查询词典 axiom

It is proved that the choice function must satisfy the axiom of consistency if the choice function meets the axiom of substitutability together with quotafilling condition; then, it is driven that the choice function is a path independence choice when it satisfies the substitutability and consistency condition.

首先证明了在替代性原理的前提下，选择函数定额充分是满足一致性原理的充分条件；得出了当选择函数满足替代性和定额充分条件时，必定满足路径无关性选择的结论。

On the base of Frege's study, Russell put forward the theory of types to settle Russell's paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.

罗素在弗雷格研究的基础上，提出逻辑类型论来解决罗素悖论，以非集合论理论为基础，以无穷公理和选择公理为前提，利用逻辑概念定义数学概念，并构造系统，通过逻辑演绎法从逻辑公理推导数学定理。

An axiom definition of similarity measure based on Li's related works, which constrains the necessary conditions of a similarity measure, is proposed. Then two new methods are introduced, and proved to satisfy the axiom defined above. Finally, an example of their application to pattern recognition is given.

在Li(2003)的相关工作之上提出一种改进的Vague集相似度量公理化定义，指出一个相似度量必须满足的约束条件，然后引人两种新Vague集相似度量方法，并证明它们满足这些公理化条件，最后给出一个它们在模式识别的应用实例。

Analyze the nature and characteristic of lattice-ordered structure,andstudy the relation between lattice-ordered preference and the incompleteinformation set of decision-makers;By discussing the relation betweenlattice-ordered preference structure and independence axiom and continuityaxiom,study whether or not independence axiom accords to continuity axiomwith lattice-ordered preference structure,which is for setting up theoreticalbase for weakening the rational behavior axioms.

分析了偏好关系的格序特征，并研究了格序偏好关系与决策人决策信息集不完备性之间的关系；从理论上研究和论证格序偏好关系与VonNeumann-Morgenstern理性行为公理中独立性公理和连续性公理的相容性问题，为公理弱化奠定理论依据

In this dissertation,Von Numann and Morgenstern Axioms are analyzedagain at first.It is pointed out not only that preference relations are often latticeordered,but also that the transitivity axiom,along with the independence axiomand the continuity axiom is still rational to a high degree,then a new set ofaxioms for lattice-order decision-making behavior is established.At last,relatedsubjects based on lattice in preference theory,utility theory,decision-makingmethods,multiattribute decision-making,and group decision-making are studied.In this way,the lattice-order decision-making theory is framed.Main creativeresults are obtained as follows

本论文重新审视了Von Neumann-Morgenstern理性行为公理体系，对以前学者较少涉及到的连通性公理提出了质疑，指出偏好关系具有格特征，而传递性公理、独立性公理以及连续性公理在很大程度上仍具有合理性，进而创建了格序决策行为公理体系，研究了基于格的偏好理论、效用理论、决策方法、多目标决策以及群决策中的相关问题，初步构建了格序决策理论框架，主要研究成果如下

As an application of the above proof, we obtain at once that there is an open and dense set in the set of Ω-stable systems such that every system in the set satisfies Axiom A and the no-cycle condition (Axiom A and the strong transversality condition, respectively).

作为上述方法的一个运用，马上可以得出在Ω稳定系统的集合中有一开稠集满足公理 A 和无环性条件(对应的，公理 A 和强横截性条件)。

Byapplying a general large deviation theorem of Kifer and Ruelle's Smale space tech-nique together with his unique equilibrium state result for non-Holder continuousfunctions,we obtain a level-2 LDT for the Axiom A endomorphism with respectto its equilibrium states,and for Axiom A attractors of the endomorphism withrespect to the Lebesgue measure.

利用Kifer的一个一般性的LDT，Ruelle的Smale空间方法及其关于非〓连续函数平衡态的存在唯一性结果，我们证明了公理A自映射相对平衡态的level-2 LDT，以及自映射的公理A吸引子相对Lebesgue测度的level-2LDT。

Say for example, when discussing on parallel axiom, which is "given a point and a line on a plane, there exists a unique line on the plan that passes through the point and is parallel to the line", if we change the axiom as "there is not any or there are infinitely many lines that will pass through the point and be parallel to the line", then we have two kinds of non-Euclidian geometry.

就像对于平行公理的讨论一样，干脆规定：过已知直线外一个固定点可以作无数条与已知直线平行的直线；或者过已知直线外一个固定点的任何直线都不能与已知直线平行；这样还产生了两个版本的非欧几何。

Experiment 1 (chapter 6), adopting procedures of the binary lottery games, with leading elements of information conditions into the practice, tested Nash bargaining model systematically and found that, under complete information conditions, axiom 4 was obviously rejected and axiom 3 which was reproachable to some extends, however was supported and therefore Raiffa solution was not observed; And associated with those, significant effect of information conditions and effect of interpersonal payoff comparisons with bargaining behaviors were founded.

结果发现，在完全信息条件下，公理4遭到明显拒绝；而引起一定程度上非议的公理3却能获得支持，故也未观测到Raiffa解的存在；与此相关，发现了议价者行为上的显著的信息条件效应和人际支付比较效应；在此基础上，作者对Nash议价模型进行了修正。

Some new basic concepts are proposed in this paper, including the approximation space of generalization, rough approximation axiom, disturbance set axiom, classification principle of rough set, principle of nondeterministic even set, principle classification, bit quantum symmetric classification, of concentration, game classification, quantum logic incomparable set, bit space set, protocol relation, rough set function of protocol relation, rough classification algebra, rough simple algebra, etc., and a guess is also proposed.

提出了广义近似空间、粗近似公理、干扰集公理、粗糙集的分类原则、粗选原则、不确定偶集原则、精选原则、对策分类、量子逻辑分类、bit量子对称分类、不可比集、bit空间集、协议关系、粗糙集函数、粗糙分类代数和粗糙单代数等基本概念，并提出了一个猜想；展示了一些新观点；基于协议关系构造了粗糙商代数和粗糙子代数，给出了回避-归并算法及算例。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。