This paper presents the development of fuzzy multiplicative metric spaces, an extended framework that combines the principles of multiplicative metric spaces with fuzzy logic to better address uncertainty and imprecision inherent in many real-world problems. By replacing additive distance measures with multiplicative ones, this approach proves particularly effective in contexts where relative variations or proportional relationships are more meaningful than absolute differences. Within this generalized setting, we establish a series of fixed-point theorems of Banach, Kannan, and Chatterjea types, along with related corollaries, each supported by concrete examples. The theoretical results are further validated through their application to the solution of nonlinear integral equations, demonstrating the versatility and applicability of the proposed framework across mathematical analysis and applied disciplines.