Hybrid Rough Sets and Applications in Uncertain Decision-Making (Systems Evaluation, Prediction, and Decision-Making)

✍ Scribed by Lirong Jian, Sifeng Liu, Yi Lin

• Publisher: Auerbach Publications
• Year: 2010
• Tongue: English
• Leaves: 272
• Edition: 1
• Category: Library

✦ Synopsis

As a powerful approach to data reasoning, rough set theory has proven to be invaluable in knowledge acquisition, decision analysis and forecasting, and knowledge discovery. With the ability to enhance the advantages of other soft technology theories, hybrid rough set theory is quickly emerging as a method of choice for decision making under uncertain conditions. Keeping the complicated mathematics to a minimum, Hybrid Rough Sets and Applications in Uncertain Decision-Making provides a systematic introduction to the methods and application of the hybridization for rough set theory with other related soft technology theories, including probability, grey systems, fuzzy sets, and artificial neural networks. It also: Addresses the variety of uncertainties that can arise in the practical application of knowledge representation systems Unveils a novel hybrid model of probability and rough sets Introduces grey variable precision rough set models Analyzes the advantages and disadvantages of various practical applications The authors examine the scope of application of the rough set theory and discuss how the combination of variable precision rough sets and dominance relations can produce probabilistic preference rules out of preference attribute decision tables of preference actions. Complete with numerous cases that illustrate the specific application of hybrid methods, the text adopts the latest achievements in the theory, method, and application of rough sets.

