BR0代数的关联MP滤子和布尔MP滤子

引入BR0代数的关联胛滤子。研究它的特征,证明如下主要结果：F是关联脚滤子,当且仅当F是布尔仰滤子。从而BR0代数成为Boole代数的充要条件是每个胛滤子均为布尔胛滤子或关联肿滤子。     

BR0代数的关联MP滤子和布尔MP滤子

引入BR₀代数的关联MP滤子。研究它的特征,证明如下主要结果：F是关联MP滤子,当且仅当F是布尔MP滤子。从而BR₀代数成为Boole代数的充要条件是每个MP滤子均为布尔MP滤子或关联MP滤子。     

Z-蕴涵代数的Fuzzy Z-滤子

研究了Z-蕴含代数的Z滤子、fuzzy Z-滤子、fuzzy关联、Z滤子等,并得到一些有趣的结果。     

剩余格上的几类n-重滤子及其特征

在剩余格上引入了n-重蕴含滤子、n-重MV滤子和n-重布尔滤子,给出它们的一系列刻画定理。通过新的刻画定理得到了这些滤子之间的关系;并且证明了滤子是n-重布尔滤子当且仅当它是n-重蕴含MV滤子。     

BL-代数的n-重模糊蕴涵滤子

引入BL-代数的n-重模糊蕴涵滤子概念,讨论了n-重模糊蕴涵滤子的性质,给出若干等价刻画,给出了验证n-重模糊蕴涵滤子的一个简单条件。用n-重模糊蕴涵滤子对n-重蕴涵BL-代数进行了刻画,证明了一个模糊滤子是一个n-重模糊蕴涵滤子当且仅当对应的商代数是一个n-重蕴涵BL-代数。     

BL-代数上的几种直觉模糊滤子

结合直觉模糊集和滤子理论,对BL-代数上的直觉模糊滤子进行了研究。首先回顾了BL-代数和直觉模糊集的有关基础知识。然后引入BL-代数上的直觉模糊滤子、直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子的概念,讨论了它们的一系列重要性质,证明了直觉模糊滤子与直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子是等价的,并用实例进行了验证。最后探讨了直觉模糊滤子和模糊滤子的关系。     

Intuitionistic Fuzzy Filters of the BL-Algebras

结合直觉模糊集和滤子理论,对BL-代数上的直觉模糊滤子进行了研究.首先回顾了BL-代数和直觉模糊集的有关基础知识.然后引入BL-代数上的直觉模糊滤子、直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子的概念,讨论了它们的一系列重要性质,证明了直觉模糊滤子与直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子是等价的,并用实例进行了验证.最后探讨了直觉模糊滤子和模糊滤子的关系.     

泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。     

FI代数上的一致拓扑空间

拓扑结构是逻辑代数中一个重要的研究内容。为描述Fuzzy蕴涵代数的拓扑结构,利用滤子诱导的同余关系在FI代数上构造一致结构和一致拓扑,证明了导出的一致拓扑空间是不连通的、零维的、局部紧的、完全正则的第一可数空间,是[T0]空间当且仅当诱导它的滤子为{1},且FI代数中的蕴涵运算关于导出的一致拓扑是连续的。此外,讨论了商空间的性质。这对从拓扑层面去揭示FI代数的内部结构具有促进作用。     

伪BL-代数的犹豫模糊滤子

提出了伪BL-代数的犹豫模糊滤子的概念，给出它的几个等价刻画，并研究了它的一些性质。进一步，引入了伪BL-代数的几种犹豫模糊滤子，如犹豫模糊Boolean滤子、犹豫模糊正规滤子、犹豫模糊超滤子和犹豫模糊固执滤子，讨论了它们的一些刻画，给出了其间的一些关系。通过研究伪BL-代数中犹豫模糊Boolean滤子与犹豫模糊正规滤子的关系，解决了伪BL-代数中是否每个Boolean滤子都是正规滤子这样一个开问题。     

