基于矩阵的奇异值分解和模糊C-均值聚类外文翻译资料

 2022-08-09 14:57:20

英语原文共 9 页，剩余内容已隐藏，支付完成后下载完整资料

摘要

由于没有可用的标准，因此有关信息系统对象的大量数据的离散化可能是从实例执行归纳学习的最大障碍。基于矩阵的奇异值分解和模糊C-均值聚类，提出了具有连续条件属性值和离散决策属性值的决策表中连续属性值的离散方法。

考虑决策表的冲突对象，将粗糙集理论用于旋转机械的诊断规则获取。

提出了一种带有诊断规则的对象弱匹配模式，通过将新对象与标准诊断规则进行比较，得出诊断结论及其可信度。本文最后的一个例子表明，所获得的规则具有良好的泛化和扩展能力，并在一定程度上提高了分类水平。

关键字：决策表、故障诊断、模糊C均值聚类

专有名词：

SVD：Singular value decomposition奇异值分解

FCM：Fuzzy C-means clustering模糊C均值聚类

RST：Rough sets theory粗糙集理论

DT ：Decision table决策表

CAs：Condition attributes条件属性

DAs：Decision attributes决策属性

CCAVs：Continuous condition attribute values连续条件属性值

DDAVs：Discrete decision attribute values离散决策属性值

SVs：Singular values of matrix矩阵的奇异值

CBD：Conclusion belief degree结论置信度

CCAVs-DDAVs-DT：Decision table with continuous condition attribute values and discrete decision attribute values具有连续条件属性值和离散决策属性值的CCAVs-DDAVs-DT决策表

S：Knowledge system or decision table知识系统或决策表

U：Domain of discourse about objects in decision table/ orthogonal matrix of construct matrix ACmtimes;n according to CCAVs-DDAVs-DT

根据CCAVs-DDAVs-DT，在决策表/构造矩阵ACmtimes;n的正交矩阵中的对象讨论区域

V：The union of attribute value sets/orthogonal matrix of construct matrix ACmtimes;n according to CCAVs-DDAVs-DT根据CCAVs-DDAVs-DT构造矩阵ACmtimes;n的属性值集/正交矩阵的并集

A：The union of condition attribute set and decision attribute set条件属性集和决策属性集的并集

C：Condition attribute set条件属性集

D：Decision attribute set决策属性集

Va：Domain of attribute aisin; A in decision table决策表中属性aisin;A的域

f(x,a)：Information function of object xisin;U about attribute aisin;A

Pos(C,D)：Decision attribute set D-positive region with regard to condition attribute set C关于条件属性集C的决策属性集D阳性区域

gamma;(C,D)：Dependent factor of decision attribute set D with respect to condition attribute set C决策属性集D相对于条件属性集C的从属因子

card(bull;)：Cardinality of set集的基数

ai：The ith condition attribute of condition attribute set C

条件属性集C的第i个条件属性

Vai：Discrete attribute value of attribute ai属性ai的离散属性值

cij：An item of discernibility matrix located in the ith row and jth column of the it

f(va1,va2,···,van;D)：Discernibility function of discernibility matrix constructed by attribute value vai,1le;ile;n of condition attribute set C={a1,a2,···,an} and decision attribute set D

条件属性集C = {a1，a2,hellip;,an}的属性值vai，1le;ile;n和决策属性集D构成的可分辨矩阵的可分辨函数

mD：The number of different discrete decision attribute values不同离散决策属性值的数量

DTIni:Initial decision table初步决策表

Obji Ini:The ith objects in initial decision table DTIni初始决策表DTIni中的第i个对象

DTCom:Decision table after combining the reduplicated objects of initial decision table DTIni合并初始决策表DTIni的重复对象后的决策表

Objcom i: 决策表DTCom中的第i个对象

Cd i：The reduplicate number of the ith objects in decision table DTCom

决策表DTCom中第i个对象的重复数量

DT Conf：Decision table after removing conflicting objects of decision table DTCom 删除决策表DTCom的冲突对象后的决策表

ObjConf i：The ith objects in decision table DTConf决策表DTConf中的第i个对象

Cck：The conflicting number of the kth objects in decision table DTConf

决策表DTConf中第k个对象的冲突数量

Ratiok：A ratio that the reduplicate number of the kth objects ObjConfi in decision table DTConf to the sum of reduplicate number of objects of DTCom that conflicting with ObjConfk决策表DTConf中的第k个对象ObjConfi的重复数量与与Objconfk冲突的DTCom的对象的重复数量之和的比率

rk：Produced decision rule of the kth objects ObjConf k in decision table DTConf决策表DTConf中产生的第k个对象ObjConf k的决策规则

STHr：Strength of the rth rule in final decision rules最终决策规则中第r条规则的强度

Sth：Symbol of rule strength规则强度的象征

Amtimes;n An mtimes;n matrix

ACmtimes;n：Construct matrix according to CCAVs-DDAVs-DT, where suppose there are m objects, with n CCAVs of one object根据CCAVs-DDAVs-DT构造矩阵，假设有m个对象，其中n个CCAV为一个对象

W：Diagonal matrix decomposed of a matrix由矩阵分解的对角矩阵

lambda;i ：The ith singular values of matrix矩阵的第i个奇异值

||A||F:The Frobenius of matrix A

(Frobenius 范数，简称F-范数，是一种矩阵范数，记为||·||F。矩阵A的Frobenius范数定义为矩阵A各项元素的绝对值平方的总和)

T: A CCAVs-DDAVs-DT

DT：The reduced DT of a CCAVs-DDAVs-DT

cl：Cluster number of a CCAVs-DDAVs-DT集群号

CLa(i)：The ith cluster lowest-limit of the column aisin;C in DT

DT中aisin;C列的第i个簇最低极限

CUa(i)：The ith cluster uppermost-limit of the column aisin;C in DT

DT中aisin;C列的第i个簇最高极限

Tbi：Index of an discrete decision table of a CCAVsDDAVs-DT when cluster number is cl群集编号为cl时CCAVs-DDAVs-DT的离散决策表的索引

DTIniTbi：The Tbi th discrete decision table of a CCAVsDDAVs-DT

CCAVsDDAVs-DT的第Tbi个离散决策表

z：The factor of discrete number of CCAVs-DDAVs-DT

CCAVs-DDAVs-D离散数的因数

N(D)：The number of different DDAVs不同DDAV的数量

NRTbi(C)：The Tbi th reduced number of CAs of DTIniTbi

CCAVs-DDAVs-DT的第Tbi个离散决策表的第Tbi个条件属性降低数目

CN：The final acquired c

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