A short note on solvability of systems of interval linear equations

In this note we formulate necessary and sufficient conditions for strong solvability and feasibility of systems of linear interval equations in terms of absolute value inequalities.     

“非平均区间数”计算及其在政府决策信息系统中的应用

本文在已有的“区间数”定义及排序算法的基础上 ,针对层次分析法提出了更加灵活 ,准确的描述主观评判的“非平均区间数”概念及其排序算法 .并结合政府决策信息系统阐述了“非平均区间数”的应用     

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.     

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.     

基于误差理论的区间主成分分析及其应用

针对区间数样本,传统的主成分分析需进行拓展。首先讨论了区间样本数据的两种主要来源,即观测误差和符号数据分析。然后将区间数看作一个由中点和半径构成的具有一定误差的数,从误差理论出发,研究基于误差传递公式的区间主成分分析方法,并获得以区间数为表达形式的主成分。最后,结合我国2005年第四季度股票市场的数据进行了实证分析。结果表明,面对海量数据,区间PCA较传统PCA更容易从总体上把握样本的属性。     

一种基于区间评分的评价算法及其实现

本文针对评审工作中打分专家对各指标熟悉度不同的实际问题，提出一种基于区间评分的评价算法。因该算法通过专家给出评分区间长度反映出专家对各评审指标的熟悉度，为此定义区间的加法、减法、数乘运算及区间值的概念，这样可解决区间无法直接排序的问题。最后给出了该算法的具体步骤和实际算例。     

区间值直觉模糊超子群

在K.Atanassov引进区间值直觉模糊集的基础上,给出了区间值直觉模糊超子群的定义,刻画了其特征结构,研究了这类区间值直觉模糊超群的同态像及原像等问题.同时,讨论了区间值直觉模糊超子群与区间值直觉模糊子群的关系.     

不确定型AHP中判断矩阵一致性的定义

文章定义了区间矩阵的几种运算，并给出了不确定型判断矩阵满足一致性的条件。     

Modified Newton method in circular interval arithmetic

The modified Newton method for multiple roots is organized in an interval method to include simultaneously the distinct roots of a given polynomialP in complex circular interval arithmetic. A condition on the starting disks which ensures convergence is given, and convergence is shown to be quadratic. As a consequence, a simple parallel algorithm to approach all the distinct roots ofP is derived from the modified Newton method.The research reported in this paper has been made possible through the support and the sponsorship of the Italian Government through the Ministero per l'Universitá e la Ricerca Scientifica under Contract MURST 60%, 1990 at the Universitá di L'Aquila.     

An interval iteration for multiple roots of transcendental equations

An iteration method for roots of algebraic functions with roots of multiplicity greater than one is established using tools and techniques from interval arithmetic. The method is based on an interval iteration functions for multiple roots and it retains the convergence order of the underlying iteration method while preserving global convergence over an initial interval. A number of simple examples are provided to show that the method is feasible and that it produces reasonable results.