数区间

Multiple attribute decision-making; ideal interval number; entropy; attribute weight coefficients; Grey Relational Analysis

多属性决策；理想区间数；信息熵；属性权系数；灰色关联分析

First, by use of the characteristic that the attributive value is a grey interval number, combining the thought and method of grey system theory with the classical risk decision-making method, the incidence degree formula among alternatives and the optimization model in decision-making system are constructed, and the problem of attribute weight unknownis rationally solved.

首先，利用属性值为区间灰数这一特性，将灰色系统理论的思想和方法与经典风险决策方法相融合，构建了决策系统中各方案之间的关联度公式以及优化模型，合理地解决了属性权重未知问题。

If is an interior point of where fails to exist

如果是区间的内点，且函数在点的导数不存在，则称点为奇异点

Two regression analysis models for interval number are proposed.

提出了两种区间数回归建模方法。

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

The linear extrapolation technique was the most practical and suitable method because of its relative high correlation with a wide range of chlorophyll content, relative simple algorithm, relative high sensitivity to chlorophyll at high or low content and application to more wider bandwidth spectra.

四点线性内插法计算的红边位置往往偏大，最大一阶导数法与叶绿素含量的关系存在着明显的不连续性，拉格朗日内插法、倒高斯模型法在一定程度上存在着对高叶绿素含量的饱和现象，多项式拟合法对拟合波段区间、最高项次及光谱分辨率等比较灵敏而导致结果不够稳定，而线性外推法计算出的红边位置对叶绿素含量最为敏感，预测的准确度最高，且计算相对比较简单，并能适用于较宽波段的遥感数据。

The Choquet upper and lower fuzzy integral i...

所给Cho quet上、下模糊积分是经典Choquet模糊积分在粗糙意义下的扩展形式，能处理粗糙区间数数据源和信息系统的对象。

Based on the analysis of existed fuzzy integral theories, the notions of the Choquet upper and lower fuzzy integral and rough interval numbers' integral form were proposed; the rough properties of Choquet fuzzy integral and an information fusion method based on rough Choquet fuzzy integral were given.

在分析现有模糊积分理论的基础上，提出了Choquet上、下模糊积分的概念和粗糙区间数的积分形式，给出了Choquet模糊积分的粗糙特性，建立了基于粗糙Choquet模糊积分形式和信息融合方法。

Some methods for dealing with the stability problem has presented and these methods include: Lyapunov function, differential inequality, matrix norm and measure, Razumikhin theorem method etc. The results of stability for these systems are derived by using these methods. This paper may be summarized as follows.

本文考察了区间Lurie型控制系统与不确定时滞系统的稳定性问题，给出了判定系统稳定的一些处理方法，这些方法包括：Lyapunov函数法、微分不等式法、矩阵范数与测度法、Razumikhin定理等方法，并且应用这些方法得到了系统稳定的判别条件。

The multiple attribute decision making problem with intervals is an important research topic.

带有区间数的多属性决策问题是有关多属性决策研究中的一个重要课题。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。