Abstract: The Fuzzy graphs serve as a practical tool in mathematics, enabling users to effortlessly represent relationships between various concepts. Their inherent fuzziness makes them adaptable and well- suited for diverse environments. A topological index is a numerical value that characterizes the structural graph of a molecule. This study aims to introduce a new topological index in the fuzzy graph theory and study its properties. In this direction, we have introduced -index of a fuzzy graph . In this paper, the -index of fuzzy generalized transformation graphs and its related bounds are studied.