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In this paper, we first propose the concept of the almost periodicity of set-valued functions on almost periodic time scales. Then based on the exponential dichotomy, we discuss the existence and uniqueness of almost periodic solutions of set dynamic equations on time scales. As an application, several examples are presented to exhibit that one can obtain the existence of almost periodic solutions to interval-valued dynamic equations (or fuzzy dynamic equations) and their discrete counterparts in a united means. [ABSTRACT FROM AUTHOR]