GM偏序图的构建和基于GM偏序图的规则提取

对形式背景上的G偏序集、M偏序集和GM偏序集的偏序关系作了进一步讨论,提出了对象上邻、对象下邻、属性上邻、属性下邻、对象上界、对象下界、属性上界、属性下界和极大对象下界等概念,并根据上下邻之间的关系给出G偏序图、M偏序图和GM偏序图的构建算法,最后给出了不需要建格而可直接在GM偏序图上进行规则提取的算法,并通过实例验证了算法的有效性。     

Reduction method for concept lattices based on rough set theory and its application

Rough set theory and formal concept analysis are two complementary mathematical tools for data analysis. In this paper, we study the reduction of the concept lattices based on rough set theory and propose two kinds of reduction methods for the above concept lattices. First, we present the sufficient and necessary conditions for justifying whether an attribute and an object are dispensable or indispensable in the above concept lattices. Based on the above justifying conditions, we propose a kind of multi-step attribute reduction method and object reduction method for the concept lattices, respectively. Then, on the basis of the defined discernibility functions of the concept lattices, we propose a kind of single-step reduction method for the concept lattices. Additionally, the relations between the attribute reduction of the concept lattices in FCA and the attribute reduction of the information system in rough set theory are discussed in detail. At last, we apply the above multi-step attribute reduction method for the concept lattices based on rough set theory to the reduction of the redundant premises of the multiple rules used in the job shop scheduling problem. The numerical computational results show that the reduction method for the concept lattices is effective in the reduction of the multiple rules.     

Mining gene expression data with pattern structures in formal concept analysis

This paper addresses the important problem of efficiently mining numerical data with formal concept analysis (FCA). Classically, the only way to apply FCA is to binarize the data, thanks to a so-called scaling procedure. This may either involve loss of information, or produce large and dense binary data known as hard to process. In the context of gene expression data analysis, we propose and compare two FCA-based methods for mining numerical data and we show that they are equivalent. The first one relies on a particular scaling, encoding all possible intervals of attribute values, and uses standard FCA techniques. The second one relies on pattern structures without a priori transformation, and is shown to be more computationally efficient and to provide more readable results. Experiments with real-world gene expression data are discussed and give a practical basis for the comparison and evaluation of the methods.     

基于优势关系的概念格

对基于优势关系的形式背景进行了讨论,在基于优势关系的形式背景上建立了对象偏序集、属性偏序集以及对象-属性偏序集,提出了基于优势关系的概念格的定义及构建方法.这些结论进一步丰富了概念格的理论,对研究基于优势关系的信息系统的规则提取提供了新的思路.     

基于属性度的属性排序算法

形式概念分析是一种从形式背景进行数据分析和规则提取的强有力工具。属性拓扑作为一种新型的形式背景表示方法,直观地描述了属性之间的关联。利用属性拓扑可以更方便直观地计算形式概念和概念格。经过对现有属性拓扑的算法与流程的研究,分析了现有属性排序算法的特异性和层次局限性,通过结合度的概念,提出了一种属性衡量的新方式--属性度,并提出了基于属性度的属性排序算法。这种排序算法得到的结果更加灵活,消除了属性排序的层次局限性,对父属性的查找有明显的优势,为基于属性拓扑中的属性排序方法提供了指引方向。     

形式概念分析与集值信息系统

形式概念分析与粗糙集理论是两种有效的知识发现工具,已在各个领域获得成功应用。本文给出了一种将形式背景转化为集值信息系统的方法,证明了形式背景分析中的对象粒协调集与由该形式背景导出的集值信息系统的协调集是等价的,并且分析了形式背景中三种不同类型的对象粒属性特征。最后给出了形式背景中属性粒的概念及相关结论。     

