interactive Fuzzy Numbers, Generalized Hukuhara Division, J-division, Completely Correlated Fuzzy Numbers

In this article, we introduce a method to calculate the division of two interactive 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 fuzzy numbers, as determined by joint possibility distributions. Additionally, we characterize these operations using α-cuts, providing insights into their behavior across different levels of confidence. Furthermore, we establish connections between our proposed division method and existing techniques, such as generalized Hukuhara division and division based on Zadeh’s extension principle. Finally, we provide illustrative examples to showcase the practical implications of our proposed method.

In this article, we introduce a method to calculate the division of two interactive 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 fuzzy numbers, as determined by joint possibility distributions. Additionally, we characterize these operations using α-cuts, providing insights into their behavior across different levels of confidence. Furthermore, we establish connections between our proposed division method and existing techniques, such as generalized Hukuhara division and division based on Zadeh’s extension principle. Finally, we provide illustrative examples to showcase the practical implications of our proposed method.