粗糙

In rough sets based on accessible relation, we merge rough set theory and accessible relation into one model. Compared with classical rough set models(including Pawlak rough set model and various precise rough set model), the new model is more general.

基于可达关系的粗糙集模型是将可达关系应用于粗糙集理论中，这种模型比传统的粗糙集模型(Pawlak模型和可变精度粗糙集模型)更一般，将粗糙集理论推广到一般的方法论。

The mutual coherence and angular correlation function of scattered wave from two dimensional rough surfaces is derived with Integral Equation Model and then calculated for perfectly conducting rough surfaces, then the scattering of incident pulse wave with different shape is calculated and the shape of scattered pulse is presented.

采用积分方程法推导出了二维粗糙面的双频互相关和角相关函数，数值计算了具有不同粗糙度的良导体粗糙面的双频互相关函数，在此基础上分别计算了二维粗糙面对δ脉冲、Gaussian脉冲和矩形脉冲的散射，并给出了散射脉冲的波形。

In chapter 2, basic knowledge of the rough set theory, such as indiscernibilityrelation, elementary set, approximate space, upper approximation, lower approximation, negative region, boundary region, rough set, etc., and algebraic properties of rough set are introduced. At the same time, the feature of the rough, set theory is also introduced.

第二章介绍了粗糙集理论基本知识，如不可分辨关系、基本集、近似空间、上近似、下近似、负域、边界域、粗糙集等概念，以及粗糙集的代数性质，同时还介绍了粗糙集理论的特点。

In this chapter, firstly, the definition of rough semigroups is given afresh. Then based on rough groups, rough subgroups, rough cosets, rough invariant subgroups, some properties of rough subgroups and rough invariant subgroups and the concept of rough quotient groups are introduced. Finally, based on some concepts of homomorphism and isomorphism of rough groups, basic homomorphism theorem and isomorphism theorem of rough groups are put forward and proved.

在这一章中，首先重新给出了粗糙半群的定义，其次在粗糙群、粗糙子群、粗糙陪集、粗糙不变子群的基础上，给出了粗糙子群的若干性质、粗糙不变子群的三个重要性质和粗糙商群的定义，最后在粗糙群同态与同构的基础上，给出了粗糙群同态基本定理与同构定理。

In this chapter, firstly, the definition of rough rings and its properties are given. Then the definition and properties of rough subrings, rough ideals and rough quotient rings are put forward and proved. Finally, homomorphism and isomorphism of rough rings is studied.

在这一章中，首先给出了粗糙环的定义及其性质，其次给出了粗糙子环、粗糙理想、粗糙商环的定义及其性质，最后研究了粗糙环的同态与同构。

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。

The method connects the exponentially attenuating dividable auto-correlation function which is often used in the study of the lubricating behaviors of rough surfaces, to the theoretical model for studying the contact behaviors of rough surfaces and it will be a foundation for studying the lubrication and failure problems of sliding frictional pairs with anisotropic surfaces.

第三章对Onions-Archard的理论接触模型进行扩展，给出了计算各向异性粗糙表面接触性能的简便方法，并将粗糙表面润滑效应研究中常用的表征粗糙表面的指数衰减可分自相关函数和粗糙表面接触性能研究的理论模型联系了起来，为研究混合润滑工况下各向异性粗糙表面摩擦副的润滑和失效问题提供了基础。

At the early 1980s, is an effective mathematic tool to deal with the uncertain or fuzzy knowledge. Rough rule theory has been widely used in information retrieval, digital library, software engineering and knowledge discovery. Its main idea includes acquisition of rough decision rules by reduction of data under the condition of keeping an invariability of classification capacity. And it basically represents a concept by a pair of approximation sets according to the partition on the given data based on the indiscernibility relation. Rough sets theory is well suited to deal with inconsistency of the rough approximations. So it is a new mathematical tool dealing with vagueness and uncertainty, and has found its applications in many areas such as AI, KDD, pattern recognition and classification and fault diagnosis.

主要完成了以下几个方面的工作：(1)对于高速移动机器人车道线跟踪问题中的规则知识获取，首先阐述了模糊逻辑系统的基本特点、工作原理和基本作法，分析了模糊规则知识获取过于依赖专家经验知识、对于每一个细节几乎都需要人工主观经验的参与、难以处理大数据集样本等方面的不足，进而阐述了粗糙集合理论的基本特点、基于粗糙集合理论的规则获取的关键技术和工作原理，为后续章节中经典粗糙集合模型的扩展及粗糙决策规则集的性能分析做好基础；(2)在经典粗糙集理论及其一般扩展的可变精度粗糙集VPRS的基础上，提出了非均匀可变精度粗糙集模型k-VPRS。

At the same time, some articles that have been studied about the theory combined pure mathematics with rough sets have been emerged, and some new mathematical notions, such as rough logic, rough ideal in semigroups, rough groups and rough subgroups, rough cosets, rough invariant subgroups and homomorphism and isomorphism of rough groups, are introduced.

同时，纯粹的数学理论与粗糙集理论结合起来进行研究已有文章出现，并不断有新的数学概念出现，如&粗糙逻辑&、&半群中的粗理想&、&粗糙陪集&、&粗糙不变子群&、&粗糙群和粗糙子群&、&粗糙群的同态与同构&。

The main factors affecting the surface roughness of wood are: species, method of machining, radial or tangential section and cell structure of wood surface.

针叶材粗糙度和粗糙感的分布范围较阔叶材的窄，阔叶材的粗糙感主要受粗糙度的影响，针叶材的粗糙感主要来源于木材的年轮宽度。

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。