Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing: 10th International Conference, RSFDGrC 2005, Regina, Canada, August 31 - September 3,

Front matter......Page 1
Rough Sets......Page 23
Flow Graphs......Page 24
Certainty and Coverage Factors......Page 28
Flow Graph and Decision Algorithms......Page 30
Conclusion......Page 32
Introduction......Page 34
Information Systems and Informational Relations......Page 35
The Information Logic IND......Page 37
Equivalence of the Abstract, Standard and Non-standard Semantics of IND......Page 38
A Complete Axiomatization of IND......Page 41
Decidability of IND......Page 42
Open Problems and Concluding Remarks......Page 44
Introductory Comments......Page 45
Shadowed Sets as a Symbolic Manifestation of Fuzzy Sets......Page 46
The Development of Shadowed Sets......Page 48
Relational Calculus with Shadowed Sets and Relational Equations......Page 50
Taxonomy of Data in Structure Description......Page 51
References......Page 53
Introduction......Page 55
Approximation Spaces and Their Inductive Extensions......Page 56
Approximate Reasoning About Vague Concepts Based on Adaptive Learning and Reasoning......Page 57
An Example: Inducing Concept Descriptions Consistent with Constraints Specified by Experts......Page 61
Conclusions......Page 63
Introduction......Page 65
Formal Contexts and Rough Approximation Operators......Page 66
Attribute Reduction in Concept Lattices......Page 70
Object Reduction in Concept Lattices......Page 72
Conclusions......Page 74
Introduction......Page 76
Problem Statement......Page 77
Dominance Relations......Page 78
Dominance Principle......Page 80
Decision and Condition Granules......Page 81
Dominance-Based Rough Approximations......Page 82
Conclusions......Page 85
Introduction......Page 86
Standard and Generalized Rough Sets......Page 87
New Approach for Rough Sets......Page 89
Conclusion......Page 94
Introduction......Page 96
Basic Definitions in Formal Concept Analysis......Page 97
Basic Connection Between FCA and RST......Page 98
Relationship Between Concept Lattice and the Power Set of Partition......Page 99
Transformation Between Concept Lattice and Partition......Page 100
Example......Page 103
Conclusions......Page 104
Introduction......Page 106
Consistent Generalized Approximation Representation Spaces......Page 107
Characterizations of Attributes in Consistent Generalized Approximation Representation Spaces......Page 111
Conclusions......Page 114
Introduction......Page 116
Proximity Structures......Page 117
Proximal Frege Structures......Page 119
Ortholattice of Exact Sets......Page 120
Models of PFS......Page 121
Conclusion......Page 123
Introduction......Page 126
The Basic Theory of Rough Sets......Page 127
Rough Group and Rough Subgroup......Page 128
Rough Coset......Page 129
Homomorphism and Isomorphism of Rough Group......Page 130
Examples......Page 133
Conclusion......Page 134
Introduction......Page 136
Formal Contexts and Concept Lattices......Page 137
Information Systems and Approximation Spaces......Page 138
General Approximation Spaces......Page 139
Representations......Page 141
Concept Lattices and Approximation Spaces......Page 142
Introduction......Page 146
Matrices Representations of Rough Sets......Page 147
Approximation Operators in Boolean Algebras......Page 149
Rough Set Algebras......Page 151
Conclusions......Page 153
Introduction......Page 154
Preliminaries......Page 155
The General Case......Page 157
Other Properties......Page 160
Conclusion......Page 162
Introduction......Page 163
Definitions and Notations......Page 164
Logic with Rough Double Stone Algebraic Semantics......Page 166
Conclusion......Page 169
Introduction......Page 171
Greedy Algorithm for Partial Cover Construction......Page 173
Greedy Algorithm for Partial Test Construction......Page 174
Results of Experiments......Page 176
Conclusion......Page 177
Introduction......Page 178
The Reduct Algorithm Based on Attribute Order [1]......Page 179
The Second Attribute and the Second Attribute Theorem......Page 180
Rules on Attribute Moving [2]......Page 182
Basic Decision Theorem......Page 183
The Second Attribute Algorithm......Page 184
The Second Attribute Algorithm......Page 185
Computational Complexity......Page 186
Conclusion......Page 187
Introduction......Page 188
Cores and Reducts......Page 189
Pairwise Core Graph......Page 192
Application of the Pairwise Cores for Reducts Finding......Page 194
Experimental Results......Page 195
Conclusions......Page 197
Introduction......Page 198
Kappa Coefficient......Page 199
Non-supervised Kappa Coefficient......Page 200
Choice Procedure......Page 201
Experimentation......Page 202
Conclusion......Page 205
Introduction......Page 207
Principle of Incremental Attribute Reduction......Page 208
