The Terse Algorihtm For Computing Reachable Matrix Based On Directed Graph Of ISM

At present the common method used in large-scale and complexy systems is the interpretative structural modeling, namely ISM. It is a macroscopic model to indicate the interrelation between the system factors, generally we use the most simple method viz. figure to express the interrelation, such as Directed Graph is widely used in the project system or in the social economy system.In nature and in the practical lives of human society, it is simple and direct-viewing using the figures to describe and express the relation of something. During creating the interpretative structural modeling, for the part of figure, there is a kind of important matrix when showing the figure with matrix, that is Reachability Matrix. In modern systems engineering, Reachability Matrix is an important means to study the relation between the Directed Graph nodes. The Adjacency Matrix of the Directed Graph is easy to build, but the reach-relation of factors is more useful when building the structure model. Howerer, the traditional algorithm of Reachability Matrix is comparative complicated, especially when there are more nodes in the Directed Graph, the arithmetic amounts are big and not enough simple.This paper introduce two algorithms, that are amelioration algorithm and transfer algorithm, they were mentioned apartly according to the characters of Adjacency Matrix and Reachability Matrix. They are used to compute the Reachability Matrix during building the structure modeling of system, mostly used to compute the Reachability Matrix of Directed Graph. They are all a kind of exoteric algebra method, that is to say we join person's subjective information in the solution process to seek the solution which needs.This paper is organized as followings:In the first chapter, in the foundation of introducing the model and the algorithm, we give the question that this article will to solve.In the second one, we introduce the interpretative structural modeling, and its theories of home and abroad, and its three elements, and its building steps. In the third part, many kinds of algorithms about Reachability Matrix are introduced.Then comes the highlight of the whole thesis, we introduce the amelioration algorithm and the transfer algorithm, and compare both with the traditional algorithm, then analyze their feasibility.We provide a clearer view of the algorithm in chapter 5.Source code of the demo is appended to help interested readers.