On the power sequence of a fuzzy matrix (III). A detailed study on the power sequence of matrices of commonly used types

Focusing on the behavior of the principal diagonal elements of Ak, a new classification has been introduced, which is called circularly k-dominating. It turns out that the convergence index or the oscillating index of the power sequence of an n x n fuzzy matrix of the circularly k-dominating type is bounded by nk + n - k from above, and if it is oscillating, then the period index P-A is a factor of k. The fuzzy matrices of the 2-dominating type were discussed in detail. It was shown that the 2-dominating type is a more general class than those have been discussed before, and the results established for matrices of 2-dominating type is as good as the results obtained for controllable matrices. Therefore most commonly used types of fuzzy matrices can be examined under the framework of 2-dominating matrices, and the convergence index or oscillating index can be estimated based on the results. (C) 1998 Elsevier Science B.V. All rights reserved.