粒度空间约简及其粗糙集模型研究

针对交可约粒度空间中覆盖、基和粒结构的关系,结合偏序关系的哈斯图,给出一种约简粒度空间的方法.另外,通过限定上、下近似算子的取值范围,重新定义了交可约粒度空间上的粗糙集模型,并讨论了其相关性质.     

基于层次内P-集合的粒计算模型

在层次内P-集合基础上,给出层次内P-集合的粒度,层次内P-集合的粒度计算,从粒的角度研究层次内P-集合之间的关系.把普通P-集合扩展为层次P-集合,并研究层次P-集合的粒计算特征.     

广义直觉模糊信息粒度

直觉模糊信息粒度是度量直觉模糊粒结构不确定性的一种重要方法。本文针对直觉模糊信息粒度在度量直觉模糊粒结构上存在的不足进行分析。首先,介绍直觉模糊粒结构距离。其次,改进了基于偏序关系提出的直觉模糊信息粒度的公理化定义,从直觉模糊粒结构距离观点出发,以最细的直觉模糊粒结构为参照物,计算每个直觉模糊粒结构与最细的直觉模糊粒结构之间的距离,距离的值越大,这个直觉模糊粒结构的信息粒度越大。最后,通过例子验证结论的合理性。     

基于矩阵的可变粒度变精度邻域粗糙集近似集更新方法

邻域粗糙集可以同时处理名义与数值属性,多粒度粗糙集提供多个粒度视角下的目标概念近似,变精度粗糙集使得近似集计算不再局限于完全包含。本文首先提出了一种同时具有以上三种粗糙集模型长处并且粒度可变的变精度多粒度邻域粗糙集模型,并设计基于矩阵的近似集计算与更新方法：首先提出静态计算近似集的矩阵算法,继而考虑在邻域粒变小时,基于静态计算算法对近似集进行更新,提出一种邻域粒变小时近似集更新的矩阵算法,最后通过UCI公开数据集实验验证了计算与更新算法的有效性。     

程度多粒度粗糙集

多粒度粗糙集模型建立在一族而非仅仅一个不可分辨关系的基础上的。在融入一定程度误差的分类思想下,本文在多粒度粗糙集模型基础上将构建程度多粒度粗糙集,其中包括程度多粒度乐观近似算子和程度多粒度悲观近似算子两种形式。讨论了程度多粒度粗糙集的相关性质,并对程度多粒度粗糙集和经典的多粒度粗糙集进行了对比分析,得出了若干具有理论和应用价值的结果,从而为知识获取提供了一个新的不确定性方法。     

多粒度语言判断矩阵的一致性研究

多粒度的语言术语是刻画决策问题不确定性差异程度的有效方式.文中定义了语言信息函数和多粒度语言判断矩阵对应的导出矩阵,在此基础上提出了多粒度语言判断矩阵完全一致性和满意一致性的概念,得到了多粒度语言判断矩阵具有完全一致性和满意一致性的充要条件.本文研究为群决策中基于不同粒度的语言判断矩阵有效集结提供了理论依据.     

基于粒度的多方法评价结论一致性研究

引入多方法评价结论粒度一致的概念,定义了多方法评价结论粒度一致的粒度计算公式,运用粒度计算公式对一个评价问题的结果进行了粒度一致性分析.     

基于动态粒度的多方法评价结论一致性研究

构建了多方法评价结论的动态粒度模型,给出了构建多方法评价结论动态粒度模型的算法.这里的动态粒度主要考察方案数量增减的粒度变化.当数量减少的方案构成子评价问题并重新进行评价时,方案间属性值的差距被拉大,更易于各种评价方法分辨方案间的优劣,给出更加精确的评价结论.根据构建的多方法评价结论动态粒度模型,对广东省主导产业选择的评价问题进行了演算,给出了有意义的结果,证实了模型的可行性.     

基于区间二型FCM和合理粒度原则的信息粒生成方法及应用

粒计算是知识表示与数据处理的一种新的理念和计算范式,现已成为复杂问题求解的有效框架之一。信息粒是粒计算的基本单位,构建信息粒以及利用信息粒实现问题求解是粒计算的两项基本任务。受认知主体的主观局限性和度量方法等因素的影响,信息粒的形成、表示与解释往往伴随着不确定性。本文基于区间二型模糊C均值(IT2FCM)聚类算法和合理粒度原则设计了二型信息粒的生成方法,不仅实现了信息粒的构建,而且能够体现出粒化过程中的不确定性。为验证所设计方法的合理性,本文在人工数据集上对粒化方法进行评估,并探讨不同参数值对粒化结果的影响。此外,利用所设计的粒化方法对船舶数据的结构信息及其不确定性进行刻画,以此来辅助船舶的分类管理。     

模糊粒度空间的性质研究

在文献[16]基础上,进一步将模糊粒度空间推广到更一般地模糊等价关系上,研究了模糊粒度空间的性质,主要获得了3个结论.首先,引入了有序的等价关系集的概念,给出了下列的四个命题是等价的:(1) 给定一个模糊等价关系;(2) 给定一个等腰归一化伪距离;(3) 给定一个有序的粒度空间;(4) 给定一个有序的等价关系集.第二,通过模糊等价关系诱导的等腰归一化伪距离的投影距离和扩展距离,建立了模糊粒度空间上的距离,即是等腰归一化距离,并且给出了模糊粒度空间上距离度量的动态性质研究.最后,给出了模糊粒度空间与模糊等价关系之间的序关系,即它们的序是一致的.这些研究工作进一步完善了模糊粒度空间的理论,为模糊粒度计算提供了更为直观的数学理论和工具.     

