Controllability of Intuitionistic Fuzzy Neutral Integro-Differential Equations with Nonlocal Conditions

This paper investigates the controllability of nonlocal intuitionistic fuzzy neutral integro-differential equations using intuitionistic fuzzy semigroups and the contraction mapping principle. By formulating a rigorous theoretical framework, we derive sufficient conditions for ensuring controllability of these systems under nonlocal constraints. The study introduces a novel approach to handling uncertainties inherent in fuzzy systems, demonstrating that intuitionistic fuzzy control functions can effectively manage these complexities. Furthermore, the results provide a foundation for addressing significant challenges in controlling systems with nonlocal features, offering new perspectives for both theoretical advancements and practical implementations. This work paves the way for future research in applying intuitionistic fuzzy control to diverse scientific and engineering problems.