基于灰色系统的模糊综合评判在产险公司偿付能力评价中的应用

本文将灰色系统中的灰关联分析理论和模糊数学中模糊综合评判法引入保险公司偿付能力的综合评价排序中。通过案例分析，对2005年我国八家主要财产保险公司（以下简称产险公司）的偿付能力作了判断比较，给出了综合排序。     

Some insight into characterizations of minimally nonideal matrices

Lehman (Polyhedral combinatorics 1 of DIMACS series in discrete math. and theoretical computer science, pp 101–105, 1990) described some conditions regular minimally nonideal (mni) matrices must satisfy. Although, there are few results on sufficient conditions for mni matrices. In most of these results, the covering polyhedron must have a unique fractional extreme point. This condition corresponds to ask the matrix to be the blocker of a near-ideal matrix, defined by the authors in a previous work (2006). In this paper we prove that, having the blocker of a near-ideal matrix, only a few very easy conditions have to be checked in order to decide if the matrix is regular mni. In doing so, we define the class of quasi mni matrices, containing regular mni matrices, and we find a generalization on the number of integer extreme points adjacent to the fractional extreme point in the covering polyhedron. We also give a relationship between the covering and stability number of regular mni matrices which allows to prove when a regular mni matrix can be a proper minor of a quasi mni. Partially supported by CONICET Grant PIP 2807/2000 (Argentina) and by CNPq/PROSUL Grant 490333/2004-4 (Brasil).     

不协调目标信息系统知识约简的比较研究

研究不协调目标信息系统的各种知识约简之间的关系。证明分布约简既是β上分布约简，也是β下分布约简，并且在一定条件下,β上、下分布约简与不协调目标信息系统的分配约简和最大分布约简等价。     

灰色预测模型的再拓广(英文)

本文通过用对数函数对原始数据列｛ｘ（０）（ｋ）｝进行预测，又提出用幂函数对原始数据列进行变换，以提高离散数据的光滑度。在此基础上再将对数变换与幂函数变换两者结合起来，产生一种新的变换——“对数函数—幂函数变换”，达到了进一步增加数据的光滑度，提高预测精度的目的。     

带核集分划问题的一个线性1／7近似算法

设有整数集Ｓ＝｛ｒ１，ｒ２；ｐ１，ｐ２，…，ｐｎ｝，这里ｒｉ≥０，ｐｊ＞０（ｉ＝１，２；ｊ＝１，２，…，ｎ），寻找一个Ｓ的最优分划Ｐ＝（Ｓ＊１，Ｓ＊２）使得：（１）ｒｉ属于不同子集，（２）Ｓ＊１与Ｓ＊２中元素总和较大者尽可能地小．这是一个ＮＰ－完备问题，本文给出一个线性时间近似算法，它的近似界为８７．     

An example of cycling in a feasible point algorithm

An example shows that, if in Rosen's [4] algorithm for calculating a point that satisfies linear constraints a natural criterion is used to select constraints to delete from active sets, then the algorithm may cycle instead of converging. There are no degeneracies in the example.     

实Banach空间中锥上的随机逼近和随机不动点定理

本文在实Ｂａｎａｃｈ空间的锥上证明了集值映射的随机逼近定理．作为应用，讨论了几个随机的不动点定理．我们的工作推广了Ｌｉｎ，Ｓｅｈｇａｌ和Ｓｉｎｇｈ的结果．     

A localization inequality for set functions

We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f₁,f₂ defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)f_i(A)+μ(B)f_i(B)+μ(A∪B)f_i(A∪B)+μ(A∩B)f_i(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this.     

A viability theorem for set-valued states in a Hilbert space

Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H.     

On the complete set packing and set partitioning polytopes: Properties and rank 1 facets

This paper studies two polytopes: the complete set packing and set partitioning polytopes, which are both associated with a binary $n$-row matrix having all possible columns. Cuts of rank 1 for the latter polytope play a central role in recent exact algorithms for many combinatorial problems, such as vehicle routing. We show the precise relation between the two polytopes studied, characterize the multipliers that induce rank 1 clique facets and give several families of multipliers that yield other facets.