<p>Due to random and uncertain market environment, financial assets exhibit long-term memory and jumps in price. This study employs a combination of fuzzy set theory, stochastic processes, and mixed fractional Brownian motion to effectively characterize the price process of financial derivatives. This study mainly introduces a novel model called the jump diffusion mixed fractional Brownian motion (JMFBM) model, which aims to accurately describe the dynamics of barrier option price. By solving the fuzzy partial differential equations driven by the JMFBM, one has successfully derived a pricing process for down-out barrier options. Significantly, numerical experiments are performed to address the influence of various parameters on option prices and examine the parameter sensitivity. Furthermore, to validate the feasibility and practicality of our results, empirical analysis is conducted using financial market data. The results show that the dynamics of fuzzy JMFBM is better suited for pricing financial derivatives in uncertain financial environments.</p>