<p>A crisp graph is defined as a collection of vertices where any set of vertices not connected by an edge forms an independent set. Fuzzy graphs extend this concept by offering greater flexibility and adaptability, enabling more nuanced representations. Identifying and determining fuzzy separate sets in fuzzy graphs, as introduced in [Jayalakshmi, Int. J. Comput. Eng. Res. 4, 2014], is of utmost importance and necessity. Muhiuddin et al. [Muhiuddin, Proc. Nat. Acad. Sci. India Sect. A: Phys. Sci. 92, 2022] introduced a novel concept of independent fuzzy graphs, which provides a fresh perspective on graph theory. Based on their approach, it can be observed that every fuzzy graph possesses a certain degree of independence, thus making it a fuzzy independent graph. This paper investigates the degree of independence in fuzzy graphs, focusing on their applications in decision-making processes. We calculate the independence degrees of fuzzy graphs incorporating various edge types, such as strong and weak edges. Additionally, we examine the relationship between the independence degree of a fuzzy graph and its complement graph. Furthermore, we explore various fuzzy graph products, including Lexicographic, Modular, and Star products, to compute their independence degrees. Finally, the practical application of these computations in medical diagnosis is demonstrated, where bipolar fuzzy graphs and the concept of independence degree are utilized to determine the optimal drug consumption strategy for individuals with dual diagnoses. This approach minimizes adverse effects and maximizes therapeutic outcomes, offering a systematic solution for managing complex treatment plans involving multiple medications.</p>