This article introduces a method to calculate the division of two interactive positive fuzzy numbers. Specifically, we focus on arithmetic operations derived from completely correlated fuzzy numbers. Our study demonstrates that the proposed division yields fuzzy numbers with smaller widths compared to any other division method for positive fuzzy numbers, as determined by joint possibility distributions. Furthermore, we characterize these operations using \(\alpha \) -cuts, providing insights into their behavior across different \(\alpha \) -cuts. Furthermore, we establish connections between our proposed division method and existing techniques, such as the generalized Hukuhara division and the division based on Zadeh’s extension principle. Finally, we provide illustrative examples to demonstrate the practical implications of our proposed method.