Exact Solution of Full Interval (Fuzzy) Linear Equation $A_{2n\times n}X_{n\times1}=b_{2n\times1}$ based on Kaucher Arithmetic

In this paper, first, we propose Kaucher arithmetic for interval number and then solve the system $A_{2n\times n}X_{n\times1}=b_{2n\times1}$ where $a_{ij}=[\underline{a_{i,j}},\overline{a_{i,j}}]$ and $x_{j}=[\underline{x_{j}},\overline{x_{j}}]$ and $b_{i}=[\underline{b_{i}},\overline{b_{i}}]$ based on Kaucher arithmetic such that $\underline{a_{i,j}}~.~\overline{a_{i,j}}\geq0$. Then, we extend this method by use of $ \alpha-$ level set for fully fuzzy system of $\tilde{A}_{2n\times n}\tilde{X}_{n\times1}=\tilde{b}_{2n\times1}$.