Incremental Attribute Reduction Algorithm Based on Elementary Sets......Page 209
Experiment Results......Page 211
Test on Inconsistent Dataset......Page 212
Continuous Incremental Learning Test......Page 213
Conclusion......Page 214
Introduction......Page 216
Rough Set Attribute Reduction......Page 217
Discernibility Matrix-Based Selection......Page 219
Finding Rough Set Reducts......Page 221
Evaluation......Page 223
Conclusion......Page 224
Introduction......Page 226
Brief of Feature Selection......Page 227
Evolution of Rough Sets Based Feature Selection......Page 228
Average Support Heuristic......Page 229
Lower Approximation with Unknown a Priori Probability......Page 230
Lower Approximation with Known a Priori Probability......Page 231
Comparison of PASH with the Other Three Methods......Page 232
Approximate Reducts with Different Parameter Levels......Page 233
Concluding Remarks......Page 234
Introduction......Page 236
Rough Set Approach......Page 237
Relative Attribute Dependency Based on Rough Set Theory......Page 238
A Heuristic Algorithm for Finding Optimal Reducts......Page 239
Experiments......Page 241
Related Work......Page 242
Summary and Future Work......Page 243
Introduction......Page 246
Preliminaries......Page 247
Extensions of Information Systems......Page 248
Generating Extensions of Information Systems......Page 252
Conclusions......Page 254
Introduction......Page 256
Categories of Information Tables......Page 257
Relations......Page 258
Granularity......Page 259
Discernibility and Reduction......Page 260
Galois Connection......Page 263
Discussion......Page 264
Conclusion......Page 265
Introduction......Page 266
Blocks of Attribute-Value Pairs......Page 268
Definability......Page 271
Lower and Upper Approximations......Page 272
Conclusions......Page 274
Introduction......Page 276
Basic Definitions......Page 277
Theoretical Foundations of Rule Generation in NISs......Page 278
A Problem on Minimal Rule Generation in NISs......Page 280
Discernibility Functions and Minimal Certain Rules......Page 281
Minimal Certain Rule Generation in DGC Class......Page 282
Minimal Possible Rule Generation in Other Classes......Page 284
Concluding Remarks......Page 285
Introduction......Page 287
Definitions......Page 288
Studies in the Propositional Case......Page 290
Studies in `Multiple Rows Per Example' Case......Page 292
Application to Predictive Toxicology......Page 294
Conclusions......Page 295
Introduction......Page 297
Background: Rough Sets and Rough Relational Database......Page 298
Rough Functional Dependencies......Page 299
Rough Normal Forms......Page 300
Rough Third Normal Form......Page 301
References......Page 303
Introduction......Page 305
Classification and Probabilistic Knowledge......Page 306
Probabilistic Dependencies Between Sets......Page 307
Probabilistic Rules......Page 308
Probabilistic Approximation Regions......Page 309
Elementary, Composed and Binary Attributes......Page 311
Probabilistic Dependencies Between Attributes......Page 312
Optimization and Evaluation of Attributes......Page 313
Conclusion......Page 314
Introduction......Page 316
Preliminaries and Notations......Page 317
Rough Sets Approach Based on Information Gain......Page 318
Extraction Method of Decision Rules from Approximate Regions......Page 320
Applications to Human Sensory Evaluation Data......Page 323
Conclusions......Page 325
Introduction......Page 326
Decision Tables......Page 327
Rough Sets and Variable Precision Rough Sets......Page 329
Agreement Ratio......Page 330
Upper Estimation of a Rough Membership Value......Page 331
Modified Approximations and Modified Agreement Ratios......Page 332
A Numerical Example......Page 333
Introduction......Page 336
Confirmation Measures......Page 338
Decision Rules and Decision Algorithm......Page 339
Confirmation Measures and Decision Algorithms......Page 340
Parameterized Rough Sets......Page 343
Conclusions......Page 346
Introduction......Page 347
Methods Based on Rough Sets......Page 348
Methods of Possible Tables......Page 350
Methods of Valued Tolerance Relations......Page 351
Revising Methods of Valued Tolerance Relations......Page 352
Conclusions......Page 355
Introduction......Page 357
Bayesian Networks......Page 358
Rough Set Flow Graphs......Page 359
The Complexity of Inference......Page 362
Other Remarks on Rough Set Flow Graphs......Page 364
Conclusion......Page 365
Introduction......Page 367
Fuzzy Plausibility and Belief Functions......Page 368
Fuzzy Rough Sets......Page 369
Connections Between Fuzzy Approximation Spaces and Fuzzy Belief Structures......Page 371
Conclusion......Page 373
Introduction......Page 376
Decision Tables with Fuzzy Attributes......Page 377
Similarity Relations for Condition and Decision Attributes......Page 378
