定义区间

First, the uncertain ordered weighted averaging is used to aggregate the decision-maker's different preference information into the interval number comparison matrix. Then, the group's overall satisfaction membership function is defined based on the decision-making's allowable error. The maximal group consistency weight model is established.

采用UOWA算子将决策者的偏好信息集结为区间数互反判断矩阵和互补判断矩阵两种形式，结合决策者给出的允许偏差，定义群满意度隶属函数，建立求解群偏好一致程度最大化的权重模型。

The definition and properties of line segment arithmetic are given,which is a special situation of point set arithmetic,but easily calculated.

文章给出了线段算术的定义和性质，它是点集算术的特殊情况，但更便于计算；提出了线段Bézier曲线的概念，就是把区间Bézier曲线中的长方形换成满足一定条件的线段，这里的线段是指该线段上所有点的集合；给出了线段Bézier曲线的性质及其细分算法。

The decay rate of a motion trajectory of the system in some interval is defined and the astringency of the switching system is investigated.

定义了系统对给定初值的运动轨迹在区间上的衰减速率，进而分析了整个系统的收敛性。

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parameterized by two positive shape parameters, typically denoted by α and β.

在概率论与统计，贝塔分布是一个连续概率分布上定义的区间[ 0 ， 1 ]参数由两个积极的形状参数，通常是指由α和β。

Then the definition of boundary value matrix for multi-multiplication interval linear systems is proposed.

对于多乘性区间线性系统，给出边界值矩阵的定义。

Week 4 The definition of continuous, the nature of continuous function, integral of elementary functions, the nature of elementary functions on closed interval

第4周 连续的定义，连续函数的性质，初等函数的连续性，闭区间上连续函数的性质。

By defining a partial ordering relation on the universal grey information domains of unit interval I,a definition of grey sets and grey relations on a lattice is given in this paper.

通过定义单位区间I的全体灰信息域上的偏序关系，给出grey集和grey关系在一个格上的定义。

Based on the interval probability and the second fuzzy probability, go a step further the definition and characters of random variables with the third fuzzy probability and the fuzzy distribution function and fuzzy probability distribution sequence were put forward.,the definition and characters of mathematical expectation and variance were studied also.

在区间概率和第二类模糊概率的基础上，进一步给出了具有第三类模糊概率的随机变量及其模糊分布函数和模糊分布列的定义和性质，并研究了模糊概率随机变量的模糊数学期望和模糊方差的定义和性质，进一步完善了模糊概率理论。

The new methodof defining spline function will generalize the concept to the more universal Hilbert space. Hence, we take into consideration the interpolation spline function, general linear differential operater in semi- open interval and the Green function defined accordingly, and the reproducing kernel to produce the Green function and prove the existence of the reproducing kernel.

采用了一种新的样条函数的定义方法，把样条函数的概念推广到更一般的Hilbert空间上，再考虑半开闭区间a，+∞上的插值样条函数，一般线性微分算子及其定义的Green函数和再生核，构造出Green函数并且证明了再生核的存在性。

After analyzing the merit and lack of 9I model, the main idea is proposed: to distill some basic topological relations from 9I model, of which the composite topological relations of complex objects are made up. In detail, the composite topological relationships between region and region, line and line, line and region are particularly discussed;(2)Analyze the characteristics and inner relations of cadastral features. According to the expressional model of complex topological relations, the author discovers the possible topological relations between parcels, parcel lines and parcel points. In addition, sum up the general topological relationship rules of cadastral data.(3) Then the topological relations model is extended to the spatio-temporal data. Time in cadastral database and change semantic are discussed. It's redefined that spatio-temporal topological relations is composed of time, location, status and event relation. Spatio-temporal topological relationships can be represented by extended 4I model. Taking cadastral parcels as example, there are different possible spatio-temporal topological relationships between parcels when they are extended, shrunken, split, merged or others. Thus, some deductions are drawn that, for example, if parcels have be coexisting for some time they are impossible to be overlapped. Furthermore, the parents of parcels alternated and their possible change types can be detected by their spatio-temporal topological relationships.(4) Before carrying out the experiment, the calculation method must be designed.

具体研究工作及成果如下：（1）根据点集拓扑理论中与拓扑空间相关的概念，本文对空间的点、线、面进行了重新定义，以区分对象的复杂性；分析了9I模型在表示简单对象方面的优点，以及在表达复杂对象上的不足，阐述了本文的研究思路和解决方案，并以复杂的面面、线线和线面为例详细探讨了复合拓扑关系的表达方法；（2）分析了地籍权属数据和地类数据的内涵、特点和要素之间的联系，根据复杂对象的拓扑关系表达模型，本文讨论了宗地、界址线、界址点之间，图斑、线状地物、零星地类之间可能存在的拓扑关系和形式化表达方法，归纳总结了地籍对象的拓扑关系满足的约束性规则；（3）将拓扑关系的研究延伸到时空领域，从地籍对象的时态性出发，本文阐述了地籍数据中时间的含义和变化语义描述的需要；从时间、位置、状态、事件等之间的拓扑关系方面，重新系统性地进行了时空拓扑关系的定义；研究了一维时间和二维空间的集成表达方式，以宗地、界址线为例，分析了变更前后不同时间区间里可能的拓扑关系，探讨了时空拓扑关系对时空变化操作类型和变化语义的推理方法和意义；（4）为实现空间拓扑关系的查询分析等应用，本文研究了空间拓扑关系的计算方法。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失