第 1章绪论 .......................................................................................................... 1
1.1稳健粗糙集理论的重要性 ............................................................................ 1
1.2粗糙集理论的产生与发展 ............................................................................ 1
1.3粗糙集理论的推广 ...................................................................................... 2
1.4稳健粗糙集及其研究现状 ............................................................................ 3
1.5本书组织结构 ............................................................................................ 4
第 2章数据噪声分类及抗噪方法 ............................................................................ 6
2.1数据噪声分类 ............................................................................................ 6
2.1.1根据数据噪声的特点分类 .................................................................. 6
2.1.2根据数据噪声的分布分类 .................................................................. 7
2.1.3根据属性类型分类 ............................................................................ 7
2.2数据噪声检测方法 ...................................................................................... 8
2.2.1基于统计方法的噪声检测 .................................................................. 8
2.2.2基于聚类方法的噪声检测 .................................................................. 8
2.2.3基于分类模型的噪声检测 .................................................................. 8
2.2.4基于 k-近邻的噪声检测 ..................................................................... 9
2.2.5其他检测方法 ................................................................................... 9
2.3稳健模型 ..................................................................................................10
2.3.1抗差估计 ........................................................................................10
2.3.2基于概率思想的抗噪声方法 ..............................................................11
2.3.3基于模型的抗噪声方法 ....................................................................11
2.4模型稳健性评价指标 .................................................................................12
2.4.1敏感度曲线 .....................................................................................12
2.4.2基于相似性度量的稳健性评价标准 ....................................................12
2.4.3基于信息熵的稳健性评价标准 ..........................................................13
第 3章粗糙集模型 ...............................................................................................15
3.1 Pawlak粗糙集 ..........................................................................................15
3.1.1基本概念 ........................................................................................15
3.1.2 Pawlak粗糙集模型 .........................................................................16
3.2优势关系粗糙集 ........................................................................................19
3.2.1优势关系 ........................................................................................19
3.2.2优势关系粗糙集模型 ........................................................................19
3.3邻域粗糙集 ...............................................................................................21
稳健粗糙集及应用
3.3.1邻域粗糙集模型 ..............................................................................21
3.3.2邻域一致性指标 ..............................................................................23
3.4模糊粗糙集 ...............................................................................................25
3.4.1模糊算子 ........................................................................................25
3.4.2模糊粗糙集模型 ..............................................................................26
第 4章基于可变精度的稳健粗糙集模型 .................................................................29
4.1变精度粗糙集 ...........................................................................................29
4.1.1多数包含关系 ..................................................................................29
4.1.2变精度粗糙集模型 ...........................................................................30
4.2 β-精度模糊粗糙集 .....................................................................................31
4.2.1 β-精度 T -范数和 T -余范数 ...............................................................31
4.2.2 β-精度模糊粗糙集模型 ....................................................................31
4.3变精度模糊粗糙集 .....................................................................................32
4.4模糊变精度粗糙集 .....................................................................................34
4.5模型稳健性对比 ........................................................................................35
第 5章基于软距离的稳健粗糙集模型 .....................................................................40
5.1稳健的软模糊粗糙集模型 ...........................................................................40
5.1.1支持向量机 .....................................................................................40
5.1.2软距离 ............................................................................................43
5.1.3软模糊粗糙集 ..................................................................................45
5.1.4模型泛化性 .....................................................................................49
5.1.5模型稳健性 .....................................................................................51
5.2基于软最小超球的稳健模糊粗糙集模型 .......................................................54
5.2.1最小超球与软最小超球 ....................................................................54
5.2.2基于软最小超球的稳健模糊粗糙集 ....................................................59
5.2.3模型性质及参数设置 ........................................................................62
5.2.4模型稳健性 .....................................................................................63
第 6章基于稳健统计量的粗糙集模型 .....................................................................65
6.1基于稳健统计量的粗糙集 ...........................................................................65
6.2模型性质 ..................................................................................................67
6.3模型稳健性 ...............................................................................................70
6.3.1理论对比分析 ..................................................................................70
6.3.2实验对比分析 ..................................................................................71
第 7章概率模糊粗糙集模型 ..................................................................................74
7.1问题的提出 ...............................................................................................74
7.2概率模糊粗糙集 ........................................................................................75
7.3模型性质 ..................................................................................................80
目录
7.4模型稳健性 ...............................................................................................84
第 8章稳健模糊粗糙分类模型 ...............................................................................86
8.1模糊粗糙决策树 ........................................................................................86
8.1.1两类分类问题的模糊粗糙决策树 .......................................................86
8.1.2多类分类问题的模糊粗糙决策树 .......................................................90
8.1.3讨论 ...............................................................................................90
8.2稳健模糊粗糙分类器 .................................................................................96
8.2.1稳健模糊粗糙分类原理 ....................................................................96
8.2.2稳健性分析 .....................................................................................99
8.3基于模糊粗糙集的原型选择及分类模型 ..................................................... 102
8.3.1原型评价指标和原型影响域 ............................................................ 103
8.3.2稳健模糊粗糙原型选择 .................................................................. 103
8.3.3基于原型覆盖的稳健分类 ............................................................... 106
8.3.4分类模型性能分析 ......................................................................... 108
第 9章稳健粗糙集的应用 ................................................................................... 115
9.1稳健粗糙集在太阳耀斑预报中的应用 ........................................................ 115
9.1.1太阳耀斑预报的研究现状 ............................................................... 115
9.1.2太阳耀斑数据介绍 ......................................................................... 115
9.1.3基于稳健模糊粗糙集的太阳耀斑预报模型 ........................................ 117
9.1.4预报模型性能分析 ......................................................................... 123
9.2稳健模糊粗糙集在风速预报中的应用 ........................................................ 125
9.2.1风电预报的不确定性 ...................................................................... 126
9.2.2风电预报模型的研究现状 ............................................................... 126
9.2.3基于稳健模糊粗糙集的风速预测模型 .............................................. 127
9.2.4预测模型性能分析 ......................................................................... 130
参考文献 ............................................................................................................... 137
