Fuzzy topological indices have a significant impact and are gaining attention due to their multiple applications in various scientific domains and daily life fields. These indices have also been thoroughly investigated in fuzzy contexts or fuzzy graphs. A topological index is a single numerical parameter associated with the structure of graphs or networks that contains information to characterize the network’s attributes as well as mathematical modelling. These indices have practical applications in a wide range of fields, including ecology, social networks, multi-criteria decision-making systems and neural networks. Due to these several applications topological indices are needed to define fuzzy graphs or networks. By modeling DNA molecular structure as a fuzzy graph where vertices represent atoms and edges are bonds with probabilistic membership values, we establish quantitative descriptors that capture the inherent uncertainties in bio-molecular interactions. We introduced the notation of several fuzzy topological indices, such as the first and second fuzzy Zagreb indices, the harmonic fuzzy Zagreb index and the randic fuzzy Zagreb index of the fuzzy backbone DNA network, in this work.