Modeling on triangulations with geodesic curves

This paper discusses the problem of modeling on triangulated surfaces with geodesic curves. In the first part of the paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. In the second part we discuss the construction of C ⁰ and C ¹ piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks. The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive the convex hull property of geodesic Bézier curves.

Invariant and attracting sets of impulsive delay difference equations with continuous variables

The aim of this paper is to study the invariant and attracting sets of impulsive delay difference equations with continuous variables. Some criteria for the invariant and attracting sets are obtained by using the decomposition approach and delay difference inequalities with impulsive initial conditions.     

Approximations and reducts with covering generalized rough sets

The covering generalized rough sets are an improvement of traditional rough set model to deal with more complex practical problems which the traditional one cannot handle. It is well known that any generalization of traditional rough set theory should first have practical applied background and two important theoretical issues must be addressed. The first one is to present reasonable definitions of set approximations, and the second one is to develop reasonable algorithms for attributes reduct. The existing covering generalized rough sets, however, mainly pay attention to constructing approximation operators. The ideas of constructing lower approximations are similar but the ideas of constructing upper approximations are different and they all seem to be unreasonable. Furthermore, less effort has been put on the discussion of the applied background and the attributes reduct of covering generalized rough sets. In this paper we concentrate our discussion on the above two issues. We first discuss the applied background of covering generalized rough sets by proposing three kinds of datasets which the traditional rough sets cannot handle and improve the definition of upper approximation for covering generalized rough sets to make it more reasonable than the existing ones. Then we study the attributes reduct with covering generalized rough sets and present an algorithm by using discernibility matrix to compute all the attributes reducts with covering generalized rough sets. With these discussions we can set up a basic foundation of the covering generalized rough set theory and broaden its applications.     

关联规则的快速提取算法

针对基于频繁项集的关联规则挖掘算法效率低,需要多次扫描数据库且生成冗余候选项集问题,该文利用频繁项集的Aprior性质和概念格的基本思想提出一种关联规则提取算法,利用极大频繁项集来进行规则提取,去除了多数冗余的候选项集,提高了提取效率。     

基于粗糙集理论的图像平滑算法研究

基于粗糙集理论,针对高斯噪声和脉冲噪声,分别采用高斯模板和中值滤波技术,提出了图像平滑算法.这两种算法在去噪的同时,都能够很好地保持图像细节,并且简单易行、处理速度快、使用范围广.通过实验,该算法对灰度图像和彩色图像的处理效果较之传统的处理方法,质量上有较大的提高.     

基于粗糙集理论的属性约简新算法

以属性在可分辨矩阵中出现的频率作为启发,对HORAFA算法做了一些改进。引入二进制可辨识矩阵,利用二进制可辨识矩阵求出相对核。以相对核为基础,依次加入属性重要度大的属性,直到不能再加。     

用Java设计的基于三层结构的答疑系统

介绍了一个用Java进行设计的基于三层结构的答疑系统,用于辅助日常教学工作.系统由客户服务器模式和浏览器服务器模式构成,包括答疑、提问和自测等各个功能模块.对系统的数据库访问及在其间存在的安全性问题做了探讨,对系统的数据通信处理问题以及关于Java的双通道Socket通路的实现办法和机制进行了详细说明,同时对三层结构的答疑系统在服务器端和客户端的消息设计等一些关键技术做了具体介绍,对系统的用户界面如教师答疑界面、学生提问等一些重要界面进行了介绍,并给出了系统开发重要环节的设计过程和系统最后运行结果的一些重要界面.测试结果表明,系统运行稳定、结果准确、能够对日常的教学工作起到一定的帮助作用.     

变精度模糊粗糙集的一种定义

模糊粗糙集模型同经典粗糙集模型类似,容易受到噪音数据的影响.针对该问题,受变精度粗糙集模型的启发,提出了变精度模糊粗糙集的概念.针对现有变精度模糊粗糙集模型尚不能满足一些基本性质的缺陷,重新定义了模糊近似空间中某一模糊集的β-下近似和β-上近似,该定义方式能够满足上述的基本性质.     

部分三值逻辑中Sheffer函数的判定算法

根据部分多值逻辑的完备性理论和部分三值逻辑中准完备集的最小覆盖,给出部分三值逻辑中Sheffer函数的判定算法。     

系统的f_p-状态与它的随机识别

利用函数单向S-粗集,提出了fp-状态、状态距离、系统状态被fp-规律随机入侵的概念。利用这些概念,给出系统状态被fp-规律入侵呈现的状态特征以及对这些状态特征的识别、识别准则与应用。函数单向S-粗集是函数S-粗集的基本形式之一,函数单向S-粗集是研究系统规律入侵预测的一个重要的理论与方法。