Convergence of the power sequence of a nearly monotone increasing fuzzy matrix

By introducing a new classification, the essential role of the principal diagonal elements for the convergence of the power sequence of a fuzzy matrix A, is exported at the level of A itself. The established theorems cover those of monotone or nearly monotone increasing fuzzy matrices. The convergence index of matrices of this type is always less than or equal to ii. The results can be considered to be a generalization of the results obtained by some authors on the one hand, and on the other it is more important that the results have laid the foundation for studying the convergence and oscillation for power sequence of an arbitrary fuzzy matrix in general. Furthermore, as a typical case which needs to be considered, the necessary and sufficient conditions for an increasing fuzzy matrix A to have the property A(n-1) < A(n) = A(n+1) were established and the typical form was represented. (C) 1997 Elsevier Science B.V.