正互反判断矩阵元素与优先权重新的逻辑关系

揭示了一种含参数的正互反判断矩阵元素与优先权重新的逻辑关系,并对参数的含义作了解释.得出了四个重要结论.通过算例与Saaty提出的层次分析法做了比较,说明了该方法的合理、科学性.     

矩阵Hadamard乘积的不等式

本文运用矩阵 Hadamard乘积及控制不等式的性质 ,获得了若干 Hermite及斜 Hermite矩阵特征值的不等式     

Hadamard乘积矩阵的一些性质

本文给出了Ｈａｄａｍａｒｄ乘积矩阵的秩和行列式的两个不等式     

衡量互反矩阵一致性的一种新指标

本文针对ＡＨＰ中利用几何平均值来估计各因素权向量的方法提出了与之匹配的一种新的衡量互反矩阵一致性的指标,并且制定了相应的衡量标准,同时将其与利用最大特征值所建立的指标入标准进行了比较与讨论。     

互反判断矩阵一致性指标研究

首先给出了互反判断矩阵与一致性互反判断矩阵集之间距离的定义,基于此定义,提出了一个新的互反判断矩阵一致性指标,并给出了此一致性指标的度量方法。对于不满足此一致性指标的互反判断矩阵,提出了一个迭代算法来提高其一致性程度。得出了群体互反判断矩阵一致性指标的下界,为提出的一致性指标应用于群决策问题提供了理论基础。最后用数值例子说明了该迭代算法的可行性和有效性以及群决策中的相关结论。     

一致性互反Fuzzy判断矩阵的传递性

研究矩阵元素为Fuzzy数的互反判断矩阵的传递性质.首先得到了判断两个Fuzzy数近似相等的等价条件,并得到了揭示Fuzzy数的核之间关系的一个充要条件.在此基础上,进一步证明了一致性互反Fuzzy判断矩阵具有传递性的两个结论.这两个结论说明:在层次分析法中,用一致性互反Fuzzy判断矩阵表示一组方案在同一目标下的两两重要性比较是符合理性决策的思维特征的.     

Hadamard乘积矩阵的一些性质

本文给出了Hadamard乘积矩阵的秩和行列式的两个不等式．     

正定矩阵的Hadamard乘积的一个矩阵不等式的精细

周知的正定矩阵A和B的Hadamard乘积矩阵不等式 :(A B) -1 ≤A-1 B-1 被精细为(A B) -1 ≤diag((A-1 (α) -1 B(α) ) -1 ,(A(α′) B-1 (α′) -1 ) -1 ) ,≤diag(A-1 (α) B(α) -1 ,A(α′) -1 B-1 (α′) )≤A-1 B-1 ,这里A(α)是A的主子矩阵且α′是α的补序列 ;同时给出了这些不等式的等式成立的充分必要条件     

关于Hadamard乘积矩阵的一些性质的注记

对文 [1 ]的主要结论作了说明 ,给出 Hadamard乘积矩阵有关性质的更一般的结果 .     

半正定矩阵Hadamard积的不等式

利用分块矩阵的方法得到了关于半正定矩阵M-P逆的H adam ard积的几个偏序不等式,推广了某些已知的不等式.     

Hadamard Matrices Modulo p and Small Modular Hadamard Matrices

We use modular symmetric designs to study the existence of Hadamard matrices modulo certain primes. We solve the 7‐modular and 11‐modular versions of the Hadamard conjecture for all but a finite number of cases. In doing so, we state a conjectural sufficient condition for the existence of a p‐modular Hadamard matrix for all but finitely many cases. When 2 is a primitive root of a prime p, we conditionally solve this conjecture and therefore the p‐modular version of the Hadamard conjecture for all but finitely many cases when , and prove a weaker result for . Finally, we look at constraints on the existence of m‐modular Hadamard matrices when the size of the matrix is small compared to m.     

区间数互反矩阵几何加权集成多属性群决策方法

研究了属性值以区间数表示的群决策问题,提出了区间数决策向量转化为互反判断矩阵的公式,定义了区间数互反判断矩阵几何加权集成算子.在此基础上,提出了区间数多属性群决策的新方法.方法首先针对每一个属性,将各决策者、各方案对应此属性的区间数向量转换为互反判断矩阵,由新定义的集成算子进行集成.由集成区间数矩阵的上界、下界矩阵计算各方案关于此属性的排序向量.由属性权重、可能度和排序公式对方案进行排序.最后给出一个实例进行分析,结果表明了此方法的实用性和可行性.     

Remarks on Hadamard Matrices and Lattices

Automorphism groups of Hadamard matrices are investigated from the point of view of integral representation theory. Interesting examples involving the Mathieu groups M ₁₂ and M ₂₄ and the Leech lattice are dicussed.     

On ‐Cocyclic Hadamard Matrices

A characterization of ‐cocyclic Hadamard matrices is described, depending on the notions of distributions, ingredients, and recipes. In particular, these notions lead to the establishment of some bounds on the number and distribution of 2‐coboundaries over to use and the way in which they have to be combined in order to obtain a ‐cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in A. Baliga, K. J. Horadam, Australas. J. Combin., 11 (1995), 123–134 is corrected and completed. Furthermore, we identify four different operations on the set of coboundaries defining ‐cocyclic matrices, which preserve orthogonality. We split the set of Hadamard matrices into disjoint orbits, define representatives for them, and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way, in terms of diagrams. Let be the set of cocyclic Hadamard matrices over having a symmetric diagram. We also prove that the set of Williamson‐type matrices is a subset of of size .     

Hadamard Matrices and Dihedral Groups

Let D _2p be a dihedral group of order 2p, where p is an odd integer. Let ZD _2p be the group ring of D _2p over the ring Z of integers. We identify elements of ZD _2p and their matrices of the regular representation of ZD _2p . Recently we characterized the Hadamard matrices of order 28 ([6] and [7]). There are exactly 487 Hadamard matrices of order 28, up to equivalence. In these matrices there exist matrices with some interesting properties. That is, these are constructed by elements of ZD ₆. We discuss relation of ZD _2p and Hadamard matrices of order n=8p+4, and give some examples of Hadamard matrices constructed by dihedral groups.     

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative -difference set where n – 1 is not a prime power.     

Some New Orders of Hadamard and Skew‐Hadamard Matrices

We construct Hadamard matrices of orders and , and skew‐Hadamard matrices of orders and . As far as we know, such matrices have not been constructed previously. The constructions use the Goethals–Seidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.     

Hadamard Matrices of Order 32

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13,710,027 such matrices up to equivalence.