面向知识结构分析的模糊概念格模型

知识空间理论使用数学语言对学习者进行知识评价与学习指导,属于数学心理学的研究范畴.技能与问题是构成知识空间的两个基本要素,深入研究两者之间的关系是知识状态刻画与知识结构分析的内在要求.在当前的知识空间理论研究中,没有明确建立技能与问题之间的双向映射,从而难以提出直观概念意义下的知识结构分析模型,也没有明确建立知识状态之间的偏序关系,不利于刻画知识状态之间的差异,更不利于规划学习者未来的学习路径.此外,现有的成果主要集中在经典的知识空间,没有考虑实际问题中数据的不确定性.为此,将形式概念分析与模糊集引入知识空间理论,建立面向知识结构分析的模糊概念格模型.具体地,分别建立知识空间与闭包空间的模糊概念格模型.首先,建立知识空间模糊概念格,并通过任意两个概念的上确界证明所有概念的外延构成知识空间.引入粒描述的思想定义技能诱导的问题原子粒,由问题原子粒的组合判定一个问题组合是否是知识空间中的一个状态,进而提出由问题组合获取知识空间模糊概念的方法.其次,建立闭包空间模糊概念格,并通过任意两个概念的下确界证明所有概念的外延构成闭包空间.类似地,定义问题诱导的技能原子粒,由技能原子粒的组合判定一个技能组合是否是闭包空间中某一知识状态所需的技能,进而提出由技能组合获取闭包空间模糊概念的方法.最后,通过实验分析问题数量、技能数量、填充因子以及分析尺度对知识空间与闭包空间规模的影响.结论表明知识空间模糊概念不同于现有的任何概念,也不能从其他概念派生而来.闭包空间模糊概念本质上是一种面向属性单边模糊概念.在二值技能形式背景中,知识空间与闭包空间中的状态具有一一对应关系,但这种关系在模糊技能形式背景中并不成立.

基于遗传算法的划分序乘积空间问题求解层选择

划分序乘积空间作为一种新的粒计算模型,可以从多个视角和多个层次对问题进行描述和求解.其解空间是由多个问题求解层组成的格结构,其中每个问题求解层由多个单层次视角构成.如何在划分序乘积空间中选择问题求解层是一个NP难问题.为此,提出一种两阶段自适应遗传算法TSAGA(two stage adaptive genetic algorithm)来寻找问题求解层.首先,采用实数编码对问题求解层进行编码,然后根据问题求解层的分类精度和粒度定义适应度函数.算法第1阶段基于经典遗传算法,预选出一些优秀问题求解层作为第2阶段初始种群的一部分,从而优化解空间.算法第2阶段,提出随当前种群进化迭代次数动态变化的自适应选择算子、自适应交叉算子以及自适应大变异算子,从而在优化的解空间中进一步选择问题求解层.实验结果证明了所提方法的有效性.

Formalization for Granular Computing Based on Logical Formulas

In order to make formalization for granular computing,some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all of the objects satisfying the formula.Therefore a granular space on the universe is produced based on the formulas, and the semantic sets separated by the formulas are taken as a formal definition for granules,and are called abstract granules.Furthermore,it is proved that any specific granule from an extended mathematical system can be formalized into an abstract granule,the conclusions is obtained that specific granules from approximate spaces and information systems can also be formalized into abstract granules. Based on a granular space and abstract granules,granular computing is defined,which finally realizes the goal of formalization for granular computing.

基于代数粒的聚类方法

聚类,是机器学习的主要任务之一,也是粒计算理论的核心任务,即信息粒化。目前,基于粒计算的聚类算法中,大多数只基于粒属性进行聚类,而没有考虑粒结构,尤其是在代数结构应用广泛的信息领域。从粒计算的角度,提出一种基于代数粒的聚类方法。基于二元代数运算定义代数粒;提出一种基于代数粒的聚类方法,通过粒集的同余划分和粒结构的同态映射进行粒度聚类;将提出的聚类方法与容差邻域模型和商空间模型进行对比分析。结果表明,该新型方法具有更好的结构完备性和应用鲁棒性。基于代数粒的聚类方法从结构上丰富和扩展了粒度计算理论,为粒计算与机器学习的融合研究提供了理论依据。

Quotient space model based on algebraic structure

In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.

The rough representation and measurement of quotient structure in algebraic quotient space model

Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.

