geometric), order weighed averaging (geometric), and hybrid averaging (geometric) aggregation operators. Next, we analyze some suitable properties of the presented operators. Moreover, we utilize the proposed 3,4-quasirung fuzzy weighted averaging (geometric) operators to develop a multiple attribute decisionmaking (MADM) model with 3,4-quasirung fuzzy data. The main advantage of 3,4-QFS is that it enables the decisionmakers to exploit additional spaces while applying to MADM problems. Finally, a numerical example concerning the selection of a learning management system is provided to check the validity of the proposed method. A comparative analysis with existing methods is given to verify the superiority of the proposed method.