Common best proximity point results in intuitionistic fuzzy metric spaces for ℛ-proximally weak commuting mappings

Best proximity point theory provides an effective framework for treating non-self mappings in situations where fixed points cannot arise. This work develops such a framework within the setting of intuitionistic fuzzy metric spaces in the sense of Park. Several new proximal structures are introduced, including the intuitionistic fuzzy [Formula: see text]-property for pairs of subsets, intuitionistic fuzzy proximal compatibility, and two generalized continuity notions termed intuitionistic fuzzy proximally reciprocal continuity and proximally weak reciprocal continuity. In addition, two classes of intuitionistic fuzzy [Formula: see text]-proximally weak reciprocal commuting mappings, referred to as Type I and Type II, are formulated and studied. Under suitable completeness and proximity assumptions, an existence and uniqueness theorem for common best proximity points of two non-self mappings [Formula: see text] is obtained. The results extend and unify several known theorems in classical metric, fuzzy metric, and intuitionistic fuzzy metric settings, and examples are provided to demonstrate the applicability and non-emptiness of the new concepts. When [Formula: see text], the theory reduces to common fixed point results in intuitionistic fuzzy metric spaces, thereby highlighting the generality of the developed approach.