从Warshall算法到求模糊矩阵传递闭包的一个简捷算法

模糊矩阵传递闭包的计算在模糊聚类中起着关键的作用,而模糊矩阵传递闭包与普通集合论中传递闭包是有密切联系的。从普通集合论中求关系闭包的Warshall算法和模糊关系图出发,论述并实现了一种求模糊矩阵传递闭包的有效算法。与经典的求模糊矩阵传递闭包的算法———平方法比较,该算法简捷,运算量小。最后分析了一个利用传递闭包法进行模糊聚类的实例。

A Simple and Direct Algorithm for Computing Transitive Closure of Fuzzy Matrix

The computing transitive closure of fuzzy matrix plays an important role in fuzzy clustering. While the transitive closure of fuzzy matrix is closely linked with the transitive closure in common sets. In deriving Warshall algorithm of the related closure from the common sets and starting from fuzzy relation chart,this paper deals with and accomplishs a kind of effective algorithm to derive the transitive closure of fuzzy matrix. In comparison with the classical algorithm to derive the transitive closure of fuzzy matrix the square algorithm, this algorithm is characterized by simplicity,agility and small calculation quantity. At last, this paper analyzes a real example of using the transitive closure method to carry out the fuzzy clustering.