The work considers the prioritized relationships between different criteria with priority labels, and develops the scaled prioritized intuitionistic fuzzy geometric interaction averaging (SPIFGIA) operator, the scaled prioritized intuitionistic fuzzy weighted geometric interaction averaging (SPIFWGIA) operator, the scaled prioritized intuitionistic fuzzy hybrid geometric interaction averaging (SPIFHGIA) operator, and the scaled prioritized intuitionistic fuzzy hybrid weighted geometric interaction averaging (SPIFHWGIA) operator. We investigate the properties of the new SPIFGIA and SPIFWGIA operators, and the prioritized relationships between criteria in different situations for decision-making problems, and we also discuss the constructions of intuitionistic fuzzy sets with granularity. Then, we develop new approaches to intuitionistic fuzzy decision-making problems based on the presented SPIFGIA, SPIFWGIA, SPIFHGIA, and SPIFHWGIA operators. Finally, the paper shows the effectiveness and feasibility of the new methods by an example, and gives some comparisons.Keywords Multi-attribute decision-making problems Á Granularity Á Scaled prioritized intuitionistic fuzzy geometric interaction operators

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