Rough Set Theory and Granular Computing

by Masahiro Inuiguchi; ?Shusaku Tsumoto; ?Shoji Hirano

ISBN13: 9783540364733

ISBN10: 3540364730

Format: Nonspecific Binding

Pub. Date: 2012-12-06

Publisher(s): Springer Nature

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Summary

This monograph presents novel approaches and new results in fundamentals and applications related to rough sets and granular computing. It includes the application of rough sets to real world problems, such as data mining, decision support and sensor fusion. The relationship of rough sets to other important methods of data analysis ' Bayes theorem, neurocomputing and pattern recognition is thoroughly examined. Another issue is the rough set based data analysis, including the study of decision making in conflict situations. Recent engineering applications of rough set theory are given, including a processor architecture organization for fast implementation of basic rough set operations and results concerning advanced image processing for unmanned aerial vehicles. New emerging areas of study and applications are presented as well as a wide spectrum of on-going research, which makes the book valuable to all interested in the field of rough set theory and granular computing.

Bayes' Theorem - the Rough Set Perspective	p. 1
Introduction	p. 1
Bayes' Theorem	p. 2
Information Systems and Approximation of Sets	p. 2
Decision Language	p. 4
Decision Algorithms	p. 5
Decision Rules in Information Systems	p. 6
Properties of Decision Rules	p. 7
Decision Tables and Flow Graphs	p. 8
Illustrative Example	p. 8
Conclusion	p. 11
References	p. 12
Approximation Spaces in Rough Neurocomputing	p. 13
Introduction	p. 13
Approximation Spaces in Rough Set Theory	p. 14
Generalizations of Approximation Spaces	p. 15
Information Granule Systems and Approximation Spaces	p. 16
Classifiers as Information Granules	p. 18
Approximation Spaces for Information Granules	p. 19
Approximation Spaces in Rough-Neuro Computing	p. 20
Conclusion	p. 21
References	p. 22
Soft Computing Pattern Recognition: Principles, Integrations and Data Mining	p. 23
Introduction	p. 23
Relevance of Fuzzy Set Theory in Pattern Recognition	p. 25
Relevance of Neural Network Approaches	p. 27
Genetic Algorithms for Pattern Recognition	p. 28
Integration and Hybrid Systems	p. 29
Evolutionary Rough Fuzzy MLP	p. 30
Data mining and knowledge discovery	p. 31
References	p. 33
Generalizations and New Theories
Generalization of Rough Sets Using Weak Fuzzy Similarity Relations	p. 37
Introduction	p. 37
Weak Fuzzy Similarity Relations	p. 38
Generalized Rough Set Approximations	p. 41
Generalized Rough Membership Functions	p. 43
An Illustrative Example	p. 44
Conclusions	p. 46
References	p. 46
Two Directions toward Generalization of Rough Sets	p. 47
Introduction	p. 47
The Original Rough Sets	p. 48
Distinction among Positive, Negative and Boundary Elements	p. 50
Approximations by Means of Elementary Sets	p. 54
Concluding Remarks	p. 56
References	p. 56
Two Generalizations of Multisets	p. 59
Introduction	p. 59
Preliminaries	p. 60
Infinite Memberships	p. 62
Generalization of Membership Sequence	p. 64
Conclusion	p. 67
References	p. 67
Interval Probability and Its Properties	p. 69
Introduction	p. 69
Interval Probability Functions	p. 70
Combination and Conditional Rules for IPF	p. 74
Numerical Example of Bayes' Formula	p. 75
Concluding Remarks	p. 77
References	p. 77
On Fractal Dimension in Information Systems	p. 79
Introduction	p. 79
Fractal Dimensions	p. 80
Rough Sets and Topologies on Rough Sets	p. 81
Fractals in Information Systems	p. 84
References	p. 86
A Remark on Granular Reasoning and Filtration	p. 89
Introduction	p. 89
Kripke Semantics and Filtration	p. 90
Relative Filtration with Approximation	p. 92
Relative Filtration and Granular Reasoning	p. 94
Concluding Remarks	p. 96
References	p. 96
Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction	p. 97
Introduction	p. 97
Approximation Granules	p. 99
Rough-Fuzzy Granules	p. 101
Granule Decomposition	p. 103
References	p. 106
Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach	p. 109
Introduction	p. 109
Data Based Probabilistic Models	p. 110
Approximate Probabilistic Models	p. 115
Conclusions	p. 120
References	p. 120
Data Mining and Rough Sets
Mining High Order Decision Rules	p. 125
