R_0代数的滤子理论

在R0代数中引入了正蕴涵滤子、奇异滤子、MV滤子的概念,讨论了这些滤子的性质及关系.得到了:在R0代数上,蕴涵滤子、正蕴涵滤子、布尔滤子是等价的;奇异滤子与MV滤子是等价的;正蕴涵滤子是奇异滤子,但反之不真.     

FI代数的滤子

研究FI代数的滤子理论，建立F滤子、P滤子、Q滤子、C滤子之间的联系．     

Quantale中的模糊滤子

在Quantale中引入模糊滤子的概念,研究了它的一系列性质,得到了若干等价刻画,讨论了Quantale中滤子和模糊滤子之间的相互确定关系,证明了Quantale态射既保模糊滤子又反射模糊滤子。给出了模糊滤子在Quantale态射下的像的具体结构。     

Some types of filters in MTL-algebras

The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters.     

R_0代数中素滤子的拓扑性质

首先讨论了R_0代数M中MP滤子、素滤子的基本性质,然后通过自然的方式在M的全体素滤子之集PF_(IL)(M)上构造拓扑,证明了PF_(IL)(M)是紧致的T_0空间.最后把PF_(IL)(M)上的拓扑限制在M的全体极大滤子之集MF_(IL)(M)上,得到MF_(IL)(M)是紧致的Hausdorff空间.     

二进小波的构造方法研究

提出两种二进小波的构造方法.首先,将Mallat构造的B-样条二进小波推广得到一种构造B-样条二进小波的新方法;其次,基于二进提升方案提出构造二进小波的另一种新方法—–构造定理,并通过调整定理中提升参数的形式、以新的B-样条二进小波作为初始二进小波,具体构造了具有有限长单位脉冲响应、高阶消失矩、线性相位的提升二进小波,这些提升二进小波不能由Sweldens提升方案得到.     

Fuzzy Weak Regular,Strong and Preassociative Filters in Residuated Lattices

In this paper, the notions of fuzzy weak regular, strong and preassociative filters are introduced with some properties of them investigated. In particular, under the context of Glivenko algebras, fuzzy weak regular filters and regular ones are equivalent and characterizations of Glivenko algebras are concluded by characterizations of fuzzy strong filters. At last the notion of fuzzy preassociative filters are defined, which are proved to coincide with fuzzy Boolean filters, and then some new alternative definitions of Boolean algebras are obtained by this type of filters.     

分配格的滤子格是空间式Frame的新证明

在分配格中引入了次极大滤子的概念,并以此给出了分配格的滤子格是空间式frame的一种新证明,然后研究了次极大滤子在Heyting代数中的一些具体性质。     

小波分析在信号去噪声中的应用

小波分析是近年来发展起来的一种数学方法,在信号与图象处理中有重要的应用.中值滤波是信号处理中常用的一种非线性滤波器,它能够有效地消除瞬时脉冲干扰,并且能够很好地保持信号的边缘信息,在信号和图象处理中得到广泛应用.对中值滤波器与小波变换的结合进行了比较系统的研究.通过实例说明中值滤波器与小波变换相结合具有比单一滤波器更好的效果.     

Parameterizations of univariate wavelet tight frames with short support

We give a sufficient condition for the filters to generate wavelet tight frames with compact support, and present the parameterizations of the filters with length from four to eight, which include spline filters and other symmetric filters. Examples of symmetric wavelet tight frames which have the maximum vanishing moments are shown.     

Using filters to describe congruences and band congruences of semigroups

It is well known that the smallest semilattice congruence can be described via filters. We generalise this result to the smallest left (right) normal band congruences and also to arbitrary semilattice (left normal band, right normal band) congruences, describing them all via filters. To achieve this, we introduce filters relative to arbitrary quasiorders on a semigroup (traditional filters are filters relative to the smallest negative operation-compatible quasiorder). We study congruences which can be described via filters. We show that the lattice of semilattice (left normal band, right normal band) congruences is a homomorphic image of the lattice of negative (right negative, left negative) operation-compatible quasiorders.     

