<p>The purpose of this work is to introduce and study a new analytical framework, namely the complex-valued intuitionistic fuzzy <i>b</i>-metric space (CVIFbMS), which combines the features of complex-valued distance, intuitionistic fuzzy structure, and the generalized <i>b</i>-metric inequality. This setting properly extends several well-known spaces in the literature, including complex-valued metric spaces, intuitionistic fuzzy metric spaces, and intuitionistic fuzzy <i>b</i>-metric spaces, and hence provides a broader platform for the investigation of fixed point problems. Within this framework, we obtain fixed point results for a class of contractive type mappings, and we show that our theorems unify and generalize a number of earlier contributions. Several illustrative examples are presented to support the validity of the new space and to demonstrate that the obtained results cannot be derived in previously known structures. Finally, as an application, we employ the main theorem to study the existence and uniqueness of solutions of a complex-valued nonlinear integral equation. The results established in this paper may be viewed as a further contribution to the ongoing development of fixed point theory in generalized intuitionistic fuzzy and complex-valued settings.</p>