The Convergence Of Matrices Over Dioids And Its Applications

This paper deals with the convergence of matrices over dioids and its applications. First, the notion of dioids is introduced, the relations between dioids and other algebraic structure such as semirings are obtained, and some properties of matrices' power over dioids are given. Secondly, the convergence of matrices over dioids is investigated, the convergent indices of matrices (resp. the periods) are studied deeply. Then the invertible matrices (resp. the standard eigenvectors of matrices, and the nilpotent matrices) over dioids are dis-cussed. Finally, an application of fuzzy convergent matrices is illustrated by an example in engineering through computing the transitive closure of fuzzy matrix.