集合论

因为RDBMS是建立在严格的数学集合论基础上的，数据结构简单、清晰，具有强大的查询能力，RDBMS成为实现信息系统的基本技术。

RDBMS is based on firm mathematics set theory with simple and clear data structure , and powerful query function , so it has become the basic technology for realization of information system .

这一问题与早期的集合论出现的问题类似。

The problem is akin to what happened in early set theory .

Fuzzy集合论在图书资料工作中的一种应用

The Application of Fuzzy Set to the Work of Library and Data Bank

Fuzzy集合论的公理系统

An axiomatics system for the fuzzy set theory

基于分形理论和模糊集合论，本文提出一种Fuzzy分维概念（简称F-分维）。

We put forward fuzzy fractional dimension conception based on fractal theory and fuzzy aggregation .

在Fuzzy集合论的基础上，提出了不确定变量决策问题的数学模型。

In the base of classical decision theory , A optimal method of fuzzy decision making involving the imprecise variables is presented .

中介逻辑演算ML与中介公理集合论MS的纯数学意义及其应用前景

The pure mathematical significance and applied perspective of the medium logical calculus and medium axiomatic set theory

在中介公理集合论系统（MS）中重新定义了良集的概念，讨论了它的性质。

Defines the concept of well sets in MS ( axiomatic medium set theory ) and discusses its characters .

将MATLAB软件与ADAMS/Rail软件相结合，建立了基于模糊集合论的车辆悬挂系统的自适应控制策略。

A fuzzy set theory of the adaptive control suspension is established by using the MATLAB and the ADAMS / Rail .

采用模糊集合论（Fuzzy）与层次分析法（AHP）相结合的方法，建立了一个对我国企业内部冲突状态进行综合量化评价的数学模型。

By using the theories of Fuzzy and AHP , the paper established a mathematics model to appraise the internal conflict in an enterprise .

同样地，中介关系代数以中介集合论MS为基础，扩充了关系代数的功能。

Similarly , based on the medium set theory MS , the medium relational algebra can extend the capability of relational algebra .

提出了印制电路板（PCB）设计时内电层分割的一般性方法，并就其使用集合论的方法给予了较严格的数学证明。

A general approach to internal power plane spliting with strict mathematical proof by set theory , is presented in this paper .

因而在由前缀逆相关ω-语言或左逆封闭ω语言组成的ω-语言类中，Fuzzyω正则语言的代数特征就可从代数和集合论的观点给出。

Thus in a class of ω - language with prefix-inverse-related ω - language or left-inverse-closed ω - language , the characteristics of fuzzy ω - regular language is given from algebra and set viewpoints .

多元统计方法的引用，为H－生态位的分析提供了合适的数学模型；运用集合论方法研究群落生态位，为深入探讨群落中物种间的竞争、共存及互作机制提供更多的信息。

Multivariate statistical method can provide appropriate models for analysing H-niche , and set-theoretic method will give more informations on the mechanisms of competition , coexistence and interaction among species in a community .

Z语言是基于一阶谓词逻辑和集合论的形式规格说明语言，采用了严格的数学理论，可产生简明、精确、无歧义且可证明的规格说明。

Z is a formal specification language based on the first order predicate logic and set theory . It can generate concise , accurate and conformable specifications .

细胞（d1，d2）－有向图语言类在集合论运算下的封闭性

The closure of cellular ( d 1 , d 2 ) - digraph language class under set theoretic operations

在DS证据理论的基础上，结合模糊集合论，给出了多传感器数据融合一般化方法，并将其应用于电机故障诊断。

A data fusion general method based on D S evidential theory and fuzzy logical theory is presented that is used in the electric machines fault diagnosis .

文章首先阐述了几种常见Petri网类型的形式化定义，给出了参数化网络类的表示方法，它包括集合论方法和范畴论方法；

The thesis firstly illustrates the formal definitions of several familiar types of Petri nets and the representation approaches of parameterized net classes , which include set-theoretical approach and categorial approach .

本文主要研究的是Z规格说明中集合论算子向C++的自动转换，文中具体讨论了Z的基本数据类型和集合论算子中属于操作的转换。

The investigate is mainly that set theory operator of Z specification converts to C + + in the paper , Z basic data type and set theory operator is discussed principally .

模糊集合论的ZB系统

The ZB system of fuzzy set theory

针对非线性和时变性系统的PID控制，应用模糊集合论，并充分考虑人工整定的经验，设计了由模糊参数整定器和变参数PID控制器构成的新的模糊PID控制器。

For specific PID control of non-linear and time varying systems , a new fuzzy controller composed of fuzzy parameter tuning device and varying parameter PID controller is designed by using fuzzy set theory and experience of manual tuning .

在策梅洛-弗兰克尔的集合论公理系统ZF中，基础公理把集合的论域限制到良基集合。

In the Zermelo-Fraenkel system ZF of set theory , the foundation axiom restricts the domain of set theory to well-founded sets .

其次，利用中介公理集合论MS的相关理论，构造了MS中的自然数系统，证明了Peano5条公理为MS中的定理。

Secondly , by using of the medium axiomatic set theory ( MS ), a natural number system in MS is constructed , and it is proved that five axioms of Peano ′ s natural number system are theorems is MS.

Borel归约是描述集合论中的&个基本概念，我们经常用它来比较不同等价关系的复杂度。

Borel reducibility is a fundamental concept in Descriptive Set Theory , we often use it to compare the complexity of different equivalence relations .

作者曾用组合方法与集合论方法，提出共轭比序列的概念，并证明了判别〔IA〕群的一系列充分必要条件。

The author introduced the concept of conjugate ratio sequence and proved a sequence of necessary and sufficient conditions for ( IA ) groups by means of combinatorics and set theory .

再次，在关系的稳定提升阶段，论文采用Fuzzy集合论与AHP方法相结合的模糊综合评判方法，对高价值的关键网络节点企业构建了关系质量评价的综合决策模型。

Thirdly , in the stage of enhanced and stable relations , this paper constructs comprehensive decision-making model of relationship quality evaluation to high-value key node enterprises in the network by using Fuzzy Integral Evaluation Method which combines Fuzzy set theory and AHP method .

Object-Z是形式规格说明语言Z的面向对象扩充，基于严格的集合论与数理逻辑，具有面向对象的特点：类、对象、继承、封装与多态等。

Object-Z is an extension to the formal specification language Z , which facilitates specification in an object-oriented style and thus has object-oriented characteristics . It improves the clarity of large specifications through enhanced structuring .

指出了数学分析改革的突破口在于用集合论和Lebesgue积分理论改造目前数学分析的内容和体系。

Points out that the break through to the reform in mathematical analysis lies in improving the present content and system of mathematical analysis by the set theory and the Lebesgue integral theory .

无穷观问题的研究（Ⅴ）&一个兼容实无限与潜无限的公理集合论系统APAS

An Outlook on the Infinity (ⅴ) - An Axiomatic Set Theory APAS for Holding the Actual Infinity and the Potential Infinity Concurrently

证明集合论假设BF（ω2）下，如果X，Y都是具有素可数k网的正则空间，那么X×Y是k空间当且仅当空间对（X，Y）满足Tanaka条件。

In this paper it is shown that under set theoretic hypoothesisBF (ω 2 ) if X , Y are regular spaces with compact-countable k-networks , then X X Y is a k-space if and only if the ( X , Y ) satisbo the Tanaka 's condition .