变精度对偶概念格的构造及其性质

形式概念分析作为进行数据分析的有效工具,吸引了世界各地研究者的关注。由于二值形式背景的局限性,人们将模糊集引入形式概念分析。但是模糊形式背景生成的模糊概念数量庞大。讨论了基于模糊形式背景的模糊对偶概念格的概念约简,构造出了模糊对偶概念格的三种变精度概念格,讨论了它们的关系。结果表明每一种变精度概念格都保留了模糊对偶概念格中相对重要的概念。变精度对偶概念格的概念数量远远少于模糊对偶概念格的概念数。     

基于信息熵的对象加权概念格

在大数据时代,由于数据规模越来越大,导致构造概念格的难度越来越高。在能够客观反映数据隐藏信息的前提下需删除冗余对象及属性,降低数据规模,构造更为简单的概念格,从而便于用户更高效地获取知识。为避免主观因素,本文由形式背景中属性的信息熵来获取单属性权重,采用均值方法计算对象权重,并用标准差计算对象重要性偏差值。通过设定的属性权重、对象权重和对象重要度偏差阈值,构造对象加权概念格。通过实例验证了,该方法可有效删除冗余概念,简化概念格构造过程。     

概念格研究进展

概念格理论是一种有效的知识表示与知识发现的工具,已被成功应用于许多领域.介绍了国内外现有的建格算法及概念格上分类规则和关联规则提取方法,比较了各种建格算法的优缺点,讨论了概念格属性约简理论的研究方法和研究进展.另外,还介绍了概念格在数据挖掘、信息检索、软件工程等领域的应用,给出了与粗糙集的关系及其它的一些研究成果.最后,给出了概念格有待完善的研究领域.     

基于互关联后继树的概念格构造算法

概念格是知识工程中一个重要的知识表达工具，同时也是形式概念分析的核心．目前已出现了许多有效的概念格构造算法．提出了一个基于互关联后继树的概念格构造算法，以扩展的互关联后继树为数据模型，通过对树的搜索和相关判定定理完成所有形式概念的生成．分析了算法的性能，并做出相关结论．     

Fuzzy and rough formal concept analysis: a survey

Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the more than 120 papers published between 2003 and 2011 on FCA with fuzzy attributes and rough FCA. We applied traditional FCA as a text-mining instrument to 1072 papers mentioning FCA in the abstract. These papers were formatted in pdf files and using a thesaurus with terms referring to research topics, we transformed them into concept lattices. These lattices were used to analyze and explore the most prominent research topics within the FCA with fuzzy attributes and rough FCA research communities. FCA turned out to be an ideal metatechnique for representing large volumes of unstructured texts.     

An application of formal concept analysis to semantic neural decoding

This paper proposes a novel application of Formal Concept Analysis (FCA) to neural decoding: the semantic relationships between the neural representations of large sets of stimuli are explored using concept lattices. In particular, the effects of neural code sparsity are modelled using the lattices. An exact Bayesian approach is employed to construct the formal context needed by FCA. This method is explained using an example of neurophysiological data from the high-level visual cortical area STSa. Prominent features of the resulting concept lattices are discussed, including indications for hierarchical face representation and a product-of-experts code in real neurons. The robustness of these features is illustrated by studying the effects of scaling the attributes.     

形式概念分析中的对象概念与属性概念

为了进一步提高数据表示和数据挖掘的效率,对两类特殊概念即对象概念和属性概念进行了研究。分析了对象概念和属性概念与不可约元的关系,提出了对象概念和属性概念的识别算法;提出了以属性概念为递归终止条件的计算内涵缩减递归算法;研究了属性排序以及属性序列在规则提取中的应用。     

从文本知识源中挖掘概念格的形式分析

文本知识挖掘是数据挖掘中一个很重要的研究领域。论文主要讨论如何在不使用概念换算方法下从文本知识中抽取概念格以及分析概念格之间的结构关联。该方法有两部分构成：一是将文本中所描述的对象转化为多值上下文;二是分析多值上下文之间的各种操作以及相应概念格之间的关联。重点分析了多值上下文的增加、删除和乘积等操作以及相应概念格之间的序嵌入映射,得到了一些重要命题。知识工程师可以利用这些命题进行文本知识分析以及从概念格上进一步抽取关联规则。     

