Traditional key generation algorithms, while mathematically sound, exhibit rigidity when confronted with noisy, uncertain, or biometric input environments. This research proposes a novel Fuzzy Algebra-Based Cryptographic Key Generation Model (FACKGM) designed to address these challenges through the integration of fuzzy set theory, fuzzy algebraic structures, and established cryptographic primitives. The proposed model leverages fuzzy membership functions, T-norm and S-norm operators, and fuzzy inference systems to transform imprecise input parameters into high-entropy cryptographic keys suitable for use in secure communication systems. The model supports adaptive key sizing between 512 and 1024 bits, demonstrating scalability across diverse security requirements.Simulation experiments were conducted to evaluate the proposed model against RSA-2048, AES-256, and Elliptic Curve Cryptography (ECC-256) across parameters including key generation time, entropy level, avalanche effect, brute-force resistance, and side-channel attack robustness. Results indicate that FACKGM achieves a key generation time of 20.4 ms, an entropy level of 148.7 bits, a key uniqueness rate of 99.93%, and brute-force resistance estimated at 10^72 years, significantly outperforming contemporary algorithms. The proposed model thus presents a computationally efficient, mathematically rigorous, and noise-tolerant cryptographic key generation solution for next-generation secure communication infrastructures.