Introduction	p. 125
Motivations	p. 126
Mining High Order Decision Rules	p. 128
Mining Ordering Rules: an Illustrative Example	p. 131
Conclusion	p. 134
References	p. 134
Association Rules from a Point of View of Conditional Logic	p. 137
Introduction	p. 137
Preliminaries	p. 137
Association Rules and Conditional Logic	p. 141
Association Rules and Graded Conditional Logic	p. 143
Concluding Remarks	p. 145
References	p. 145
Association Rules with Additional Semantics Modeled by Binary Relations	p. 147
Introduction	p. 147
Databases with Additional Semantics	p. 148
Re-formulating Data Mining	p. 150
Mining Semantically	p. 151
Semantic Association Rules	p. 152
Conclusion	p. 153
References	p. 155
A Knowledge-Oriented Clustering Method Based on Indis-cernibility Degree of Objects	p. 157
Introduction	p. 157
Clustering Procedure	p. 158
Experimental Results	p. 164
Conclusions	p. 166
References	p. 166
Some Effective Procedures for Data Dependencies in Information Systems	p. 167
Preliminary	p. 167
Three Procedures for Dependencies	p. 168
An Algorithm for Rule Extraction	p. 173
Dependencies in Non-deterministic Information Systems	p. 173
Concluding Remarks	p. 176
References	p. 176
Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength	p. 177
Introduction	p. 177
Temporal Data	p. 178
Rule Induction and Classification	p. 181
Postprocessing of Rules	p. 182
Experiments	p. 182
Conclusions	p. 184
References	p. 184
The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining	p. 187
Introduction	p. 187
The VPRS model and future test cases	p. 188
The VPRSILP model and future test cases	p. 189
A simple-graph-VPRSILP-ESD system	p. 190
VPRSILP and Web Usage Graphs	p. 191
Experimental details	p. 191
Conclusions	p. 195
References	p. 195
Rough Set and Genetic Programming	p. 197
Introduction	p. 197
Rough Set Theory	p. 198
Genetic Rough Induction (GRI)	p. 199
Experiments and Results	p. 202
Conclusions	p. 206
References	p. 207
Conflict Analysis and Data Analysis
Rough Set Approach to Conflict Analysis	p. 211
Introduction	p. 211
Conflict Model	p. 212
System with Constraints	p. 216
Analysis	p. 216
Agents' Strategy Analysis	p. 218
Conclusions	p. 220
References	p. 220
Criteria for Consensus Susceptibility in Conflicts Resolving	p. 223
Introduction	p. 223
Consensus Choice Problem	p. 224
Susceptibility to Consensus	p. 226
Conclusions	p. 232
References	p. 232
Li-Space Based Models for Clustering and Regression	p. 233
Introduction	p. 233
Fuzzy c-means Based on L₁-space	p. 234
Mixture Density Model Based on L₁-space	p. 236
Regression Models Based on Absolute Deviations	p. 237
Numerical Examples	p. 239
Conclusion	p. 239
References	p. 240
Upper and Lower Possibility Distributions with Rough Set Concepts	p. 243
The Concept of Upper and Lower Possibility Distributions	p. 243
Comparison of dual possibility distributions with dual approximations in rough set theory	p. 245
Identification of Upper and Lower Possibility Distributions	p. 245
Numerical Example	p. 248
Conclusions	p. 250
References	p. 250
Efficiency Values Based on Decision Maker's Interval Pairwise Comparisons	p. 251
Introduction	p. 251
Interval AHP with Interval Comparison Matrix	p. 252
Choice of the Optimistic Weights and Efficiency Value by DEA	p. 254
Numerical Example	p. 257
Concluding Remarks	p. 259
References	p. 259
Applications in Engineering
Rough Measures, Rough Integrals and Sensor Fusion	p. 263
Introduction	p. 263
Classical Additive Set Functions	p. 264
Basic Concepts of Rough Sets	p. 264
Rough Measures	p. 265
Rough Integrals	p. 265
Multi-Sensor Fusion	p. 268
Conclusion	p. 270
References	p. 271
A Design of Architecture for Rough Set Processor	p. 273
Introduction	p. 273
Outline of Rough Set Processor	p. 273
Design of Architecture	p. 275
Discussions	p. 279
Conclusion	p. 280
References	p. 280
Identifying Adaptable Components - A Rough Sets Style Approach	p. 281
Introduction	p. 281
Defining Adaptation of Software Components	p. 281
Identifying One-to-one Component Adaptation	p. 282
Identifying One-to-many Component Adaptation	p. 288
Conclusions	p. 289
References	p. 290
Analysis of Image Sequences for the UAV	p. 291
Introduction	p. 291
Basic Notions	p. 292
The WITAS Project	p. 293
Data Description	p. 294
Tasks	p. 295
Results	p. 296
Conclusions	p. 299
References	p. 300
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