<p>Synchronization of non-identical 4-D integer-order chaotic financial systems and chaotic laser systems are remodeled into linear system by using T-S fuzzy techniques combined with reachable set estimation for the first time. In this paper, the synchronization of a sender and receiver system with applications in image encryption and decryption is addressed. The proposed work ensures high-level security through the analysis of various metrics, in addition to numerical simulations. The proposed encryption algorithms have several advantages, such as high-level randomness and key sensitivity to the encrypted image. This work highlights the potential of integrating T-S fuzzy techniques with reachable set estimation for practical applications in secure communication and data protection. The suggested methods have been shown to be effective, efficient, and feasible for real-world applications by numerical modeling and experimental findings.</p>