Research of optimization to solve nonlinear equation based on granular computing

In this article,a real number is defined as a granulation and the real space is transformed into real granular space[1].In the entironment,solution of nonlinear equation is denoted by granulation in real granular space.Hence,the research of whole optimization to solve nonlinear equation based on granular computing is proposed[2].In classical case,we solve usually accurate solution of problems.If can't get accurate solution,also finding out an approximate solution to close to accurate solution.But in real space,approximate solution to close to accurate solution is very vague concept.In real granular space,all of the approximate solutions to close to accurate solution are constructed a set,it is a granulation in real granular space.Hence,this granulation is an accurate solution to solve problem in some sense,such,we avoid to say vaguely "approximate solution to close to accurate solution".We introduce the concept of granulation in one dimension real space.Any positive real number a together with moving infinite small distance ε will be constructed an interval [a-ε,a+ε],we call it as granulation in real granular space,denoted by ε(a)or [a].We will discuss related properties and operations[3] of the granulations.Let one dimension real space be R,where each real number a will be generated a granulation,hence we get a granular space R based on real space R.Obviously,R∈R.Infinite small number in real space R is only 0,and there are three infinite small granulations in real number granular space R:[0],[ε] and [-ε].As the graph in Fig.1 shows.In Fig.1,[-ε] is a negative infinite small granulation,[ε] is a positive infinite small granulation,[0] is a infinite small granulation.[a] is a granulation of real number a generating,it could be denoted by interval [a-ε,a+ε] in real space [3-5].Fig.1 Real granulations [0] and [a] Let f(x)=0 be a nonlinear equation,its graph in interval [-3,10] is showed in Fig.2.Where-3≤x≤10 Relation ρ(f| |,ε)is defined as follows:(x1,x2)∈ρ(f| |,ε)iff |f(x1)-f(x2)| < ε Where ε is any given small real number.We have five approximate solution sets on the nonlinear equation f(x)=0 by ρ(f| |,ε)∧|f(x)|[a,b]max,to denote by granulations [(xi1+xi2)/2],[(xi3+xi4)/2],[(xi5+xi6)/2],[(xi7+xi8)/2] and [(xi9+xi10)/2] respectively,where |f(x)|[a,b]max denotes local maximum on x∈[a,b].This is whole optimum on nonlinear equation in interval [-3,10].We will get best optimization solution on nonlinear equation via computing f(x)to use the five solutions denoted by granulation in one dimension real granular space[2,5].

On Granularity in Information Systems Based on Binary Relation

In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.

Extension of Rough Set on Granular Structures and Axiomatic Characterizations

In granular computing granular structures represent knowledge on universe,in this paper several important granular structures are considered.In a general granular structure the notions of interior point, accumulation point and boundary point etc are proposed,by use of these notions and referring to topological method,the lower and upper approximations of a subset of universe are defined such that they are one kind of generalization of the existing approximations based on some special granular structure.Basic properties of new rough set approximations are investigated.Furthermore,granular structures on universe are characterized by the lower and upper approximation operators.

多粒度广义近似空间的模糊粗糙集

针对多粒度广义近似空间中各元素之间关联度的问题,给出了元素之间相似度以及论域上相似矩阵的概念.结合粗糙集和模糊集理论,构建了多粒度广义近似空间中的模糊粗糙集模型并讨论了多粒度广义近似空间中的模糊粗糙下、上近似算子的性质.最后研究了多粒度广义近似空间中模糊粗糙的精确度和粗糙度.

以时间序列分析为基准的航站楼安检客流预测

目前在民航旅客流量预测方面,仍存在诸如序列粒度考虑过粗、未涉及到未来一天某个短时段内流量预测等问题。在单一时段内利用安全检查技术开展客流预测工作是交通系统的重要部分。为此,首先针对安检客流时间序列进行相空间重构;其次,使用Wolf方法进行安检客流时间序列混沌性判别;再次,采用BP神经网络预测方法对混沌时间序列进行预测;最后,讨论一天的高峰时间,并将该时段划分为2 min,3 min,5 min,10 min等时间间隔,利用曲线拟合方法对每天的客流趋势进行相似性分析。文中数据来源于北京首都国际机场T3航站楼安检客流数据。实验结果表明,文中方案具有较好的预测性能,在高峰期情况下,以2 min为时间间隔,采用BP神经网络方法能够在短时间内完成人员与资源动态调度。

一种场地污染环境的多粒度时空对象模型

目前针对污染场地的研究主要围绕污染态势及其发展状况,对于污染场地的实体特征缺乏较完整的表达,难以可视化展示污染场地多维度的信息。本文基于多粒度时空对象模型的构建思路,研究构建多粒度场地污染环境时空对象模型,将污染场地信息实体抽象成数据模型,进而对其时空实体的相关特征进行描述及可视化表达,实现污染场地的全空间信息大数据的集成与融合,并以重庆市某钢铁厂为例进行试验验证。试验结果表明,场地污染环境多粒度时空对象建模,可以高效表达污染场地多维度的特征,更全面地可视化展示污染场地信息,为污染场地的精准管控、污染评估和治理修复提供技术支撑。

一种引入格网的时空序列快照改进模型

将时间引入地理空间动态研究,能更加准确地定义地理空间的变化状态,分析地理空间变化成因及相关影响。提出将格网引入序列快照模型,并承担起空间快照的指代产品,与时间、属性构成三维变量模型。这一模型的优势在于将不能直接用于分析对比的3个变量从变化状态角度上集合至一个向量体内,根据变量的自身特点进行对照分析,得出体现变化状态的灰度体,以此变化结果与3个变量进行相关分析,获得状态变化与3个变量的相关性,进一步揭示变量对地理空间变化的影响度。

粒计算的集合论描述

粒计算的形式化研究一直没有被仔细讨论.文中在集合论框架下,对粒计算做了系统研究,给出了粒度空间的三层模型(论域,基,粒结构).借用逻辑语言L判定粒的可定义性,将经典粗糙集通过此模型重新解释.根据模型中从基到粒结构不同的构造规则,引出并可约和交可约粒度空间的定义,分别讨论了不同粒度空间下覆盖、基和粒结构的关系,从而给出从覆盖求基的方法;进一步,利用子系统表示方法对扩展粗糙集以及一般的交可约与并可约空间的上下近似进行了研究,分析了现有的4种基于覆盖的粗糙集模型的合理性;研究了形式概念分析以及知识空间的粒度空间模型,给出这两种理论中上下近似的概念.

