动态粒度下的粗糙集双向近似

经典的粗糙集理论刻画目标概念运用静态的粒度分析,不便于刻画人们问题求解的动态认知过程。已有文献分别用正向近似和逆向近似对目标概念和目标决策进行刻画,并成功地应用于分层聚类算法和规则提取方面。基于动态粒度原理,提出双向近似的概念,获得双向近似的一些重要性质,并将其应用于决策表中决策规则的获取。     

一种改进的图像增强算法及其应用

为改进图像增强算法,使之更适合医学领域图片的处理,采用了粗糙集的上逼近和下逼近思想,将图像分为物体区和背景区,使用不同的函数进行增强,进而提出了一种改进的基于粗糙集的增强算法,并首次应用于医学图像处理领域.实验结果显示改进的基于粗糙集的增强效果优于直方图均衡化方法.     

A parallel approach to calculate lower and upper approximations in dominance based rough set theory

Feature selection plays an important role in data mining and machine learning tasks. Rough set theory has been a prominent tool for this purpose. It characterizes a dataset by using two important measures called lower and upper approximation. Dominance based rough set approach (DSRA) is an extension to conventional rough set theory. It is based on persistence of preference order while extracting knowledge from datasets. Dominance principal states that objects belonging to a certain decision class should follow the preference order. Preference order states that an object having higher values of conditional attributes should belong to higher decision classes. However, some of the basic concepts like checking preference order consistency of a dataset, dominance based lower approximation and upper approximation are computationally too expensive to be used for large datasets. In this paper, we have proposed a parallel incremental approach called Parallel Incremental Approximation Calculation or PIAC for short, for calculating these measures of lower and upper approximations. The proposed approach incrementally calculates lower and upper approximations using parallel threads. We compare our method with the conventional approach using ten widely used datasets. Whilst achieving the same accuracy levels as the conventional approach, our approach significantly reduces the average computation time, i.e., 71% for the lower approximation and 70% for the upper approximation. Over all datasets, the decrease in memory usage achieved was 99%.     

Frequency-weighted optimal Hankel-norm approximation of stable transfer functions

This paper shows how to introduce arbitrary frequency weighting into the optimal Hankel-norm approximation problem for scalar, finite-dimensional, linear, time-invariant systems. The procedure has applications to the closed-form design of reduced-order controllers.     

近似算法之测度视角

标准近似、微分近似和占优分析是三种不同的近似算法度量方法。标准近似比度量近似解偏离最优解的相对误差。微分近似关注近似解解值在最优解值和最差解值所形成的区间内所处的位置。占优分析考虑近似解在所有可行解中的排名。本文综述相关概念和主要成果,以及各测度方法的优缺点。尤其关注以PCP定理及唯一博弈猜想为代表的不可近似性成果。     

Kernel shapes of fuzzy sets in fuzzy systems for function approximation

The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.     

模糊系统逼近理论：现状与展望

近年来,各类模糊系统已被证明是万能函数逼 近器,它们能实现任意的非线性连续控制规律和动态模型．本文综述与分析了模糊系统逼近 理论研究的最新成果,并指出了进一步研究工作的方向．     

Rough集高效算法的研究

深入分析了现有Rough集算法低效性的根源，围绕不可区分关系和正区域两个核心概念，研究了不可区分关系的性质，给出并证明了正区域的一种等价计算方法，从而得出高效的Rough集基本算法；随后，分析了正区域的渐增式计算，并给出了一种完备的同性约简算法．理论分析和实验结果表明，该约简算法在效率上较现有的算法有显著提高．     

渐进迭代逼近方法在等距曲线逼近中的应用

渐进迭代逼近(PIA)方法在CAD领域有很好的自适应性和收敛稳定性,在曲线或曲面的逼近和拟合问题上具有很好的应用前景.文中将该方法应用于二维自由曲线的等距曲线(也称offset曲线)的逼近,提出基于PIA的等距曲线逼近算法.首先在等距曲线上采样数据点,采用Floater的方法对数据点进行参数化,并以这些采样点作为初始控制顶点,由这些初始控制顶点产生初始逼近曲线;然后考察相同参数值处采样点和逼近点的误差,并运用PIA方法逐步逼近等距曲线.该算法分别考虑了等距曲线的多项式逼近和有理逼近.数值实例结果表明,综合控制顶点数和算法误差这2项因素,文中算法具备较好的优势.     

