粒集理论:粒计算的新模型

在已有的有关粒计算研究成果的基础上,表述了信息的粒化、层次化和动态性原理,并综合了粒的表示形 式后,提出了粒集的概念,确认了粒的二元组的表示形式#同时借用统一集的形式对粒集进行了描述,分析了统一 集与粒集的异同,给出了与粒集相关的一些概念,讨论了用粒集形式来表达其他各种各样的集合,诸如经典集合、 模糊集合、可拓集合、Vague集合、粗糙集合等后,又讨论并表示了粒运算和粒集运算,最后给出了粒集理论的初步 应用框架。粒集理论为粒计算提供很好的理论基础，从而使粒计算确立自己独立的研究领域。     

一种基于粒计算的知识隐藏方法

对数据中蕴涵的敏感知识的隐藏与保护是私有保护数据挖掘中重要一个研究课题。粒计算具有在不同的粒度层次上进行问题求解的能力。本文讨论了基于粗糙集粒计算模型的数据中知识隐藏与保护方法。首先,介绍了不完备信息系统下的相容关系、相容信息粒和信息粒度;其次,提出基于粒计算的知识隐藏与保护方法;最后,通过具体实例和在真实数据集上的测试表明了所提出方法的可行性。     

粒计算未来发展方向探讨

互联网时代大规模复杂信息的涌现,带来处理（计算）复杂性的高度增加,粒计算在解决这个问题上应该有所贡献。复杂信息具有复杂的结构,并具有显著的不确定性。因此,粒计算未来的发展,既要考虑不确定性的处理,又要分析处理信息的结构,所以只有通过将有效的结构分析与不确定性方法以及多粒度计算结合起来,才能解决网络时代提出的信息处理任务。     

一种可伸缩的粒计算知识获取方法

粒计算是一种新的智能信息处理理论,它很大程度上模拟了人脑认识和解决问题的过程.通过对信息表分层粒化模型的研究,引入了粒分布链表的概念来生成粒子,并改进了一个粒计算算法.改进算法使用数据库技术对原始数据集进行粒化来生成粒分布链表,能够直接处理海量数据集,同时不影响原算法的有效性.通过试验测试了该方法的有效性及可伸缩性.     

基于信息系统的概念粒及其距离计算

在信息系统的基础上引人概念粒的概念,给出其规范的形式化方法,对概念粒的距离进行了定义,并研究了其距离的一些性质及应用.这些研究结果有助于理解粒的本质,能更准确的表述属性与对象之间的不确定性关系.     

基于粒集的概念粒系统

在作者提出的粒计算新模型──粒集理论的基础上,提出了粒系统、概念粒系统和粒概念等概念,并对它们分别进行了描述,其中粒系统的描述是五元组形式,即(U,D,L,H,J).当约束J的形式为一种特殊形式,即为概念中内涵与外延间反变关系的数学描述时,(U,D,L,H,J)就是概念粒系统.由此给出了概念粒系统的一些基本数学性质,证明了全体粒概念构成一个完备格──粒概念格,同时初步探讨了形式背景与概念粒系统之间的关系,从而进一步扩充了粒集理论的内容,完善了粒集理论.     

复合粒计算模型研究进展

粒计算（granular computing,GrC）是人工智能领域中的一种模拟人类思考和解决复杂问题的新理念和新方法,粗糙集理论、商空间理论和模糊集理论是3种主要的粒计算模型。首先回顾几种基本的粒计算模型,介绍了几个复合粒计算模型,最后探讨了粒计算模型的进一步发展方向。     

基于粒计算的认知模型

事物的认知过程是一个非常复杂的过程,粒计算是人工智能领域中的一种新理念和新方法.概要介绍了几种典型的认知模型,结合粒计算的方法论提出了基于粒计算的认知模型,并分析了图像认知过程中的粒计算方法和讨论了图像认知必须解决的关键问题.     

基于粒计算的元胞自动机交通流的研究

将粒计算技术引入到元胞自动机的交通流研究中,从而为进一步提出基于元胞、粒和交通网络三层结构的交通流系统奠定基础,继而改进传统交通流模拟系统的架构.在此交通流模拟系统中,粒及粒计算的思想反映为系统设计中的车队概念,而在某一时间步进内,交通网络中所有车辆的更新将按照路段、车队、车辆的层级顺序进行.     

基于相容粒度空间模型的图像纹理识别

信息粒广泛存在于现实世界中,是对现实的抽象.信息粒化旨在建立基于外部世界的有效的并以用户为中心的概念,同时简化人们对物理世界和虚拟世界的认识.使用信息粒进行计算是粒度计算的基本思想,在问题描述和求解中都具有重要的意义.主要研究一种新的粒度计算模型-相容粒度空间模型在图像纹理识别中的应用.该模型基于这样的思想,即人类具有根据具体的任务特性把相关数据和知识泛化或者特化成不同程度、不同大小的粒的能力,并进一步根据这些粒和粒之间的关系进行问题求解的能力.通过在多个数据集上和10种其他图像纹理识别算法的比较实验表明,该方法在图像纹理识别上具有良好的应用效果.     

A rough granular computing in discovery of process models from data and domain knowledge

The rapid expansion of the Internet has resulted not only in the ever growing amount of data therein stored, but also in the burgeoning complexity of the concepts and phenomena pertaining to those data. This issue has been vividly compared by the renowned statistician, prof. Friedman of Stanford University, to the advances in human mobility from the period of walking afoot to the era of jet travel. These essential changes in data have brought new challenges to the development of new data mining methods, especially that the treatment of these data increasingly involves complex processes that elude classic modeling paradigms. “Hot” datasets like biomedical, financial or net user behavior data are just a few examples. Mining such temporal or stream data is on the agenda of many research centers and companies worldwide. In the data mining community, there is a rapidly growing interest in developing methods for process mining, e.g〖DK〗., for discovery of structures of temporal processes from data. Works on process mining have recently been undertaken by many renowned centers worldwide. This research is also related to functional data analysis , cognitive networks , and dynamical system modeling, e.g., in biology. In the lecture, we outline an approach to discovery of processes from data and domain knowledge which is based on the roughgranular computing.     

