完备剩余格上的蕴涵闭包算子

利用蕴涵运算,在完备剩余格上定义了蕴涵闭包算子,给出了它的若干等价刻画及其表示定理。     

基于最小定义完备集实现复杂工程图数据提取

使用简单通用的描述定义完成复杂工程图数据提取是工程图数据管理中的关键技术。基于自由度理论分析了复杂工程图的数据组织结构,提出了描述复杂工程图数据的最小定义完备集。以直线表格化与文字表格化相结合改进了工程图表格识别技术,提高了工程图数据识别的准确性和完整性。结合最小定义完备集和工程图表格改进识别技术提出了能够处理复杂工程图数据提取的通用解决方案。运用Teigha技术开发的复杂工程图数据提取组件与PDM/PLM等管理系统集成,较好的完成了复杂工程图数据提取工作。     

约束概念格的代数性质及其知识表示的完备性

约束概念格是一种依据用户对数据集的兴趣、认识等作为背景知识而构造的概念格结构。文中利用约束概念格结点之间的上下确界运算,构造约束概念格的代数系统,证明约束概念格的若干代数性质,以及知识表示的完备性,从而为约束概念格的应用奠定理论基础。     

完备剩余格上的蕴涵闭包系统

在完备剩余格上引入了蕴涵闭包系统的概念,讨论了蕴涵闭包系统与闭包系统之间的关系。给出了蕴涵闭包系统的一些性质及其表示定理。进一步研究了蕴涵闭包算子和蕴涵闭包系统的关系。     

不完备形式背景下近似概念格的公理化方法

提出了由两个完备形式背景构造不完备形式背景的方法.基于完备形式背景公理化的方法得到了近似概念格的公理组,并给出了近似概念格的构造方法,其发展了不完备形式背景下近似概念格的理论.     

基于概念格的不完备信息系统最简规则提取算法

概念格是以概念为元素的偏序集,通常可以对形式背景描述的完备信息系统进行分析和处理,然而在多数情况下信息系统是不完备的,粗糙集理论是一种刻画不完整、不确定性问题的有效方法.针对此问题,从粗糙集的角度出发,基于概念格理论定义一种描述不完备信息系统的增广形式背景,在此基础上,定义并讨论极概念和极概念格及其相关性质,进而提出增广形式背景的极概念生成算法.为了获得更加简洁的决策规则,同时提出一种新的无冗余属性的决策规则获取算法.通过实例计算和UCI数据集的对比实验,表明了所提出算法的可行性和有效性,特别地,当信息系统完备时极概念将退化为经典的概念.     

最小一致性覆盖在不完备规则集中的应用

将Martin Ester提出的最小一致性覆盖方法应用于不完备规则集的规则提取。首先对不完备数据分别进行两种方法的预处理,然后通过定义数据间的一致性来使规则提取的覆盖问题转化成划分问题。经过UCI上两个数据集的测试,证明了这种方法的有效性。     

概念格在不完备形式背景中的知识获取模型

为了使概念格模型具有更强的数据处理能力,消除不完备信息带来的影响,针对经典概念格的局限性,本文将粗糙集中的粒化思维融入到概念格中。首先探讨了概念格视角下的信息粒化方法,然后提出了基于等价类和基于极大相容类的知识获取方法,最后给出了实例分析。这些方法一方面有助于概念格与粗糙集的融合,另一方面也为探索不完备形式背景的分析处理机制提供了有益思路。     

基于粗糙集不完备信息系统的离散化算法

针对不完备信息系统提出了一种新的粗糙集离散化算法。通过分析候选断点与决策类之间的影响关系,定义了候选断点对决策类的区分能力,并以此作为断点重要性的度量,实现不完备信息系统中连续属性的离散化。仿真实验验证了该算法的有效性。     

基于完备格的重构滤波器在红外图像目标检测中的应用

对红外图像中的目标进行检测和跟踪是精确制导武器中非常困难的也是急需解决的难点之一,针对红外图像的特点,提出了一种新的用于红外图像序列弱小目标检测和跟踪的处理方法,并首先探讨了完备格下的图像连通性,其重构滤波器具有简化图像,并能保证轮廓完整的特性。该新方法包括帧内处理和帧间处理,其中帧内处理使用灰度级重构tophat滤波器实现背景去除和图像简化,再结合目标的灰度、形状、面积信息完成图像分割;帧间处理使用目标的空间、时间运动信息实现序列的目标检测和跟踪。仿真实验结果表明,这种方法在检测和跟踪红外图像中的弱小目标时,具有有效性和鲁棒性。     

The spectra of reducible matrices over complete commutative idempotent semifields and their spectral lattices

Previous work has shown a relation between L-valued extensions of Formal Concept Analysis and the spectra of some matrices related to L-valued contexts. To clarify this relation, we investigated elsewhere the nature of the spectra of irreducible matrices over idempotent semifields in the framework of dioids, naturally ordered semirings, that encompass several of those extensions. This initial work already showed many differences with respect to their counterparts over incomplete idempotent semifields, in what concerns the definition of the spectrum and the eigenvectors. Considering special sets of eigenvectors also brought out complete lattices in the picture and we argue that such structure may be more important than standard eigenspace structure for matrices over completed idempotent semifields. In this paper, we complete that investigation in the sense that we consider the spectra of reducible matrices over completed idempotent semifields and dioids, giving, as a result, a constructive solution to the all-eigenvectors problem in this setting. This solution shows that the relation of complete lattices to eigenspaces is even tighter than suspected.     

剩余格上的MTL-滤子及其刻画

滤子理论在多值逻辑及相关代数研究中起到了非常重要的作用。在交换剩余格上引入了MTL-滤子的概念,并给出了这类滤子的若干的刻画。从MTL-滤子的角度证明了MTL-代数的特征定理。     

剩余格上n-重MTL-滤子及其刻画

在有界交换整剩余格上引入了一类新的滤子--n-重MTL-滤子,并给出了它的一系列的刻画。     

On the role of complete lattices in mathematical morphology: From tool to uncertainty model

Mathematical morphology has a rich history. Originally introduced for binary images, it was quite soon extended to grayscale images, leading to grayscale morphology with the threshold approach and the umbra approach. Later on, different models based on fuzzy set theory were introduced. These models were based on the observation that, from a formal point of view, grayscale images and fuzzy sets are modeled in the same way. Consequently, techniques from fuzzy set theory could be applied in the context of mathematical morphology, and fuzzy mathematical morphology was born. In that framework, fuzzy set theory was only a tool to construct morphological models, and was not employed to model any fuzziness or uncertainty. Quite recently however, new extensions have led to the construction of fuzzy interval-valued and fuzzy intuitionistic mathematical morphologies. Here, extensions of fuzzy set theory actually take into account the uncertainty that comes along with image capture, specifically regarding the grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. In this framework, (extended) fuzzy set theory not only serves as a tool to deal with grayscale images, but also as a model for uncertainty. This paper sketches this evolution of fuzzy set theory in the field of mathematical morphology, and also points out some directions for future research.     

Modeling and control of discrete event systems using finite state machines with variables and their applications in power grids

Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. In an attempt to mitigate the state explosion problem, we propose an efficient representation that appends finite sets of variables to finite state machines in modeling discrete event systems. We also present the control synthesis techniques for such finite state machines with variables (FSMwV). We first present our notion and means of control under this representation. We next present our algorithms for both offline and online synthesis of safety control policies. We then apply these results to the control of electric power grids.