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: 277
Series: Systems Evaluation, Prediction, and Decision-Making'',
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ 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

Contents......Page 6
Preface......Page 12
Acknowledgments......Page 14
Authors......Page 16
1.1 Background and Significance of Soft Computing Technology......Page 19
1.1.1 Analytical Method of Data Mining......Page 20
1.1.2 Knowledge Discovered by Data Mining......Page 22
1.2 Characteristics of Rough Set Theory and Current Status of Rough Set Theory Research......Page 24
1.2.1 Characteristics of the Rough Set Theory......Page 25
1.2.2 Current Status of Rough Set Theory Research......Page 26
1.3 Hybrid of Rough Set Theory and Other Soft Technologies......Page 27
1.3.2 Hybrid of Rough Sets and Dominance Relation......Page 28
1.3.3 Hybrid of Rough Sets and Fuzzy Sets......Page 29
1.3.4 Hybrid of Rough Set and Grey System Theory......Page 30
1.3.5 Hybrid of Rough Sets and Neural Networks......Page 31
1.4 Summary......Page 32
2.1 Information Systems and Classification......Page 35
2.1.2 Set and Approximations of Set......Page 36
2.1.3 Attributes Dependence and Approximation Accuracy......Page 41
2.1.4 Quality of Approximation and Reduct......Page 43
2.1.5 Calculation of the Reduct and Core of Information System Based on Discernable Matrix......Page 44
2.2.1 The Attribute Dependence, Attribute Reduct, and Core......Page 49
2.2.2 Decision Rules......Page 50
2.2.3 Use the Discernibility Matrix to Work Out Reducts, Core, and Decision Rules of Decision Table......Page 51
2.3 Data Discretization......Page 54
2.3.1 Expert Discrete Method......Page 55
2.3.4 Chimerge Method......Page 56
2.4.1 Quick Reduct Algorithm......Page 57
2.4.2 Heuristic Algorithm of Attribute Reduct......Page 58
2.4.3 Genetic Algorithm......Page 59
2.5 Application Case......Page 61
2.5.2 Data Discretization......Page 62
2.5.3 Attribute Reduct......Page 67
2.5.5 Simulation of the Decision Rules......Page 70
2.6 Summary......Page 73
3.1 Rough Membership Function......Page 75
3.2 Variable Precision Rough Set Model......Page 78
3.2.1 β-Rough Approximation......Page 79
3.2.2 Classification Quality and β-Reduct......Page 80
3.2.3 Discussion about β-Value......Page 82
3.3.1 Knowledge Granularity......Page 85
3.3.2 Relationship between VPRS and Knowledge Granularity......Page 86
3.3.3 Construction of Hierarchical Knowledge Granularity......Page 87
3.4.1 Bayes’ Probability......Page 91
3.4.2 Consistent Degree, Coverage, and Support......Page 92
3.4.3 Probability Rules......Page 93
3.4.4 Approach to Obtain Probabilistic Rules......Page 94
3.5 Summary......Page 96
4.1 Dominance-Based Rough Set......Page 97
4.1.1 The Classification of the Decision Tables with Preference Attribute......Page 98
4.1.2 Dominating Sets and Dominated Sets......Page 99
4.1.3 Rough Approximation by Means of Dominance Relations......Page 100
4.1.4 Classification Quality and Reduct......Page 101
4.1.5 Preferential Decision Rules......Page 102
4.2.1 Inconsistency and Indiscernibility Based on Dominance Relation......Page 104
4.2.2 β-Rough Approximation Based on Dominance Relations......Page 105
4.2.5 Algorithm Design......Page 107
4.3.1 Post-Evaluation of Construction Projects Based on Dominance-Based Rough Set......Page 111
4.3.2 Performance Evaluation of Discipline Construction in Teaching–Research Universities Based on Dominance-Based Rough Set......Page 121
4.4 Summary......Page 140
5. Hybrid of Rough Set Theory and Fuzzy Set Theory......Page 143
5.1.1 Fuzzy Set and Fuzzy Membership Function......Page 144
5.1.2 Operation of Fuzzy Subsets......Page 146
5.1.3 Fuzzy Relation and Operation......Page 149
5.1.4 Synthesis of Fuzzy Relations......Page 150
5.1.5 λ-Cut Set and the Decomposition Proposition......Page 151
5.1.6 The Fuzziness of Fuzzy Sets and Measure of Fuzziness......Page 152
5.2.1 Rough Fuzzy Set......Page 155
5.3 Variable Precision Rough Fuzzy Sets......Page 156
5.3.1 Rough Membership Function Based on λ-Cut Set......Page 157
5.3.2 The Rough Approximation of Variable Precision Rough Fuzzy Set......Page 158
5.3.4 The Probabilistic Decision Rules Acquisition of Rough Fuzzy Decision Table......Page 159
5.3.5 Algorithm Design......Page 160
5.4.1 Fuzzy Equivalence Relation......Page 163
5.4.2 Variable Precision Fuzzy Rough Model......Page 164
5.4.4 Measure Methods of the Fuzzy Roughness for Output Classification......Page 166
5.5 Summary......Page 170
6.1 The Basic Concepts and Methods of the Grey System Theory......Page 173
6.1.1 Grey Number, Whitening of Grey Number, and Grey Degree......Page 174
6.1.2 Grey Sequence Generation......Page 178
6.1.3 GM(1, 1) Model......Page 180
6.1.4 Grey Correlation Analysis......Page 183
6.1.5 Grey Correlation Order......Page 190
6.1.6 Grey Clustering Evaluation......Page 193
6.2 Establishment of Decision Table Based on Grey Clustering......Page 201
6.3 The Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function......Page 203
6.4 Grey Rough Approximations......Page 206
6.5 Reduced Attributes Dominance Analysis Based on Grey Correlation Analysis......Page 211
6.6 Summary......Page 214
7. A Hybrid Approach of Variable Precision Rough Sets, Fuzzy Sets, and Neural Networks......Page 217
7.1 Neural Network......Page 218
7.1.1 An Overview of the Development of Neural Network......Page 219
7.1.2 Structure and Types of Neural Network......Page 220
7.1.3 Perceptron......Page 222
7.1.4 Back Propagation Network......Page 226
7.1.5 Radial Basis Networks......Page 230
7.1.6 Probabilistic Neural Network......Page 235
7.2 Knowledge Discovery in Databases Based on the Hybrid of VPRS and Neural Network......Page 238
7.2.2 Construction of Decision Table......Page 240
7.2.3 Searching of β-Reduct and Generation of Probability Decision Rules......Page 241
7.3 System Design Methods of the Hybrid of Variable Precision Rough Fuzzy Set and Neutral Network......Page 248
7.3.1 Construction of a Variable Precision Rough Fuzzy Neutral Network......Page 251
7.3.2 Training Algorithm of the Variable Precision Rough Fuzzy Neutral Network......Page 255
7.4 Summary......Page 256
8.1 A Survey of Transport Scheme Choice......Page 257
8.2.2 Probability Choice Decision Based on VPRS......Page 259
8.2.4 Probability Choice Decision Based on the Hybrid of VPRS and Probabilistic Neural Network......Page 261
8.3.1 Choice Decision Based on the Dominance Rough Set......Page 263
8.3.2 Choice Decision Based on the Dominance-Based VPRS......Page 264
Bibliography......Page 267

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