Decision problems that involve uncertain judgments together with periodic information require a representation capable of retaining both the degree and the phase of an assessment. Complex intuitionistic fuzzy sets (CIFSs) provide this representation by expressing membership and non-membership as complex-valued quantities in the unit disk, with amplitude and phase recorded within the same uncertainty model. In this study, the Aczel–Alsina (AA) t-norm and t-conorm, introduced in 1980, are used as the parametric operational basis for aggregation; their structure differs from commonly used families such as the Hamacher norms. These operations are incorporated into the Aczel–Alsina Heronian mean generalized shapley choquet integral (AAHMGSCI) framework under a CIF environment. The resulting construction yields four operators: CIFAAHMWAGSCI, CIFAAHMWGGSCI, GCIFAAHMWAGSCI, and GCIFAAHMWGGSCI. Their structural behavior is studied through idempotency, boundedness, and monotonicity. The operators are subsequently embedded in a MADM procedure and used in the selection of biometric-based attendance devices represented by CIFSs. To examine whether the decision outcome is stable across formulations, the rankings obtained from the proposed operators are compared with those produced by existing methods.