A Refined Approach to Interactive Division of Fuzzy Numbers Under Complete Correlation

Abstract This paper introduces an enhanced framework for performing division operations on interactive fuzzy numbers characterized by complete correlation. Unlike traditional methods reliant on the independence assumption, we build on the sup-J extension framework to support correlated input fuzzy values. The proposed method establishes precise conditions under which the result aligns with, diverges from, or subsumes conventional divisions such as Zadeh’s and the generalized Hukuhara division. Additionally, we investigate invertibility conditions for the proposed division with respect to multiplication. These refinements offer valuable theoretical insights and have implications for models involving uncertainty, including difference equations.