完备集

In this kind of incomplete information system, a new kind of binary relation based on relative degree is proposed according to the set pair analysis, this binary relation is only reflective.

在此基础上，分析了这种二元关系在两种特殊情形的不完备信息系统中的表现形式，然后根据新建立的基于联系度的粗集模型，使用决策矩阵讨论了规则生成方法，最后用一个实例说明了此方法的有效性。

We proved that there exists a dense G (subscript δ) subset of the complete metric space consisting of the vector optimization problems satisfying some conditions ,and each problem in the dense G (subscript δ) subset has stable solution set, which generalized the corresponding results in the literature.

证明了满足一定条件的向量优化问题构成的完备度量空间中，存在一个稠密G集，在此稠密集中每个问题的解集都是稳定的，推广了文献中的相应结果。

Does research in a common fixed point theorem of fuzzy mapping s in inequality conditions and the cut set is the nonempty closed bounded subsets of,while is complete metric space.

2，研究了在完备度量空间中一对模糊映象满足一些特定不等式条件，以及当其截集是中非空有界闭集时，该对模糊映象的公共不动点的存在性问题。

Under the conditions of compatibility or sub-compatibility between a single-valued mapping and a set-valued mapping,a necessary and sufficient condition for set-valued mapping pair and single-valued mapping which have the common fixed point in complete convex metric space are given.

在单值映象与集值映象相容或次相容的条件下，给出了完备凸度量空间中集值映象对与单值映象存在公共不动点的一个充要条件，改进和推广了某些已知结果。

At the same time, some properties of rough Set in quotient ring are given and proved. The fifth chapter is Rough Primary Ideals and Rough Fuzzy Primary Ideals in Semigroups, the concept of rough primary ideals and fuzzy rough primary ideals in semigroups are introduced. Under the condition of the complete congruence relation, a rough set of a primary ideal in semigroups is proved to be its primary ideal.

同时，在商环中讨论了粗糙集的一些性质，并给出这些结论的严格证明；第五章是半群中的粗准素理想和粗模糊准素理想，首次提出了半群中的粗准素理想与粗模糊准素理想的概念，证明了在完备同余关系下，半群中准素理想的粗糙集是准素理想。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

But when their informationset is not complete,it is hard for decision-makers to determine,that is to say,the preference relation is not complete.

实际上，在一般决策问题中，决策人对备择方案的优劣判断主要依赖于决策人的信息集，而当决策人的信息集不完备时，决策人就可能难以对一些备择方案的优劣做出判断，这时完全性或连通性就不满足。

Service messages were described by tree grammar and operations for service adaptation were defined based on tree automata algebra.

提出了以树型文法表示服务的消息，并基于树型自动机的代数操作定义了服务的适配操作集，分析了该操作集的完备性。

Completeness of the set of real numbers is its basic character, and it is stable theory background of calculus.

摘要实数集的完备性是实数集的1个基本特征，它是微积分学的坚实的理论基础。

A basic set of transformation rules was given and it was proved to be complete and consistent,so that the theoretic and technologic foundation to translate operator language to procedure language was provided.

给出了基本变换规则集，证明了该变换规则集的完备性和一致性，为该类语言到过程语言的翻译提供了理论和技术基础。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。