集合代数

集合代数P（X）上的对称运算都是X上的对合映射所导出的映射；

The symmetry operation on a set algebra P ( x ) is induced mapping by doubly mapping on X ;

集合代数上几种代数运算的极小完备集

Minimal Complete Sets of Several Operations on Set Algebra

B-模糊集合代数和广义互信息公式

B-fuzzy Set Algebra and a General Cross-information Equation

提出了一种能够把图像关系查询和基于内容查询相统一的集合代数模型。

A set algebraic model that can uni1 ~ the keywords-based relation query and content-based retrieval is presented .

在本文中，作者讨论了纯不可测集的基本性质，并给出了纯不可测集类在集合代数方而的结构。

In this paper , the author discusses some basic properties of pure nonmeasurable sets , and presents the algebraical construction of non - measurable class .

由于布尔代数、集合代数、逻辑学和二进制算术之间的内在联系，使得布尔代数的理论在电子数字计算机的开发研制中举足轻重。

The relationships among Boolean algebra , set algebra , logic , and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers .

在分析图像数据库信息特征的基础上，讨论了图像数据库的一般关系模型和图像数据库基于内容查询的定义，提出了相应的集合代数模型，指出遥感图像基于内容查询实现的两种方案。

Based on the analysis of the information characteristic of image database ( IDB ) the general relation schema of IDB and the conception of Content_based Image Retrieval ( CBIR ) were investigated , and then a set model of CBIR was introduced .

本文研究了满足条件N的局部群系集合的代数性质，同时对于这类群类，给出了极小非-群的结构。

In this paper we investigate algebraic properties of the set of local formations which satisfy N , and for such formation we give the structure of minimal non group .

本文研究自反Banach空间中nest代数上的局部自同构，并考察nest代数上自同构集合的代数自反性。

This paper is concerned with the local automorphisms of nest algebras on reflexive Banach spaces and the algebraic reflexivity of the sets of all automorphisms on these algebras .

论优化问题的公理方法（Ⅴ）&优化集合的代数表达式

Axiomatic method to optimization problems (ⅴ)── an algebraic expression of optimizing sets

本文的创新成果具体如下：首先，我们讨论了软集合的代数超结构，代数超结构是代数结构的扩展。

The contributions of this thesis are concretely as follows : Firstly , we consider the algebraic hyperstructures of soft sets .

超算符方法中算符集合的李代数结构

The Lie algebraic structure of the set of operators in the hyper-operator method

本文主要讨论了线性拓扑空间中集合的固有代数边界点集的性质。

The properties of the proper algebraic boundary point sets of the sets in topological linear spaces were discussed .

第一种算法能够求得较为完备的离散化划分，但基于粗糙集和集合论的代数运算，计算量大，不利于处理大量数据信息。

The first algorithm could achieve a more complete discrete division , but with obvious drawback that required a large amount of algebraic computing involved in Rough Set and Set Theory , resulting in ineffectiveness of massive data information processing .

利用矩阵的张量积给出了偏序集基数积的一种矩阵表示，得到了检验有限集合上的代数运算满足结合律的一种方法。

In this paper , the authors give a representation of the relation matrix of the cardinal product of two partial ordered sets by the tensor product of their relation matrices , which helps to obtain a kind of method to check the associative law of binary operation .

字符串集合X~上的代数结构

An algebraic structure in the set X ~ of strings

分片代数簇作为多元样条组的公共零点集合，是经典代数簇的推广，丰富和发展。

As the zeros of multivariate splines , the piecewise algebraic variety is a generalization of the classical algebraic variety .

例如，上文定义的集合T的集合代数就对应与一个有32个元素的布尔代数。

For example , the set algebra for the set T defined above corresponds to a Boolean algebra of32 elements .

具体如下：首先，本文结合构件的静态结构特征和动态行为特征，基于谓词逻辑、集合论以及进程代数π演算，提出了一种构件的形式语义模型。

Specifically , major contributions are as follows : Firstly , this thesis develops a formal semantic model for component that is based on predicate logic , set theory and Pi-calculus .

条件事件代数是在确保规则概率与条件概率相容的前提下，把布尔代数上的逻辑运算推广到条件事件（规则）集合中的逻辑代数系统。

In this paper , a relatively new logic system named Conditional Event Algebra ( CEA ) which rigorously extends standard probability theory to include events which are contingent such as rules and conditionals is described .

形态滤波器是一种非常重要非线性滤波器，它是基于集合的几何结构代数理论&数学形态学，在图像分析与处理、计算机视觉和模式识别等领域获得了广泛的应用。

Morphological filters are a class of very important nonlinear filters based on algebraic theory of the geometrical structure of sets which called mathematical morphology . They have found wide applications in many research fields , such as image analysis and processing , computer vision and mode recognition .

有限的对称布尔代数都是某个带有一个对合映射的集合X上的集合代数。

All finite symmetry Boolean algebra are set algebra of a certain set X , Which has a doubly mapping .

提出了描述条件模糊事件的数学方法，研究了条件模糊事件的集合表示，讨论了Fuzzy格上条件事件的构建和条件事件集合的代数结构。

A new method for describing conditional fuzzy events is suggested , and then the set representation of conditional fuzzy events is studied . Finally , the construction of the conditional events on fuzzy lattices and the structure of the set of conditional events on fuzzy lattices are discussed .

并且，首次给出一个集成多维对象集合和该对象集合上的Skyline结果集的形式化模型，该模型适合目前Skyline查询计算的应用，并在该模型的实例上研究Skyline集合的查询代数操作。

A formalized model is also first proposed , which brings the set of multiple dimensional objects and the result set of skyline query together . And the instances of this formalized model can be used to study the query algebra operations on the skyline sets .