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Keywords:
fuzzy algebra; interval matrix equation; tolerance solvability; weak tolerance solvability
fuzzy algebra; interval matrix equation; tolerance solvability; weak tolerance solvability
Summary:
This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation $\mathbf{A} \otimes X\otimes \mathbf{C}=\mathbf{B}$, where $\mathbf{A}, \mathbf{B}, \mathbf{C}$ are given interval matrices and $X$ is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability and provide polynomial algorithms for checking them.
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