基于相容粒度空间模型的图像纹理识别

信息粒广泛存在于现实世界中,是对现实的抽象。信息粒化旨在建立基于外部世界的有效的并以用户为中心的概念,同时简化人们对物理世界和虚拟世界的认识。使用信息粒进行计算是粒度计算的基本思想,在问题描述和求解中都具有重要的意义。主要研究一种新的粒度计算模型—相容粒度空间模型在图像纹理识别中的应用。该模型基于这样的思想,即人类具有根据具体的任务特性把相关数据和知识泛化或者特化成不同程度、不同大小的粒的能力,并进一步根据这些粒和粒之间的关系进行问题求解的能力。通过在多个数据集上和10种其他图像纹理识别算法的比较实验表明,该方法在图像纹理识别上具有良好的应用效果。     

数计大类新生基本情况调查

通过对06级数学大类学生关于信息与计算科学专业的了解程度，对大学学习生活的了解与适应情况，前景规划等几个方面的调查分析，探讨了信息与计算科学专业的定位与办学思路，提出了相关对策和建议．     

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 granu-lar 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 classicalcase, we solve usually accurate solution of problems. If can't get accurate solution, also finding out an approximate solutionto close to accurate solution. But in real space, approximate solution to close to accurate solution is very vague concept. Inreal granular space, all of the approximate solutions to close to accurate solution are constructed a set, it is a granulation inreal granular space. Hence, this granulation is an accurate solution to solve problem in some sense, such, we avoid to sayvaguely "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 movinginfinite small distance ε will be constructed an interval [a-ε,a ε], we call it as granulation in real granular space, denotedby 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 granularspace R* based on real space R. Obviously, R∈R*. Infinite small number in real space R is only O, and there are three in-finite 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].Letf(x)=0 be a nonliner equation,its graph in interval[-3,10]id showed in Fig.2.Where -3≤x≤10 Relation ρ(f‖,ε)is defied is follows:(x1,x2)∈ p(f‖,ε)iff |f(x1)- f(x2)|<εWhere ε is any given small real number.We have five appoximate solution sets on the nonliner 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 nonliear equation in interval [-3,10].We will get best opmension solution on nonliner equation via computing f(x)to use the five solutions dented by grandlation in one dimension real granlar space[2,5].     

DNA计算技术进展

论述DNA计算技术进展。先介绍DNA计算的基本原理,论述DNA计算的特点方法和存在的问题,接着介绍DNA计算的国内外研究现状,最后指出DNA计算研究中需要解决的问题。     

基于可达关系的Rough集

根据Rough集的思想提出了一种新的基于可达关系的Rough集模型,这种Rough集模型的思想是基于信息粒和可达关系的,比经典的Rough集更一般.除了Rough集原来的应用外,这种Rough集模型还可望有更广泛的应用.基于可达关系的Rough集思想将Rough集思想推广到一般的方法论.     

数学问题解决中形象思维的意义及其培养

数学形象思维在问题解决中可分为直观形象思维、经验形象思维、数觉形象思维、观念形象思维4类,数学形象思维的意义体现在有利于开发右脑、有助于记忆、有益于发展创造性思维等,在问题解决中培养学生的数学形象思维的做法有调整课程总体设计、重视问题直观教学、揭示新旧知识的联结点、重视问题解决后的思考、加强问题模型的教学.     

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach (DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions. DRSA has also some merits within granular computing, as it extends the paradigm of granular computing to ordered data, specifies a syntax and modality of information granules which are appropriate for dealing with ordered data, and enables computing with words and reasoning about ordered data. Granular computing with ordered data is a very general paradigm, because other modalities of information constraints, such as veristic, possibilistic and probabilistic modalities, have also to deal with ordered value sets (with qualifiers relative to grades of truth, possibility and probability), which gives DRSA a large area of applications.     

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach(DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions.DRSA has also some merits within granular computing,as it extends the paradigm of granular computing to ordered data,specifies a syntax and modality of information granules which are appropriate for dealing with ordered data,and enables computing with words and reasoning about ordered data.Granular computing with ordered data is a very general...     

颗粒材料热力学理论在简单剪切流中的应用

颗粒物质由大量离散的粗大固体颗粒聚集而成,在外界作用下可能发生准静态变形、变形局部化和破坏,直至流动,其中采用固体力学和流体力学对准静态变形和流动开展的研究较为系统,而变形局部化和破坏的研究非常薄弱．分析内部结构演化规律,建立颗粒体系非平衡态热力学,统一描述颗粒体系力学行为是重要的基础研究课题,Granular Solid Hydrodynamics（GSH）理论为该研究提供了基础．本文完善了该理论涉及的颗粒温度表达式,确定了相应参数数值;与动理学理论和离散元模拟一起对恒定体积简单剪切流进行了分析,对比了三种方法得到的正应力与颗粒体积分数的关系,发现由于基本假设的限制,动理学理论只能适用于稀疏颗粒流,而完善后的颗粒体系热力学理论比动理学涵盖范围更广,可以从稀疏体系到密集体系．这样该理论可以连贯地描述颗粒体系准静态变形、变形局部化和破坏,直至流动的力学行为．