效应代数的(η,γ]-模糊滤子

在Lu D L和Wang G J提出效应代数中模糊滤子(简称LW-模糊滤子)概念的富有成效的工作基础上,利用模糊点与模糊集的属于与重于关系给出了一种新的模糊滤子——(η,γ]-模糊滤子的定义,指出LW-模糊滤子、(∈,∈Vq)-模糊滤子和(∈,∈Vq)-模糊滤子是它的三个特例,获得了这些模糊滤子的等价刻画.     

R0-代数的（λ,μ）-fuzzy滤子理论

利用模糊点与模糊集之间的属于关系(∈)和拟重合关系(q)在R0-代数中引入了(λ,μ)-fuzzy滤子的概念,其中λ和μ是集合{∈,q,∈∨q,∈∧q}中的任意元素且λ≠∈∧q,并讨论它们的性质和相互关系;获得(∈,∈∨q)-fuzzy滤子的若干等价刻画;给出(∈,∈∨q)-fuzzy滤子成为(∈,∈)-fuzzy滤子以及一个模糊集成为(q,∈∨q)-fuzzy滤子的条件。     

Synthesis of Suboptimal Filters for Multivariable Multicriteria Discrete Systems

Differential Equations - We consider the problem of constructing suboptimal filters (lower-order optimal filters, i.e., filters for linear vector functionals of the system state vector) for...     

效应代数的直觉模糊滤子

引入效应代数的直觉模糊滤子和它的水平滤子的概念,讨论了直觉模糊滤子与水平滤子间的关系,给出了直觉模糊滤子的等价描述,研究了直觉模糊滤子的几个运算性质。在两个经典效应代数的效应态射与效应同构意义下,讨论了这种直觉模糊滤子的像和前像问题。     

Asymptotic Behavior of the Daubechies Filters

We discuss the asymptotic behavior of the phase of the Daubechies filters when the length of the filter goes to + ∞. We study especially the minimum-phased filters and the almost linear phased filters.     

Some Properties of Fuzzy Filter and Its Category

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Multi-step prediction of time series with random missing data

Multi-step prediction is still an open challenge in time series prediction. Moreover, practical observations are often incomplete because of sensor failure or outliers causing missing data. Therefore, it is very important to carry out research on multi-step prediction of time series with random missing data. Based on nonlinear filters and multilayer perceptron artificial neural networks (ANNs), one novel approach for multi-step prediction of time series with random missing data is proposed in the study. With the basis of original nonlinear filters which do not consider the missing data, first we obtain the generalized nonlinear filters by using a sequence of independent Bernoulli random variables to model random interruptions. Then the multi-step prediction model of time series with random missing data, which can be fit for the online training of generalized nonlinear filters, is established by using the ANN’s weights to present the state vector and the ANN’s outputs to present the observation equation. The performance between the original nonlinear filters based ANN model for multi-step prediction of time series with missing data and the generalized nonlinear filters based ANN model for multi-step prediction of time series with missing data is compared. Numerical results have demonstrated that the generalized nonlinear filters based ANN are proportionally superior to the original nonlinear filters based ANN for multi-step prediction of time series with missing data.     

适合于图像压缩的7/5小波基的构造

通过利用提升算法和检验双正交小波稳定性的充分必要条件Cohen-Daubechies准则,构造了一个适合于图像压缩的7/5双正交小波基.为了便于小波变换的硬件实现,选取四个提升系数中的三个为二进制分数,而另一提升因子为1/10的倍数.本文中所构造的7/5小波基虽然在压缩性能上低于CDF9/7小波,但由于提升系数为二进制分数和1/10的倍数,所以该小波基的小波变换更易于采用硬件来实现,并且其小波变换速度比CDF9/7小波要快.实验的结果表明该小波的压缩性能优于Daubechies5/3小波,同时与[6]所构造的两组7/5小波基相比较,该小波变换不仅能方便于硬件的实现,而且其压缩性能优于或相当于[6]中的两组7/5小波基.