高维Cotes优化积分数值算法及其余项估计

利用一维Cotes公式及高维积分Cartesian积空间上的求积法则,将Cotes公式推广到了n维空间上,并给出了简单的误差估计.该公式具有比文[4],[5],[6]相关结果更小的误差和更高的收敛阶等优点.     

Conjugate directions method for solving interval linear systems

We propose the interval version of the conjugate directions method, to solve the problem of linear systems, with symmetric and positive definite interval matrix A, and a right-hand side interval vector b. This revised version was published online in June 2006 with corrections to the Cover Date.     

混合型多属性决策的灰色关联分析法

针对属性权重信息不完全且属性取值为精确数,区间数和模糊数相结合的混合型多属性决策问题,提出了一种基于理想解的多属性决策的灰色关联分析方法.首先将三种不同形式的属性值均转化为区间数形式,然后依据灰色关联分析的思路,给出了解决该问题的计算步骤,其核心是构建并求解一个单目标最优化模型,得到每个方案与正、负理想方案的关联度,进而计算出每个方案对正理想方案的相对关联度,即可得到所有方案的排序结果.最后给出了一个数值例子,结果表明方法简单,有效和易于计算.     

Parametric importance of criteria and intervals of value tradeoff uncertainty in the analysis of multicriteria problems

Multicriteria decision-making problems under bounded (above, below, or from both sides) continuous or discrete criteria are considered. Methods for comparing variants of solutions using the information accumulated in the form of interval estimates of replacing the values of some criteria by the values of others (such replacements are called tradeoffs; in other words, this can be considered as a compensation of the deterioration of some criteria by improving the values of others) are proposed along with simple consistency conditions of such information. The issue of constructing the set of nondominated variants is discussed.     

区间中立型大系统的强壮稳定性

本文讨论中立型大系统,获得了这类问题稳定性的一些充分判据,作为特殊情况,还得到了与[1-11]中相应的一些不同的结果.这些结果并不象文献[1]和[2]那样,要求a_(ii)的上界q_(ii)小于零.     

Trapezoidal approximations of fuzzy numbers preserving the expected interval — Algorithms and properties

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. Algorithms for calculating the proper approximations are proposed and some properties of the approximation operators are discussed. It is shown that an adequate approximation operator might be chosen through the comparisons of some characteristics of the fuzzy number, like its ambiguity, width, its value and weighted expected value.     

Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

A note on iterative roots of PM functions

In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized.     

Slope enclosures for functions given by two or more branches

In this paper, we consider the automatic computation of slope enclosures for continuous real functions given by two or more branches, such as piecewise defined nonsmooth functions. We show that a commonly used formula found in the literature does not always provide a slope enclosure for such functions. Furthermore, we prove a similar formula that always holds. AMS subject classification (2000)  65G20     

Linear interval equations with symmetric solution sets

Criteria for symmetry and boundedness are found for the combined solution set of a system of linear algebraic equations with interval coefficients. It is shown that the problem of the best inner interval estimation of a symmetric solution set can be exactly solved by linear programming methods.