✦ Table of Contents

Title Page
......Page 4
Contents......Page 6
Preface......Page 12
Acknowledgments......Page 14
Authors......Page 15
1.1 Background and Significance of Soft Computing Technology......Page 18
1.1.1 Analytical Method of Data Mining......Page 19
1.1.2 Knowledge Discovered by Data Mining......Page 21
1.2 Characteristics of Rough Set Theory and Current Status of Rough Set Theory Research......Page 23
1.2.1 Characteristics of the Rough Set Theory......Page 24
1.2.2 Current Status of Rough Set Theory Research......Page 25
1.3 Hybrid of Rough Set Theory and Other Soft Technologies......Page 26
1.3.2 Hybrid of Rough Sets and Dominance Relation......Page 27
1.3.3 Hybrid of Rough Sets and Fuzzy Sets......Page 28
1.3.4 Hybrid of Rough Set and Grey System Theory......Page 29
1.3.5 Hybrid of Rough Sets and Neural Networks......Page 30
1.4 Summary......Page 31
2.1 Information Systems and Classification......Page 33
2.1.2 Set and Approximations of Set......Page 34
2.1.3 Attributes Dependence and Approximation Accuracy......Page 39
2.1.4 Quality of Approximation and Reduct......Page 41
2.1.5 Calculation of the Reduct and Core of Information System Based on Discernable Matrix......Page 42
2.2.1 The Attribute Dependence, Attribute Reduct, and Core......Page 47
2.2.2 Decision Rules......Page 48
2.2.3 Use the Discernibility Matrix to Work Out Reducts, Core, and Decision Rules of Decision Table......Page 49
2.3 Data Discretization......Page 52
2.3.1 Expert Discrete Method......Page 53
2.3.4 Chimerge Method......Page 54
2.4.1 Quick Reduct Algorithm......Page 55
2.4.2 Heuristic Algorithm of Attribute Reduct......Page 56
2.4.3 Genetic Algorithm......Page 57
2.5 Application Case......Page 59
2.5.2 Data Discretization......Page 60
2.5.3 Attribute Reduct......Page 65
2.5.5 Simulation of the Decision Rules......Page 68
2.6 Summary......Page 71
3.1 Rough Membership Function......Page 73
3.2 Variable Precision Rough Set Model......Page 76
3.2.1 β-Rough Approximation......Page 77
3.2.2 Classification Quality and β-Reduct......Page 78
3.2.3 Discussion about β-Value......Page 80
3.3.1 Knowledge Granularity......Page 83
3.3.2 Relationship between VPRS and Knowledge Granularity......Page 84
3.3.3 Construction of Hierarchical Knowledge Granularity......Page 85
3.4.1 Bayes’ Probability......Page 89
3.4.2 Consistent Degree, Coverage, and Support......Page 90
3.4.3 Probability Rules......Page 91
3.4.4 Approach to Obtain Probabilistic Rules......Page 92
3.5 Summary......Page 94
4.1 Dominance-Based Rough Set......Page 95
4.1.1 The Classification of the Decision Tables with Preference Attribute......Page 96
4.1.2 Dominating Sets and Dominated Sets......Page 97
4.1.3 Rough Approximation by Means of Dominance Relations......Page 98
4.1.4 Classification Quality and Reduct......Page 99
4.1.5 Preferential Decision Rules......Page 100
4.2.1 Inconsistency and Indiscernibility Based on Dominance Relation......Page 102
4.2.2 β-Rough Approximation Based on Dominance Relations......Page 103
4.2.5 Algorithm Design......Page 105
4.3.1 Post-Evaluation of Construction Projects Based on Dominance-Based Rough Set......Page 109
4.3.2 Performance Evaluation of Discipline Construction in Teaching–Research Universities Based on Dominance-Based Rough Set......Page 119
4.4 Summary......Page 138
5. Hybrid of Rough Set Theory and Fuzzy Set Theory......Page 140
5.1.1 Fuzzy Set and Fuzzy Membership Function......Page 141
5.1.2 Operation of Fuzzy Subsets......Page 143
5.1.3 Fuzzy Relation and Operation......Page 146
5.1.4 Synthesis of Fuzzy Relations......Page 147
5.1.5 λ-Cut Set and the Decomposition Proposition......Page 148
5.1.6 The Fuzziness of Fuzzy Sets and Measure of Fuzziness......Page 149
5.2.1 Rough Fuzzy Set......Page 152
5.3 Variable Precision Rough Fuzzy Sets......Page 153
5.3.1 Rough Membership Function Based on λ-Cut Set......Page 154
5.3.2 The Rough Approximation of Variable Precision Rough Fuzzy Set......Page 155
5.3.4 The Probabilistic Decision Rules Acquisition of Rough Fuzzy Decision Table......Page 156
5.3.5 Algorithm Design......Page 157
5.4.1 Fuzzy Equivalence Relation......Page 160
5.4.2 Variable Precision Fuzzy Rough Model......Page 161
5.4.4 Measure Methods of the Fuzzy Roughness for Output Classification......Page 163
5.5 Summary......Page 167
6.1 The Basic Concepts and Methods of the Grey System Theory......Page 169
6.1.1 Grey Number, Whitening of Grey Number, and Grey Degree......Page 170
6.1.2 Grey Sequence Generation......Page 174
6.1.3 GM(1, 1) Model......Page 176
6.1.4 Grey Correlation Analysis......Page 179
6.1.5 Grey Correlation Order......Page 186
6.1.6 Grey Clustering Evaluation......Page 189
6.2 Establishment of Decision Table Based on Grey Clustering......Page 197
6.3 The Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function......Page 199
6.4 Grey Rough Approximations......Page 202
6.5 Reduced Attributes Dominance Analysis Based on Grey Correlation Analysis......Page 207
6.6 Summary......Page 210
7. A Hybrid Approach of Variable Precision Rough Sets, Fuzzy Sets, and Neural Networks......Page 212
7.1 Neural Network......Page 213
7.1.1 An Overview of the Development of Neural Network......Page 214
7.1.2 Structure and Types of Neural Network......Page 215
7.1.3 Perceptron......Page 217
7.1.4 Back Propagation Network......Page 221
7.1.5 Radial Basis Networks......Page 225
7.1.6 Probabilistic Neural Network......Page 230
7.2 Knowledge Discovery in Databases Based on the Hybrid of VPRS and Neural Network......Page 233
7.2.2 Construction of Decision Table......Page 235
7.2.3 Searching of β-Reduct and Generation of Probability Decision Rules......Page 236
7.3 System Design Methods of the Hybrid of Variable Precision Rough Fuzzy Set and Neutral Network......Page 243
7.3.1 Construction of a Variable Precision Rough Fuzzy Neutral Network......Page 246
7.3.2 Training Algorithm of the Variable Precision Rough Fuzzy Neutral Network......Page 250
7.4 Summary......Page 251
8.1 A Survey of Transport Scheme Choice......Page 252
8.2.2 Probability Choice Decision Based on VPRS......Page 254
8.2.4 Probability Choice Decision Based on the Hybrid of VPRS and Probabilistic Neural Network......Page 256
8.3.1 Choice Decision Based on the Dominance Rough Set......Page 258
8.3.2 Choice Decision Based on the Dominance-Based VPRS......Page 259
Bibliography......Page 262