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Visual communication design, as a type of artistic and three-dimensional design behavior, helps to spread visual behavior by designing it. The rapid development of new media technology has provided rich channels and vast space for visual communication design, and the elements and modes of visual communication design are constantly being updated, better promoting the development of visual communication technology. The Teaching quality evaluation of visual communication design based on the cultivation of innovative and creative abilities based on the cultivation of innovative and creative abilities is a multiple-attribute decision-making (MADM). In this paper, some calculating laws on IVIFSs, Hamacher sum, Hamacher product are introduced, and the induced interval-valued intuitionistic fuzzy Hamacher interactive hybrid weighted averaging (I-IVIFHIHWA) operator is proposed based on the interval-valued intuitionistic fuzzy Hamacher interactive hybrid weighted averaging (IVIFHIHWA) operator and induced ordered weighted averaging (I-OWA) operator. Meanwhile, some ideal properties of I-IVIFHIHWA operator are studied. Then, the I-IVIFHIHWA operator is employed to cope with the MADM under IVIFSs. Finally, an example for Teaching quality evaluation of visual communication design based on the cultivation of innovative and creative abilities is employed to test the I-IVIFHIHWA operator. Thus, the main research aim of this paper is concluded as follows: [1] the I-IVIFHIHWA operator is constructed based on classical IOWA operator; [2] the I-IVIFHIHWA operator is put forward to cope with the MADM under IVIFSs; [3] an empirical example for Teaching quality evaluation of visual communication design based on the cultivation of innovative and creative abilities has been put forward to show the I-IVIFHIHWA operator. [ABSTRACT FROM AUTHOR]