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。     

Grouping fuzzy sets by similarity

The paper presents results on factorization of systems of fuzzy sets. The factorization consists in grouping those fuzzy sets which are pairwise similar at least to a prescribed degree a. An obstacle to such factorization, well known in fuzzy set theory, is the fact that “being similar at least to degree a” is not an equivalence relation because, in general, it is not transitive. As a result, ordinary factorization using equivalence classes cannot be used. This obstacle can be overcome by considering maximal blocks of fuzzy sets which are pairwise similar at least to degree a. We show that one can introduce a natural complete lattice structure on the set of all such maximal blocks and study this lattice. This lattice plays the role of a factor structure for the original system of fuzzy sets. Particular examples of our approach include factorization of fuzzy concept lattices and factorization of residuated lattices.     

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。     

多粒度数据的区间形式概念分析方法

经典概念格和面向属性（对象）概念格都是形式概念分析中重要的数据结构，将区间集引入到这些概念格中，可以得到区间集概念格和面向属性（对象）区间集概念格。证明了面向属性区间集概念格与面向对象区间集概念格是反序同构的，将多粒度的思想引入到形式概念分析中，研究粒化前后区间集概念之间的关系；在多粒形式背景下，进一步研究了面向对象（属性）区间集概念之间的内在联系。     

一种区间数分解与定标算法及其扩展形式背景的概念格生成方法

现有的概念格模型无法处理既包含以布尔值表示的信息,又包含以标量、模糊数及区间数表示的信息。因此,针对包含所有这些信息类型的扩展的形式背景提出它的处理方法,在此基础上,生成经扩展的概念格,是一项有意义的工作。提出了一种新的区间数分解与定标算法,以处理含有多种类型的扩展形式背景,并给出了相应的扩展格生成算法。最后,实验表明,该方法具有良好的效果。     

序列模糊概念格模型及其渐进式构造

传统的序列模式挖掘主要是挖掘满足最小支持度的频繁序列,没有考虑序列在实际中的重要度。为了能够有效地挖掘重要的序列模式,提出了一种序列模糊概念格模型,对所有序列的项目引入了重要度权值,定义了序列的重要度及可以动态调整最小支持度minsup的自适应系数;扩展了模糊形式背景,使其能够方便地表示序列,定义了概念的Galois闭包连接、序列模糊概念及序列模糊格结构,并给出了序列模糊概念格的渐进式构造算法 ScqFuzCL。实验表明,序列模糊概念格模型可以方便有效地组织自适应序列模式,在时间与空间上都具有良好的性能,并为进一步挖掘自适应序列模式提供了理论支持。     

A note on variable threshold concept lattices: Threshold-based operators are reducible to classical concept-forming operators

The present paper deals with formal concept analysis of data with fuzzy attributes. We clarify several points of a new approach of [S.Q. Fan, W.X. Zhang, Variable threshold concept lattice, Inf. Sci., accepted for publication] which is based on using thresholds in concept-forming operators. We show that the extent- and intent-forming operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication] can be defined in terms of basic fuzzy set operations and the original operators as introduced and studied e.g. in [R. Belohlavek, Fuzzy Galois connections, Math. Logic Quarterly 45 (4) (1999) 497-504; R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277-298; S. Pollandt, Fuzzy Begriffe, Springer-Verlag, Berlin/Heidelberg, 1997]. As a consequence, main properties of the new operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], including the properties studied in [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], can be obtained as consequences of the original operators from [R. Belohlavek, 1999; R. Belohlavek, 2004; S. Pollandt, 1997].     

概念格属性约简的判定

引入Galois联络,利用Galois联络深入研究了概念格的基本性质。指出概念格同构是格同构。为了寻求更为简洁、合理的约简算法,在更一般的形式背景（即对象集和属性集有限或无限）中,给出协调集的四类判定定理,将已有结果做了推广而且丰富了协调集的判定。举例说明在一般的形式背景中,约简不一定存在。     

基于经典-模糊变精度概念格的决策规则获取及其推理算法

在模糊形式背景上引入了4种经典一模糊变精度概念,形成4种变精度概念格,在此基础上得到4种决策规则集.利用包含度构建不同决策规则集中的推理算法,进而得到所有对象组合的决策规则.证明了由决策规则得到的决策集分别是必然性与可能性决策集,且推理算法具有协调性和相容性.     

概念格与粗糙集的关系研究

概念格理论和粗糙集理论是两种不同的知识表示与知识发现的工具,都已被成功应用于许多领域.粗糙集理论的数据表现方式是信息系统,其研究基础是对象之间的等价关系;概念格理论的数据表现方式是形式背景,其研究基础是一种有序的层次结构--概念格.本文讨论了概念格理论与粗糙集理论之间的基本联系;重点分析了形式概念与等价类之间、概念格与分划之间的关系;证明了概念格与分划之间可以相互转换,给出了转换算法,并用例子加以说明.     

Multi-adjoint t-concept lattices

The t-concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non-commutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a non-commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways, and this generates a pair of concept lattices. In this paper, we show that the information common to both concept lattices can be seen as a sublattice of the Cartesian product of both concept lattices. The multi-adjoint framework can be applied to this general t-concept lattice, and its usefulness is illustrated by a working example.     

