公理体系

In the doctoral dissertation,which focuses in lattice-ordered preferencestructure theory and lattice-ordered decision-making theory,lattice-orderedpreference relation displaces complete preference relation in order to makecharacterization of preference structure general,and in order to propose a newthinking of weakening completeness axiom,and also in order to put forward atheoretical base for setting up the rational behavior axioms and utility theorywith lattice-ordered preference structure.

本文有关格序偏好关系理论的研究将Von Neumann-Morgenstern理性行为公理中偏好关系的全序描述推广为格序描述，使得对偏好结构的描述更为一般化，并且为弱化公理体系中完全性或连通性假使提供一条新思路，为建立基于格序理论的理性行为公理及其相关的效用理论提供理论依据。

The axiomatic system in Pawlak rough approximation space is studied by use of matrix expression of fuzzy relation and its operation.

利用模糊关系及其运算的矩阵表示，建立Pawlak粗近似空间的公理体系，该公理系统由三条相互独立的非常简洁的表达式构成。

But things develop in the opposite direction when axiomatic system is extremely perfect and the limitation is bigger. This will offer a chance for scientific revolution and lead to changes in axiomatic system.

但事与愿违，越是形式化的公理体系发现其理论的局限越大，出现矛盾的可能性越大，这就为科学理论变革，即公理体系的变换提供了契机，也就是提出了新的科学问题，使科学认识进入到一个新的境界。

It is undoubtedly result of scientific theory systematization. When axiomatic system reaches a fairly perfect stage, theorists hope axiomatic system more abundant by formalization method.

当公理体系达到相当完善的阶段后，理论家们往往希望用形式化的方法使公理体系更精致，推理能力更强，更能发挥科学理论的认识功能。

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

By using modern mathematical theory,the ordering axiom is generalized tothe lattice-order axiom,and the continuity axiom is weakened to constructlattice-order decision-making behavior axioms,of which rationality is confirmed.

应用现代数学理论，将Von Neumann-Morgenstern理性行为公理体系中的全序刻划推广为格序刻划，并相应地弱化连续性公理，建立起新的格序决策行为公理体系，研究了该公理体系的合理性。

In this paper, the connectivity axiom and the continuity axiom in Von Neumann-Morgenstern Rational behavior axioms are weakened. Then, a set of axiom for lattice ordered decision-making behavior, which can describe the decision-making behavior more rationally, is constructed. At last, the relative unique existence theorem for utility function is obtained.

根据偏好关系所具有的格序特征，将Von Neumann-Morgenstern理性行为公理体系中的连通性公理弱化为格连通性公理，并相应地弱化连续性公理，得到了一集能更为合理地描述具有"有限理性"的决策行为的格序决策行为公理体系，构造并证明了在格序决策行为公理体系之下，效用函数的存在惟一性定理。

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

The axioms mentioned here are a system of axioms, which comprise potential axiom, motivational axiom, reflexive axiom,aesthetic axiom and intermendiate.

这里提出的，是由潜在公理、动因公理，反身公理、美学公理和中介公理所组成的公理体系。

Since Von Neumann and Oskar Morgenstern put forward the set ofrational behavior axioms in 1944,the linear expected utility theory that is themost important theoretical base of modern decision-making science has madegreat progress,and a lot of research achievements have been obtained in thisfield.

1944年Von Neumann和Morgenstern提出期望效用的公理体系，即&理性行为公理&后，作为现代决策科学最重要的理论基础的期望效用理论，得到了巨大发展，并取得了许多重要的研究成果。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。