The current definition of the Complex Hesitant Fuzzy Set (CHFS), derived from the Ramot form of complex numbers, cannot process information as in Tamir’s complex fuzzy form. We have data with uncertainty and extra information that cannot be described by any other structure than Tamir’s complex fuzzy form. Hence, in this article, we initiated the idea of CHFS based on Tamir’s complex fuzzy form and established its operational laws. Since Decision-Making (DM) theory is central to nearly all disciplines, we have proposed a novel complex hesitant fuzzy Multi-Criterion Decision-Making (MCDM) model. This method can handle all sorts of real-life MCDM problems, where the data contains uncertainty, hesitancy, and extra fuzzy information. While developing this method, we also develop and apply Dombi aggregation operators in this manuscript. After that, we discussed a case study that concerns energy storage system selection for AI-controlled microgrids and discussed how the theory we have developed can be applied to real-world challenges. Last, we conferred on how this proposed theory is superior to other theories and why it should be adopted.