Isotone fuzzy Galois connections with hedges

We study isotone fuzzy Galois connections and concept lattices parameterized by particular unary operators. The operators represent linguistic hedges such as “very”, “rather”, “more or less”, etc. Isotone fuzzy Galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes. We show that hedges enable us to control the number of formal concepts in the associated concept lattice. We also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices.     

容差近似空间的广义概念格模型研究

在粗糙集合理论中,近似空间概念格之间存在着有趣的对应关系,利用概念格研究知识的约简和发现。更直观和更有效,但已有的概念格模型是基于近似空间的等价类划分的。等价类划分过于苛刻,扩展的基于容差关系的近似空间具有更广泛的意义,但目前未见有相应的格模型被提出。该文提出了容差近似空间的一种格模型,称为广义概念格,给出了定义,描述了建立方法和由它产生规则的原则,讨论了空间复杂性问题,并且与其它相近方法做了比较     

An outlier mining algorithm based on constrained concept lattice

Traditional outlier mining methods identify outliers from a global point of view. These methods are inefficient to find locally biased data points (outliers) in low dimensional subspaces. Constrained concept lattices can be used as an effective formal tool for data analysis because constrained concept lattices have the characteristics of high constructing efficiency, practicability and pertinency. In this paper, we propose an outlier mining algorithm that treats the intent of any constrained concept lattice node as a subspace. We introduce sparsity and density coefficients to measure outliers in low dimensional subspaces. The intent of any constrained concept lattice node is regarded as a subspace, and sparsity subspaces are searched by traversing the constrained concept lattice according to a sparsity coefficient threshold. If the intent of any father node of the sparsity subspace is a density subspace according to a density coefficient threshold, then objects contained in the extent of the sparsity subspace node are considered as bias data points or outliers. Our experimental results show that the proposed algorithm performs very well for high red-shift spectral data sets.     

对偶区间集概念格上区间集协调集的判定方法

对偶区间集概念格是将区间集引入到对偶概念格产生的,它将对偶概念的外延与内涵从经典集合推广到区间集,使之成为一种描述不确定性概念的数学方法。而属性约简是数据挖掘的核心内容之一,是一种研究概念格本质特征的方法,它通过删除冗余属性使数据表中概念的获取与表示变得更简洁。文中主要研究对偶区间集概念格上区间集协调集的判定方法。首先基于对偶区间集概念格的同构,引入了区间集协调集,给出了对偶区间集概念格上区间集协调集的一系列判定定理,进而讨论了利用区间集协调集获取区间集属性约简的方法。     

基于iceberg概念格并置集成的闭频繁项集挖掘算法

由于概念格的完备性,在基于概念格的数据挖掘过程中,构造概念格的时间复杂度和空间复杂度一直是影响其应用的主要因素.结合iceberg概念格的半格特性和概念格的集成思想,首先在理论上分析并置集成后的iceberg概念格与由完备概念格裁剪得到的iceberg格同构;然后分析了iceberg概念格集成过程中的映射关系;最终提出一个新颖的基于iceberg概念格并置的闭频繁项集挖掘算法(Icegalamera).此算法避免了完备概念格的计算,并且在构造过程中采用集成和剪枝策略,从而显著提高了挖掘效率.实验证明其产生的闭频繁项集的完备性.使用稠密和稀疏数据集在单站点模式下进行了性能测试,结果表明稀疏数据集上性能优势明显.     

构造概念格的权值优化改进算法

针对基于信息熵与偏差的加权概念格在合并加权概念子格时,所得多属性内涵集权值较其整体在形式背景中的实际权重偏大,权重取值阈值的设置受主观因素干扰导致合并后的概念格规模过大的问题,提出了一种构造概念格的权值优化改进算法.以多属性内涵集在形式背景中的整体信息熵来设置其权值;采用方差计算各概念结点属性内涵集权值的阈值区间,克服了主观意识对阈值设置的影响;通过剪除不满足阈值区间的冗余概念结点,缩小了构造概念格的整体规模,减少了构造概念格的时间消耗.实验结果表明:对比基于信息熵与偏差的加权概念格减少了9.87％的冗余结点,构造整体概念格的时间消耗减少了7.36％,有效提高了加权概念格的构造效率.     

模糊本体构建的概念距离聚类方法

针对手工构建模糊本体工作量大且构建效率低的问题,结合模糊集理论和模糊概念格的结构惟一性等特点,提出一种基于模糊概念格的概念距离聚类方法来构建模糊本体.用渐进式方法构建出模糊概念格,并计算模糊概念格中节点的模糊参数,对其进行概念距离聚类处理,得到模糊概念层次,最后映射为模糊本体.其构建实例验证了该构建方法的可用性和有效性.     

概念格的公理化

概念格是数据分析和知识表示的一种有效工具。研究概念格的公理化问题。得到了两组关于概念格的公理组,且每组含有六个独立的公理。公理化的研究有助于概念格理论的进一步完善。