The Bonferroni mean (BM) can portray the inter-relationships among the arguments, which is based on algebraic norm. Archimedean norm is the generalization of algebraic norm. In this work, the intuitionistic fuzzy (IF) BMs on the basis of the Archimedean norm are investigated, including the Archimedean norm-based IF arithmetic BM (AN-IFABM) and the Archimedean norm-based IF geometric BM (AN-IFGBM). Then, we discuss their typical properties and several particular cases of the AN-IFABM and

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... in detail. Moreover, we design the Archimedean norm-based IF weighted arithmetic BM (AN-IFWABM) and the Archimedean norm-based IF weighted geometric BM (AN-IFWGBM) to consider the importance of each argument and their interconnections. Applying the proposed extensions, an approach is designed to cope with the multiattribute decision-making (MADM) problems. Finally, an efficiency evaluation problem of some public companies in China is analyzed by the proposed approach to demonstrate its applicability and validity.