属性约简中一种新的求核算法

属性约简是粗糙集理论中的一个重要内容,其核心任务是得到属性集的核。本文提出了一种基于二进制运算的属性核求解算法,该算法简单直观且易于实现。我们通过设计C语言程序验证了算法的有效性。     

闭环连续系统仿真若干问题的分析研究

分析研究了对闭环系统的纯滞后环节如何处理的问题,找到开环系统和闭环系统的理论输出值计算方法,并比较3种Pade近似和全极点近似的精度。将此算法应用到闭环系统中,进一步比较4种近似,以求得闭环系统中误差最小的近似方法。同时提出在计算过程中对纯滞后处理的改进方法,使得误差大大减小,精度提高了一个数量级。研究结果表明,在开环系统和闭环系统,全极点近似由于没有引入零点,使得误差最小;改进方法使误差精度提高了一个数量级。     

结合广义重心坐标与Voronoi 剖分的函数分片逼近

结合广义重心坐标理论,提出了一个新方法,以解决在平面区域上的函数逼近问题。 该方法通过构建基于广义重心坐标的最优分片函数来逼近目标函数。采用Voronoi 图来划分区域, 并提出一个度量逼近误差的能量函数。推导出该函数的导数后,采用一种高效的Voronoi 节点更 新方法来获得区域的最优剖分,并通过最优剖分构建最优分片函数。由于该方法对不连续函数具 有良好地逼近能力,因此将其应用在图像逼近问题中。分别在解析函数和彩色图像上对该方法进 行实验,均获得了很好的逼近效果。     

非线性系统的模糊辨识误差分析

该文讨论了模糊系统的数字逼近特性,同时分析了逼近误差和初始状态误差对模糊系统的影响.最后得出一个重要结论：在一定条件下,模糊系统的输出与实际系统相差不大.     

On Characteristics of Information System Homomorphisms

The notion of information system homomorphism as a powerful tool to study the relation between two information systems was introduced by J.W. Grzymala-Busse. In this work, we will present some characteristics of information system homomorphism, which reveal the interdependence of the three mappings, namely, object mapping, attribute mapping and value domain mapping. Besides, given a partition on universe, we can derive a new information system homomorphism defining a partition on universe identical with the partition given. In the mean time, some invariant characteristics of upper approximation and lower approximation under information system homomorphism are investigated. At last, we establish a surjection between rough sets of information systems under an information system homomorphism.     

Application of weighting functions to the ranking of fuzzy numbers

This paper proposes a new ranking method for fuzzy numbers, which uses a defuzzification of fuzzy numbers and a weighting function. Following Saeidifar and Pasha (2008), first, we define a weighted distance measure on fuzzy numbers, and then, by minimizing this distance, the weighted interval and point approximations of fuzzy numbers are obtained. These indices are applied to rank the fuzzy numbers. This method is new and interesting for ranking fuzzy numbers, and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment.     

A Note on the Universal Approximation Capability of Support Vector Machines

The approximation capability of support vector machines (SVMs) is investigated. We show the universal approximation capability of SVMs with various kernels, including Gaussian, several dot product, or polynomial kernels, based on the universal approximation capability of their standard feedforward neural network counterparts. Moreover, it is shown that an SVM with polynomial kernel of degree p − 1 which is trained on a training set of size p can approximate the p training points up to any accuracy. This revised version was published online in June 2006 with corrections to the Cover Date.     

Structural shape optimization using self-adjusted convex approximation

This study researches the applications of Self-Adjusted Convex Approximation (SACA) in structural shape optimization problems. The B-spline curve is adopted as the mathematical representation of the structural shapes. The SACA method is based on the CONvex LINearization (CONLIN) method and has better accuracy and convergent rate. Numerical examples are offered and the results show that the proposed method is effective in the structural shape design.     

两类B样条模糊系统及其应用

能够同时逼近函数及其导函数的模糊系统在应用中具有重要意义.本文利用B样条函数作为推理前件,得到了两类能够同时逼近函数及其导函数的B样条模糊系统.其中第一类B样条模糊系统是插值系统且对函数及其一阶导函数分别具有二阶和一阶逼近精度,第二类B样条模糊系统是拟插值系统且对函数及其一阶、二阶导函数均具有二阶逼近精度.最后,将这两类模糊系统应用到一级倒立摆的稳定控制中,仿真结果表明利用这两类模糊系统设计的控制器是可行的,且具有一定的鲁棒性.     

Accurate pseudopotential description of the GW bandstructure of ZnO

We present the GW band structure of ZnO in its wurtzite (WZ), zincblende (ZB) and rocksalt (RS) phases at the Γ point, calculated within the GW approximation. We have used a Zn²⁰⁺ pseudopotential which is essential for the adequate treatment of the exchange interaction in the self-energy. The accuracy of the pseudopotential used is also discussed. The effect of the p–d hybridization on the GW corrections to the band gap is correlated by comparing the ZB and RS phase.