【摘要】 本文讨论了模糊等价矩阵的一些性质,并给出了一个模糊相容矩阵是等价的充要条件.在此基础上,提出了某些模糊相容矩阵改造为等价矩阵的简便方法以及在模糊相容矩阵R上直接进行聚类分析的一种方法,这个方法将整个聚类过程化为在表格R上的作业法.更多还原

【Abstract】 In this paper, some properties of fuzzy equivalent matrices are discu-ssed, and a necessary and sufficient condition that the fuzzy consistentmatrix is the fuzzy equivalent matrix is given. On this basis, the simplemethods of rebuilding some fuzzy consistent matrices to fuzzy equivalentmatrices are given. At the same time, a kind of the clustering method on the consistent matrix R are related.Let(?)is the fuzzy consistent matrix, where γii = 1(i = 1,2,?,n). 0≤γii=γii≤1 .Definition 1. If γii(i≠j)is the maximum element in the i-th row of fuzzy consistent matrix R except the diagonal element γii, then the pair (i,j) of natural numbers is called the fuzzy equivalent point of the fuzzy set R. And ?ii is called equivalent level of the point (i,j) .Definition 2. Suppose the fuzzy equivalent points of R constitute mequivalent chains e1, e2 ,… ,em( m≤ (?)) , we write E = {e1 ,e2 , … , em).R(2) is the fuzzy consistent relation on E X E,R(2)=[γii] 1≤i,j≤mThe fuzzy equivalent points on R(2) are called the second order fuzzyequivalent points on R.Similar, the k-th order fuzzy equivalent points of R may be defined. From the fuzzy consistent matrix, the procedure for direct clustering may be given as follows:1. Write all the first order equivalent points and levels of R , denote by γii/(i,j);2. Write equivalent chains of R. If all equivalent points of R constitute a chain, then turn to 4;3. Write the maximum element of intersection points of each equivalent chain. Make matrix R(2). Replicate procedure 1, 2, until the equivalent points of R(4) constitute a chain.4. Apply each order equivalent points and levels γii(i, j), make the clustering graph.更多还原