Securing the integrity of IoT devices in the ever-evolving world of smart healthcare technologies is essential to ensure security. While they are effective, traditional cryptographic methods work in a hard and fast manner often too rigid to deal with the inherent uncertainties or variances of an IoT world. To address this matter and to enhance the security and dependability of smart healthcare IoT devices, we explored a new paradigm for utilizing pentagonal fuzzy numbers (PFNs) along with cryptographic network security approaches. By using the fuzziness and dynamism of PFNs, we have a solid framework for key management similar to secure communication and dynamic authentication. Our method comprises establishing secure encrypted communication in a fuzzy range, using device authentication, and distributing the fuzzy keys derived from PFNs to IoT devices. In this paper, we have explained how this integration of PFNs with cryptographic techniques can indeed enhance the security framework of smart healthcare and make the safety from cyber threats more rigid while keeping the operational and user-friendliness aspects proportional via various realistic modeling elucidations and a feature-wise systematic implementation plan.