The Calculation, Simplification And Application Of The Transitive Closure Of The General Fuzzy Matrix

This paper is attributed to the research of the theory arid application of fuzzy matrices, aiming at the calculation, simplification and application of the transitive closure of the general (not similar) fuzzy matrices.We first define the maximum road in the net and indicate that its strong is equal to the element of the transitive closure of a fuzzy matrix. It is a new result to apply the transitive closure of the general fuzzy matrix into net analysis. Due to the wide use of net analysis, this result is of great value.We transform the calculation of the transitive closure of the general fuzzy matrix into that of the reflexive fuzzy matrix, which gives us a gradual square algorithm to calculate the transitive closure of the general fuzzy matrix. This algorithm greatly reduces the calculation of the transitive closure, so it is possible for us to apply the transitive closure theory of the general fuzzy matrix into the techniques of the computer and information.Moreover, we pay much effort on simplifying the transitive closure's expression by its sequence powers. We lessen the number of the sequence powers by defining the distance and the analogy rank of the fuzzy matrix. Furthermore, we construct three typical fuzzy matrices, which gives us a sufficient and necessary condition for simplifying the transitive closure's expression, and provides us new models for the maximum road analysis in the net.