Set-based granular computing: A lattice model

Set-based granular computing plays an important role in human reasoning and problem solving. Its three key issues constitute information granulation, information granularity and granular operation. To address these issues, several methods have been developed in the literature, but no unified framework has been formulated for them, which could be inefficient to some extent. To facilitate further research on the topic, through consistently representing granular structures induced by information granulation, we introduce a concept of knowledge distance to differentiate any two granular structures. Based on the knowledge distance, we propose a unified framework for set-based granular computing, which is named a lattice model. Its application leads to desired answers to two key questions: (1) what is the essence of information granularity, and (2) how to perform granular operation. Through using the knowledge distance, a new axiomatic definition to information granularity, called generalized information granularity is developed and its corresponding lattice model is established, which reveal the essence of information granularity in set-based granular computing. Moreover, four operators are defined on granular structures, under which the algebraic structure of granular structures forms a complementary lattice. These operators can effectively accomplish composition, decomposition and transformation of granular structures. These results show that the knowledge distance and the lattice model are powerful mechanisms for studying set-based granular computing.     

Granular computing applied to ontologies

Granular Computing is an emerging conceptual and computing paradigm of information-processing. A central notion is an information-processing pyramid with different levels of clarifications. Each level is usually represented by ‘chunks’ of data or granules, also known as information granules. Rough Set Theory is one of the most widely used methodologies for handling or defining granules.Ontologies are used to represent the knowledge of a domain for specific applications. A challenge is to define semantic knowledge at different levels of human-depending detail.In this paper we propose four operations in order to have several granular perspectives for a specific ontological commitment. Then these operations are used to have various views of an ontology built with a rough-set approach. In particular, a rough methodology is introduced to construct a specific granular view of an ontology.     

Allocation of information granularity in optimization and decision-making models: Towards building the foundations of Granular Computing

The highly diversified conceptual and algorithmic landscape of Granular Computing calls for the formation of sound fundamentals of the discipline, which cut across the diversity of formal frameworks (fuzzy sets, sets, rough sets) in which information granules are formed and processed. The study addresses this quest by introducing an idea of granular models – generalizations of numeric models that are formed as a result of an optimal allocation (distribution) of information granularity. Information granularity is regarded as a crucial design asset, which helps establish a better rapport of the resulting granular model with the system under modeling. A suite of modeling situations is elaborated on; they offer convincing examples behind the emergence of granular models. Pertinent problems showing how information granularity is distributed throughout the parameters of numeric functions (and resulting in granular mappings) are formulated as optimization tasks. A set of associated information granularity distribution protocols is discussed. We also provide a number of illustrative examples.     

基于超群的粒计算理论

首次将代数中的超群理论应用于粒计算研究之中。首先,引入正规超群和强正规超群的定义,证明了正规超群可由强正规超群生成;然后将粒计算商空间模型(X,f,T)中的T取为超群结构,利用超群同态证明了在模型(X,f,T)中,x与y在同一条路径上当且仅当在商空间模型([X],[f],[T])中,[x]与[y]在同一条路径上;并进一步证明了:若X与Y为超群同态的,则它们导出的商空间也是超群同态的。其次,我们研究了正规超群与可能性理论中的备域、超群与Paw lak近似空间及超群与拓扑空间的联系。指出:(1)强正规超群与备域是等价的;(2)强正规超群与Paw lak近似空间是等价的;(3)利用超群可定义集合的上、下近似,并利用集合的上、下近似刻画了超群同态;(4)强正规超群可由拓扑空间生成,正规超群可由拓扑空间生成的强正规超群生成;(5)可能性理论中的备域与Paw lak近似空间是等价的,且备域恰好是近似空间中所有可定义集合的全体。我们的研究表明:可能性理论中的备域与Paw lak的近似空间可利用正规超群来刻画。因此超群理论可用于粒计算的研究中。     

Computing the lifetime of granular activated carbon filters by means of travelling waves solutions

The aim of this paper is to propose a very simple way of computing the quantities relevant to the lifetime of a granular active carbon (GAC) filter. Our analysis is based on a sorption law, which, being linear separately in the adsorbed and non-adsorbed pollutant concentrations, allows the explicit computation of solutions in the form of a travelling wave. It is then easy to realize that, if the wave speed is much smaller than the advection velocity in the filter (as it happens in usual cases), then the travelling wave is an excellent approximation of the real profile of the pollutant concentration. The model is calibrated using laboratory experiments on a reduced scale. A linear stability analysis of the travelling waves is performed. Phenomena of diffusion–dispersion are neglected, however their effects are considered in the last sections, showing when they are really negligible and how they may influence the wave shape. The case of more pollutant species competing for the same adsorption sites on the GAC is also considered.     

基于泛系粗糙集等价算子上的粒计算模型

标准粗糙集使用等价类作为粒来描述概念.本文弱化对等价关系的要求, 将更广泛的粒计算模型建立到泛系粗糙集上去.本文通过对全域的分割和覆盖来诱导出泛系粗糙集上的粒计算模型.     

Extending ggplot2 for Linked and Animated Web Graphics

Interactive web graphics are great for communication and knowledge sharing, but are difficult to leverage during the exploratory phase of a data science workflow. Even before the web, interactive graphics helped data analysts quickly gather insight from data, discover the unexpected, and develop better model diagnostics. Although web technologies make interactive graphics more accessible, they are not designed to fit inside an exploratory data analysis (EDA) workflow where rapid iteration between data manipulation, modeling, and visualization must occur. To better facilitate exploratory web graphics that are easily distributed, we need better interfaces between statistical computing environments (e.g., the R language) and client-side web technologies. We propose the R package animint for rapid creation of linked and animated web graphics through a simple extension of ggplot2’s implementation of the Grammar of Graphics. The extension allows one to write ggplot2 code and produce a standalone web page with multiple linked views. Supplementary material for this article is available online.