一种新型双正交小波滤波器的设计

本文提出了一种从对称正则滤波器中得到一系列对称双正交小波的新技术,其主要思路是找出所给出滤波器的一个对称互补正则滤波器,这样得到的滤波器与理想半谱带滤波器之间存在最小二次方振幅偏差。因此,从给出的正则对称滤波器,或者从已知的对称双正交小波,都可以很容易得到一系列带有更好频率选择特性的对称双正交小波滤波器组。一旦找到互补滤波器,此互补滤波器的另外一个互补滤波器也就可以以同样的方法得到。系列双正交小波滤波器源自于标准An-otonini9/7双正交小波。应用此小波滤波器来压缩著名的Lena、Barbara和Goldhill等图像,改善了峰值信噪比(PSNR)。     

On regular realizability problems for context-free languages

We consider regular realizability problems, which consist in verifying whether the intersection of a regular language which is the problem input and a fixed language (filter) which is a parameter of the problem is nonempty. We study the algorithmic complexity of regular realizability problems for context-free filters. This characteristic is consistent with the rational dominance relation of CF languages. However, as we prove, it is more rough. We also give examples of both P-complete and NL-complete regular realizability problems for CF filters. Furthermore, we give an example of a subclass of CF languages for filters of which the regular realizability problems can have an intermediate complexity. These are languages with polynomially bounded rational indices.     

On filter theory of residuated lattices

The aim of this paper is to develop the filter theory of general residuated lattices. First, we extend some particular types of filters and fuzzy filters in BL-algebras and MTL-algebras naturally to general residuated lattices, and further enumerate some relative results obtained in BL-algebras or MTL-algebras, which still hold in general residuated lattices. Next, we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices, which are two new types of filters and fuzzy filters, and derive some of their characterizations. Finally, we discuss the relations between (fuzzy) regular filters and several other special (fuzzy) filters, and also characterize some special classes of residuated lattices by filters or fuzzy filters.     

A Lattice-Based Minimal Gray-Scale Switching Algorithm for Obtaining the Optimal Increasing Filter from the Optimal Filter

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.     

Boolean filters and positive implicative filters of residuated lattices

The aim of this paper is to introduce the notions of Boolean filters and positive implicative filters in residuated lattices and to investigate their properties. Several characterizations of Boolean filters and positive implicative filters are derived. The extension theorems of implicative filters and positive implicative filters are obtained. The relations among Boolean filters, implicative filters and positive implicative filters are investigated and it is proved that Boolean filters are equivalent to implicative filters, and that every Boolean filter is a positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a positive implicative filter is a Boolean filter are established.     

基于匹配Gabor滤波器的规则纹理缺陷检测方法

许多工业产品表面纹理都可以被认为是由基本纹理单元在空间按照一定的规则进行排列组合的结果,但由于各种原因,这些有规则纹理图象经常出现的一些缺陷,因而检测这些有规则纹理图象的缺陷是机器视觉检测的重要内容,为了对这种缺陷进行有效地检测,在对这类纹理图象进行功率谱分析的基础上,根据人眼的视觉原理,设计了两类匹配Gabor滤波器,即正常纹理匹配Gabor滤波器和缺陷纹理匹配Gabor滤波器,前者能够突出正常纹理,抑制缺陷纹理,而后者恰恰相反,在将这两类滤波器用于规则纹理图象缺陷的自动检测时,均获得了良好的检测精度和速度。     

Analyzing a biorthogonal information channel by the Walsh-Hadamard transform

This paper reports the development of optimal processors to be used on a biorthogonal information channel for both Gaussian noise and impulsive noise. The biorthogonal system makes use of the Walsh-Hadamard transform (WHT). An efficient method to filter noise from a system which has unused capacity is developed. For Gaussian noise, three filters (linear, hard-limiting and sign detection) were used before processing. Hard-limiting is best for a large signal-to-noise ratio because it gives the lowest probability of error. When impulsive noise is added to the Gaussian noise, two optimal filters are designed, one from the standpoint of a whitening filter and the other from hypothesis testing to see if the noise is Gaussian or impulsive.