This paper introduces a Fuzzy Quasi Newton Davidon Fletcher Powell (FQNDFP) optimization algorithm incorporating with Armijo line search technique to effectively handle imprecisely defined optimization problems. Unlike traditional probabilistic methods, this approach leverages fuzzy set theory to model uncertainties in optimization variables given in the objective function. The proposed algorithm integrates the Davidon Fletcher-Powell (DFP) update formula, ensuring computational efficiency and rapid convergence by approximating the inverse Hessian matrix. The Armijo line search guarantees sufficient descent while adapting the step size dynamically. This combination enhances the algorithm’s ability to navigate complex, nonlinear, and uncertain objective landscapes effectively. The performance of the algorithm is evaluated on benchmark problems and fuzzy objective functions, demonstrating accuracy, robustness, and convergence compared to existing methods.