This research paper discusses the concept of interval type - 2 fuzzy rhotrix, by focusing its definitions, properties, and significant results. The study begins by defining interval type - 2 fuzzy rhotrix as an extension of traditional rhotrix theory that incorporates interval type - 2 fuzzy logic, with uncertainty and imprecision. The algebraic properties such as addition, multiplication, identity elements, determinant, transpose, codeterminant function and Index of IT2FR are systematically discussed, with rigorous proofs and examples provided to substantiate these fundamental characteristics, this work aims to enhance the understanding of interval type - 2 fuzzy rhotrix in both mathematical theory and real-world situations.