集合关系

Department of Applied Mathematics;University of Science and Technology of Suzhou;Suzhou 215009

为提高算法效率，采用了集合的精确匹配代替高代价的子集关系的检验。

It is difficult to judge a transitive binary-relation by using the definition of transitivity of binary relation directly.

0引言定义在某一集合上的二元关系具有自反性、反自反性、对称性、反对称性以及传递性等性质。

This thesis is about the establishment of semantic Web based on the binary relation ,advances the formal definition of the semanteme in the semantic Web,based on it,advances the way semanteme is described and derived and discusses the semantic completeness.

基于二元关系讨论了语义Web的建立过程，具体给出语义Web中相关语义的形式化定义，并基于此给出了语义描述和挖掘方法，进行了集合相关语义的完备性的证明。

This paper establishes a series of equations on IFS inclusion degrees by using fuzzy implication operators and set cardinal numbers,reveals the relationship between inclusion degrees and similarity measures and proposes an inclusion degree based IFS similarity measure.The instance indicates that the proposed method can not only resolve the problem,and that it provide a new approach for the research on theory of IFS similarity measurement as well.

借助模糊蕴涵算子和集合基数，建立了IFS包含度的一系列具体公式，揭示了IFS包含度与相似度的关系，提出了一种基于包含度的IFS相似度量方法，并以具体算例表明该方法不仅可以解决中部分存在的问题，而且为研究IFS相似度量理论开辟一个新的途径。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

Data structure,Have one or many kinds of characteristic datum set of element of relation each other.

数据结构，互相之间存在一种或多种特点关系的数据元素的集合。

We also show that the one-to-one defensive competition problem is a generalization of the Tukey median problem and the smallest enclosing circle problem which are two famous problems in computational geometry.

同时我们也讨论了竞争性区位设施之防御问题与其他计算几何领域内的著名题目例如，Tukey 中间值及最小圆盘集合之间的关系。

In this thesis, we will mainly do research on the novel scheme for Digital image Steganography, Digital Image Secret Transmission in network and the development of the information hiding device for application. The main contributions of this thesis are as following: The novel conversion method for mapping image to complex number is proposed, and the plus, minus, multiply and complex conjugate operation of image are defined based on Positional number systems and complex number system. Following new results have been gotten: 1 The suitable complex number basis to be used to express integers is a big set. 2 Any image can be mapping into a one-to-one point. 3 Lots of image processing problem can be considered based on geometric theory.

在本论文中，研究工作集中在数字图像伪装算法的新模型、图像在网络中的加密传输的新方案和信息伪装设备的研发等三个方面，主要包括：基于位值制记数法和复数系理论，提出利用复数作为基底的数字图像新的表示方法，用复数运算定义了图像和图像间的"加"、"减"、"乘"、"共轭"等运算关系；得到理论结果： 1、能表示任何整数的复数基是很大的一个集合。2、任何一幅图像，都能和复平面上的一个点一一对应。3、可以将图像问题化归为平面几何问题处理。4、复数系下的图像表示适合用于信息伪装。

Three ways were first put forward to describe QoS preference information based on the theory of multiple-attribute decision, which were orders vector, AHP matrix and language valuation collection, and the concrete methods of conversion and computation were given out.

基于多属性决策理论，首先提出了QoS偏好信息的三种描述方式：序关系向量、AHP矩阵和语言评价集合，并给出了相应的转化和计算方法。

Three ways were first put forward to describe QoS preference information based on the theory of multiple-attribute decision,which were orders vector,AHP matrix and language valuation collection,and the concrete methods of conversion and computation were given out.

基于多属性决策理论，首先提出了QoS偏好信息的三种描述方式：序关系向量、AHP矩阵和语言评价集合，并给出了相应的转化和计算方法。随后，把QoS偏好的处理策略应用于服务选择，提出一个相对最优服务的确定方法，该方法可以反映用户的QoS偏好，满足用户按需服务的需求。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。