商空间粒度计算理论在数据库和数据仓库中应用

商空间理论是研究不同粒度世界的一种新的数学工具。它用三元组(X,f,Т)描述一个问题,其中X表示问题的论域,f(·)是论域属性,Т是论域的结构。通过分析求解问题(X,f,Т),对论域X及其有关的结构、属性进行深入分析和研究,从而完成不同粒度世界的描述,并有着完整的理论基础。该文首次将商空间粒度理论应用于对数据仓库中数据进行了粒度分析,取得了很好的确定结果。

不同知识粒度下粗糙集的不确定性研究

粗糙集的不确定性度量方法,目前主要包括粗糙集的粗糙度、粗糙熵、模糊度和模糊熵.在不同知识粒度下,从属性的角度,给出了分层递阶的知识空间链,发现在分层递阶的知识粒度下部分文献中定义的粗糙集的粗糙熵和模糊度随知识粒度的变化规律不一定符合人们的认识规律.从信息熵的角度提出了一种粗糙集不确定性的模糊度度量方法,证明了这种模糊度随知识粒度的减小而单调递减,弥补了现有粗糙熵和模糊度度量粗糙集不确定性的不足.最后,分析了在不同知识粒度下粗糙度和模糊度的变化关系.

粒计算及其在机械故障智能诊断中的应用

为了更好地揭示原发性、早期微弱以及复合故障的发生发展规律,以粒计算理论为基础,提出了基于相容粒度空间模型的智能故障诊断方法.该方法通过层次化和粒度化来表示原始数据中蕴涵的不同设备运行状态的信息,使得不同故障状态被高效地映射到粒结构的不同层次上,达到正确区分各类故障的目的.利用得到的约简属性集构建相容粒度空间模型,对电力机车轮对轴承的早期微弱故障、严重故障以及复合故障进行诊断,取得了较高的分类精度.实验结果表明,与RBF神经网络方法相比,模型有着很高的分类性能,对9类故障状态的分类准确率达到了91.11%,说明相容粒度空间模型在机械故障诊断方面具有很好的分类性能.由于约简方法可以弥补特征评估技术不能直接获得最优特征组合的不足,因此提高了模型的工作效率.

粗糙集、商空间及概念格中粒的统一描述

粗糙集、商空间及概念格被认为是粒计算研究的重要方面,之所以如此是因为其中均包含了粒的概念。为对这些来自不同领域的粒实施统一的描述,在给定的论域上构造了逻辑公式,由此引出了对应论域的粒空间,并给出了粒空间中抽象粒的定义。通过分析处理,证明了粗糙集、商空间和概念格中出现的粒都可以采用粒空间中的抽象粒予以描述,使得以不同方式获取的粒得到了统一,从而为粒计算的形式化定义提供了思路。

基于等腰归一化距离的模糊粒度空间研究

本文将等腰归一化距离引入到模糊商空间中,提出了基于等腰归一化距离的模糊粒度空间理论。研究了它的结构和性质,并得到了四个重要结论。首先,下面3个叙述是等价的(定理3.2):(1)给定X上的一个模糊等价关系;(2)给定X上的一个等腰归一化距离;(3)给定X上的一个分层递阶结构(或有序的粒度空间)。其次,讨论了等腰归一化距离与Fuzzy等价关系间相互确定的对应关系,且都是一对多的关系(定理2.2,定理2.3)。最后,给出了通过X上的模糊等价关系R诱导的等腰归一化距离d确定其引导的粒度上的度量dλ,且dλ正好是d在粒度X(λ)上压缩的等腰归一化距离(定理4.1),同时给出了确定粒度空间上等腰归一化距离的方法。这些研究结论为模糊粒度计算的理论研究和应用提供了强有力的数字模型和工具,同时表明模糊商空间的粒度计算可以在等腰归一化距离的范畴内进行,为模糊粒度计算提供了更为直观的几何解释。

基于风险最小化的多粒度三支决策模型

为减小传统的二支决策中直接接受或拒绝决策带来的决策风险,分析问题决策的多粒度空间,研究了基于风险最小化的多粒度三支决策模型.在三支决策风险代价分析基础上,为寻求最优的粒度空间,结合不同属性特征在粒度空间中具有不同决策权重的特点,以粒化重要度和粒化决策权重为启发式信息,从多个不同的粒度层次出发,寻求风险最小的决策行动.最后针对不承诺选项中一些急需决策的现实问题,给出了基于风险控制的二支决策转化方法,并进行了具体的实例应用.