Implication Theory and Algorithm for Reachability Matrix Model
Implication Theory and Algorithm for Reachability Matrix Model
复制标题
可达性矩阵模型的蕴涵理论与算法
DOI：
10.1109/tsmc.1986.289267
复制
发表时间：
1986
期刊：
影响因子：
--
通讯作者：
I. Kaji
中科院分区：
文献类型：
--
作者：
A. Ohuchi;M. Kurihara;I. Kaji
可达性矩阵 M 是具有自反和传递性质的二元矩阵，即 M + I = M，且 M2 = M，其中 I 是单位矩阵。矩阵 M 的条目被显示为形成使用传递性属性导出的多级蕴涵结构。导出定义该结构的基本蕴涵矩阵P。定义了 P 的传递闭包的矩阵 Q，即完全蕴涵矩阵。证明Q=p2。考虑有效填充部分填充的可达性矩阵的问题。提出了一种用于确定从所提供的值导出的部分填充的可达性矩阵M的未知元素的所有隐含值的算法。该算法需要 0(n2) 计算机时间和 0(n2) 存储，其中 n 是矩阵 M 的大小。将该算法用于解释结构建模 (ISM) 过程使得可以进行灵活且高效的传递嵌入。
A reachability matrix M is a binary matrix with the reflexive and transitive property, i.e., M + I = M, and M2 = M, where I is the identity matrix. The entries of the matrix M are shown to form a multilevel implication structure derived using the transitivity property. The fundamental implication matrix P that defines this structure is derived. The matrix Q of the transitive closure of P, the complete implication matrix, is defined. It is proved that Q = p2. The problem of efficiently filling the partially filled reachability matrix is considered. An algorithm for determining all of the implied values of the unknown elements of the partially filled reachability matrix M derived from a supplied value is proposed. The algorithm requires 0(n2) computer time and 0(n2) storage, where n is the size of the matrix M. Use of the algorithm to the interpretive structural modeling (ISM) process makes it possible to do a flexible and an efficient transitive embedding.