基于不同蕴涵算子的模糊概念格建格算法研究

概念格是进行数据分析的有力工具,模糊集是数据处理的有效方法之一,模糊概念格有重要的理论与应用价值,但它的结构与性质依赖于蕴涵算子的选择,基于此,介绍了基于下半连续三角模生成的剩余蕴涵以及模糊概念格的算子和定义,提出了基于不同蕴涵算子的模糊概念格的实现算法,分析了算法的复杂度等性能,最后通过实例说明了基于Godel 蕴涵和Lukasiewicz 蕴涵的模糊概念格的建格方法。     

纵向合成背景的面向对象概念格属性约简

随着计算机网络的发展,多个形式背景分布存储在不同的网络节点,研究合成背景的属性约简就显得十分重要。提出了一种多背景纵向合成的面向对象概念格的属性约简方法,给出了面向对象概念格的属性近似算子真子集的定义,并给出了各子形式背景和合成形式背景的属性特征间的关系,在此基础上,给出了合成形式背景的属性近似算子真子集、子形式背景的属性近似算子真子集和属性等价类间的关系,并利用它们间的关系给出了合成背景的各种属性判别的充要条件,进而给出了合成背景属性约简的构造算法。     

Assessing semantic annotation activities with formal concept analysis

This paper describes an approach to assessing semantic annotation activities based on formal concept analysis (FCA). In this approach, annotators use taxonomical ontologies created by domain experts to annotate digital resources. Then, using FCA, domain experts are provided with concept lattices that graphically display how their ontologies were used during the semantic annotation process. In consequence, they can advise annotators on how to better use the ontologies, as well as how to refine these ontologies to better suit the needs of the semantic annotators. To illustrate the approach, we describe its implementation in @note, a Rich Internet Application (RIA) for the collaborative annotation of digitized literary texts, we exemplify its use with a case study, and we provide some evaluation results using the method.     

基于并不可约元的面向对象概念格的属性约简

概念格的属性约简是知识处理的重要研究问题之一。提出了一种面向对象概念格的属性约简方法。首先介绍了求面向对象概念格中并不可约元的方法,进而给出了面向对象概念格的并不可约元的外延集与面向对象概念格的协调集和约简集之间的关系,在此基础上,给出面向对象概念格的属性特征、并不可约元的外延集、属性等价类三者间的关系,最后利用这三者间的关系给出了面向对象概念格的约简集的构造。     

Meet continuity properties of posets

In this paper we consider a number of properties of posets that are not directed complete: in particular, meet continuous posets, locally meet continuous posets and PI-meet continuous posets are introduced. Characterizations of (locally) meet continuous posets are presented. The main results are: (1) A poset is meet continuous iff its lattice of Scott closed subsets is a complete Heyting algebra; (2) A poset is a meet continuous poset with a lower hereditary Scott topology iff its upper topology is contained in its local Scott topology and the lattice of all local Scott closed sets is a complete Heyting algebra; and (3) A poset with a lower hereditary Scott topology is meet continuous iff it is locally meet continuous, iff it is PI-meet continuous.     

基于粗概念格模型的电子商务领域本体的构建研究

以构建电子商务系统中的本体为出发点,分析现有的本体构建技术中存在的缺陷。针对这些不足,综合考虑变精度粗糙集模型和形式概念分析的相关理论,提出基于粗概念格模型来构建本体。将变精度粗糙集的β选取算法和可辨识矩阵属性约简算法进行了改进,使β 上、下分布的约简方法适用于形式背景的约简,从而提出基于变精度粗糙集的概念格约减算法;然后计算语义概念相似度,并以联合国标准产品与服务分类代码的本体元模型为核心本体,结合领域专家知识,建立电子商务领域本体模型。实验表明了粗概念格构建本体的高效性。