This study focuses on the theoretical study of the fuzzy graph of an aromatic hydrocarbon called tetracene hydrocarbon and calculates several degree topological indices based on fuzzy logic, including the first and second Zagreb index, Randic index, Harmonic index, Forgotten index, and Y-index. The research introduces new definitions for the first Zagreb fuzzy index, forgotten index, and Y-index, and provides a general formula for fuzzy topology indices of hydrocarbons by considering the degree of each edge. Furthermore, a general formula is presented to determine the topological indices of tetracene hydrocarbon based on the number of rows and columns. In continuation, the topological indices of linear tetracene were compared, and among them, the Harmonic and Randic indices had the highest values respectively, while the values of other indices were very close to each other. Additionally, the surface of the Y-index of multi-cyclic tetracene was plotted to determine the effect of row and column parameters on the index, and it was concluded that when the number of parameters is equal, the Y-index has the highest value.