基于凸锥的近似空间（毕业学术论文设计）.doc

基于凸锥的近似空间 学生： 指导教师： 老师 学科专业：信息与计算科学 学号： 摘 要 粗糙集理论是一种新的处理模糊和不确定性的知识的数学工具。其主要思想就是在保持分类能力不变的前提下，通过知识约简，导出问题的决策或分类规则。而关于凸集和凸函数的一些定理在最优化问题的理论证明及算法研究中具有重要作用。 本文首先介绍了凸集、凸锥、凸包等凸分析的基本概念及其相关性质，然后又介绍了经典集与等价关系、粗糙集及其近似的概念及性质。之后基于粗糙集的基本理论，提出了可利用含原点的凸锥构造一个近似空间，定义了此空间的上、下近似，并根据近似的定义，直接验证得到基于一个含原点的凸锥，的一些性质是否成立。最后，总结验证了凸锥以及凸包的运算性质。 关键词：凸锥；凸包；上、下近似 Abstract The Theory of Rough Set is a new mathematical tool, which is deal with the knowledge of ambiguity and uncertainty. Its main idea is export the decision-making or Classification rules through knowledge Reduction, on the premise that keeps the same capacity for classifying. And some theorems on the convex and convex function play an important role in the theory proving and algorithm researching of Optimization. In the first place, this thesis introduces some basic concept and interrelated nature of Convex Analysis such as the convex, the convex cone and the convex hull, and then it introduces the concept and nature of them, which are the classic sets, the equivalent, the rough sets and its approximation　space. After that ,according to the basis theory of rough set, we propose the definition of　an approximation space which is basing on the convex cone that contain the origin, and define the upper and the lower approximation of convex cone. And according to the definition of approximation, we proof some properties of ， immediately, which are base on a convex cone that　contain　the　origin. Finally we discuss and proof perties of the convex cone and the convex hull. Key words: convex cone；convex hull；the lower and the upper rough approximation 目 录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc201466190 第一章 引 言 PAGEREF _Toc201466190 \h 1 HYPERLINK \l _Toc201466191 1.1 关于粗糙集 PAGEREF _Toc201466191 \h 1 HYPERLINK \l _Toc201466192 1.2 关于最优化 PAGEREF _Toc201466192 \h 2 HYPERLINK \l _Toc201466193 第二章 关于凸锥 PAGEREF _Toc201466193 \h 4 HYPERLINK \l _Toc201466194 2.1 关于凸集与凸包 PAGEREF _Toc201466194 \h 4 HYPERLINK \l _Toc201466195 2.2