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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。

The most famous rough algebras are Rough Double Stone Algebra, Rough Nelson Algebra and Approximation Space Algebra, and their corresponding general algebra structures are regular double Stone algebra, semi-simple Nelson algebra and pre-rough algebra respectively.

其中最有影响的粗代数分别是粗双Stone代数、粗Nelson代数和近似空间代数,它们对应的一般代数结构分别是正则双Stone代数、半简单Nelson代数和预粗代数。

In this paper,the main work is to extended the premitive model of rough sets;Accorting to the Rough structure and algebra structure,the main work is to study the application of rough set theory on algebra system-group,so that rough algebra system is better perfectly.

本文在现有的Pawlak粗糙集模型基础上,对模型进行推广;根据粗糙结构和代数结构及已有的研究成果的基础上,更进一步地研究了粗糙集理论在代数系统一群上的应用,以此建立较为完善的粗糙代数系统。

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。

The main contributions and innovations in this dissertation are as follows:(1) The uncertainty of knowledge and rough set is discussed and a fuzzy entropy measure method based on boundary region is put forward. It redefines knowledge rough entropy and rectifies the definition of rough entropy of rough set.

论文的主要贡献及创新如下:(1)对知识和粗集的不确定性进行了深入研究,提出一种基于边界域的模糊熵度量方法,重新定义了知识粗糙熵并修正了粗集粗糙熵的定义。

Main business: CNC engraving machine Series: Applications: stainless steel, copper engraving Case insets processing; stainless steel, copper Case Shouban; spherical, Globoidal processing, text, sculpture ★ Case 5-axis double-headed insets engraving machine ★ Case 5-axis three insets engraving machine ★ Case 4-axis linkage double-headed insets engraving machine ★ Case 4-axis linkage three insets engraving machine ★ high triaxial strong double-headed die machine ★ high strength triaxial 3 Die machine ★ Case Drilling Machine, surface drilling machine ★ Case-meter pit, watches and clocks, glass-processing machine production testing of aircraft series:● test the waters Series: 10 automatic machine manually test the waters, six automatic Manual examination of water, really test the water leak-loaded needle ● Series: Semi-automatic assembly line of watches and clocks, watches and clocks, with three-pin CNC machines, semi-automatic machine ● single needle assembly Series: Semi-automatic cutting the core of machines, Case glass adhesive glue Machines, pneumatic pressure Digai ● strap-test: strap Rally torque testing machine, clasp switch testing machine, strap swing testing machine ● first test table: Table heading to the functional testing of aircraft, form the first vibration test machines, Table first parabolic dynamic testing machine has been with the German company Rexroth, Japan Yasukawa, Panasonic, Mitsubishi, and other well-known international companies have a long-term stability of technical cooperation, continue to study and absorb the advanced technology at home and abroad.

主营业务: CNC雕刻加工机系列:应用:不锈钢、铜表壳镶石雕刻加工;不锈钢、铜表壳手板;球面、弧面加工、文字雕刻★表壳五轴联动双头镶石雕刻机★表壳五轴联动三头镶石雕刻机★表壳四轴联动双头镶石雕刻机★表壳四轴联动三头镶石雕刻机★高强力三轴双头模具加工机★高强力三轴三头模具加工机★表壳钻孔机、表面钻孔机★表壳米坑位、玻璃位加工机钟表生产测试机系列:●试水系列:十头自动手动试水机、六头自动手动试水机、真水试漏机●装针系列:半自动钟表装配生产线、数控钟表装三针机、半自动单针机●装配系列:半自动切把芯上的机、表壳玻璃胶水粘接机、气动压底盖机●表带测试:表带拉力扭力测试机、表扣开关测试机、表带摇摆测试机●表头测试:表头按的功能测试机、表头震动测试机、表头抛动测试机一直以来,公司与德国Rexroth、日本安川、松下、三菱等国际知名企业有着长期稳定的技术合作,不断地学习和吸收国内外的先进技术。

From an extensive molecular epidemiological surveillance around the H5N1 infected regions in the past several years, H5N1 viruses were isolated from the wild birds, eg. Bar-headed goose, brown-headed gull, great black-headed gull and common cormorant form Qinghai province and tree sparrow from henna province.

通过开展高致病性禽流感疫区的分子流行病调查,从野生鸟类分离到这种H5N1亚型的禽流感病毒,如从青海湖斑头雁、棕头鸥、渔鸥、鸬鹚,从河南的树麻雀等都分离到这种病毒。

Likewise, there were three main forms of government, each supported by a social "principle": monarchies (free governments headed by a hereditary figure, e.g. king, queen, emperor), which rely on the principle of honor; republics (free governments headed by popularly elected leaders), which rely on the principle of virtue; and despotisms (enslaved governments headed by dictators), which rely on fear.

同样的,存在三种主要的政府形式,每一种由一种社会&原则&支撑:君主制(以一个继承的人物,比如国王,王后或皇帝为首的自由政府)依赖于荣誉原则;共和制(以大众选举的领导者为首的自由政府),依赖于美德的原则;独裁制(以独裁者为首的奴役政府),依赖于恐惧。

The application of rough set theory in incomplete information systems is one of the key problems to study rough set theory in practice. However, it is difficult for classical rough set theory to deal with those incomplete information systems.

粗糙集理论在不完备信息系统中的应用,是将粗糙集理论进一步推向实用的关键之一,而经典的粗糙集理论对不完备信息系统的处理显得束手无策。

Kuroki N firstly put forward the notion of rough subsets and rough ideals in semigroups, testifying that Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N首先研究了半群中的粗理想,首次提出了粗子半群和粗理想的概念,证明了在同余关系下,半群的粗糙集是半群,左理想的粗糙集是左理想。

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