Aczel-Alsina t-norm and t-conorm are a valuable and feasible technique to manage ambiguous and inconsistent information because of their dominant characteristics of broad parameter values. The main theme of this analysis is to explore Aczel-Alsina operational laws in the presence of the complex interval-valued intuitionistic fuzzy (CIVIF) set theory. Furthermore, we derive the theory of aggregation frameworks based on Aczel-Alsina operational laws for managing the theory of CIVIF information. The CIVIF Aczel-Alsina weighted averaging (CIVIFAAWA), CIVIF Aczel-Alsina ordered weighted averaging (CIVIFAAOWA), CIVIF Aczel-Alsina hybrid averaging (CIVIFAAHA), CIVIF Aczel-Alsina weighted geometric (CIVIFAAWG), CIVIF Aczel-Alsina ordered weighted geometric (CIVIFAAOWG) and CIVIF Aczel-Alsina hybrid geometric (CIVIFAAHG) operators are proposed, and their well-known properties and particular cases are also detailly derived. Further, we derive the theory of the WASPAS method for CIVIF information and evaluate their positive and negative aspects. Additionally, we demonstrate the multi-attribute decision-making (MADM) strategy under the invented works. Finally, we express the supremacy and dominancy of the invented methods with the help of sensitive analysis and geometrical shown of the explored works.