Variable Precision Fuzzy Rough Approximations......Page 379
Example......Page 382
Conclusions......Page 384
Introduction......Page 386
Compatibility Relations......Page 387
Generalized Rough Set Approximations......Page 388
Generalized Rough Membership Functions......Page 390
An Illustrative Example......Page 392
Conclusions......Page 393
Introduction......Page 395
Fuzzy Sets and Mass Assignment......Page 396
Rough Fuzzy Sets......Page 397
Roughness Measures of Fuzzy Sets......Page 398
Rough Approximation Quality of a Fuzzy Classification......Page 399
An Illustration Example......Page 401
Conclusions......Page 403
Induction of Decision Rules Based Upon Rough Sets Theory......Page 405
Rules in Fuzzy Form......Page 408
The Genetic Algorithm Application for Rules Fuzzification......Page 409
Numerical Examples......Page 410
Conclusions......Page 411
Introduction......Page 414
FLC Design for MIMO System......Page 415
RST-Based Rapid Algorithm of Fuzzy Rules Extraction......Page 417
Simulation Research......Page 420
Conclusion......Page 422
Introduction......Page 424
Interpretable Rule Extraction from I/O Data Using Grid Partitioning......Page 425
Interpretable Rule Extraction from I/O Data Using Clustering Partitioning......Page 427
Example of Interpretable Rule Extraction Using the TaSe Model......Page 429
Conclusions......Page 432
Introduction......Page 434
The ReliefF Algorithm......Page 435
The Feature Weighted Clustering Algorithm......Page 436
Experiment with Numerical Data Set......Page 438
Experiment with Categorical Data Set......Page 439
Experiment with Mixed Data Set......Page 440
Conclusions......Page 441
Introduction......Page 443
Unsupervised Fuzzy Partition of the Feature Space......Page 444
Structural Data Analysis......Page 446
Partially Supervised Clustering for Semantic Classification......Page 448
Experimental Results......Page 450
Conclusions......Page 451
Introduction......Page 453
Similartaxis and Dissimilation......Page 454
The Application of MEA......Page 455
Clone Mind Evolutionary Algorithm (CMEA)......Page 456
Convergence Analysis of CMEA......Page 458
Research Example......Page 460
Conclusion......Page 461
Introduction......Page 463
Estimation of Distribution Algorithm with Infinite Population Size......Page 464
Upper Bounds on Time Complexity of Global Convergence......Page 466
Computation of Global Convergence Stopping Time......Page 469
References......Page 471
Introduction......Page 473
Related Rough Set Concepts......Page 474
Standard PSO Algorithm......Page 475
Representation of Velocity......Page 476
Velocity Limitation (Maximum Velocity, Vmax)......Page 477
Experiments......Page 478
Conclusions......Page 480
Introduction......Page 483
Influence on LFMCW Radar of Nonlinearities of VCO......Page 484
Brief Introduction of MEA......Page 486
The Conception of the Subsection Nonlinearity Correction Method Based on MEA......Page 487
Structure for Fitness Function......Page 488
Experiment Results......Page 489
Conclusion......Page 491
Introduction......Page 493
Notations......Page 494
Rank of Contingency Table (Multi-way)......Page 495
Rank and Subdeterminant......Page 496
Determinantal Divisors......Page 497
Divisors and Degree of Dependence......Page 498
Degree of Granularity and Dependence......Page 499
Conclusion......Page 501
Introduction......Page 503
The Problem of Learning from the Statistical Point of View......Page 504
Bounds for Classifier Error Estimation......Page 505
Model Selection and Assessment......Page 511
Introduction......Page 513
Causal Discovery with Graphical Models......Page 514
DepenBag......Page 515
Empirical Study......Page 517
Comparison on Generalization Error......Page 518
Error-Ambiguity Decomposition......Page 519
Conclusion......Page 520
Introduction......Page 523
Metric Based Generalization of Minimal Consistent Rules......Page 524
Effective Classification by Minimal Consistent Rules......Page 525
Metric Based Generalization of Classification by Minimal Consistent Rules......Page 526
Combination of k Nearest Neighbors with Generalized Rule Induction......Page 529
Experimental Results......Page 531
Conclusions......Page 532
Introduction......Page 534
Classifier Combination for WSD......Page 536
Bayesian Combination Strategy......Page 537
The Combination Strategy Based on OWA Operators......Page 538
Multi-representation of Context for WSD......Page 540
Experimental Results......Page 541
Conclusion......Page 542
Introduction......Page 544
Fusion of Degradation Factors Sequenced by Time......Page 548
Machine Learning in Time-Sequenced Data Fusion Model......Page 550
Example of Predicting Jet Engine Disintegration......Page 551
Conclusion......Page 552
Introduction......Page 554
Definitions......Page 556
The Block Algorithm......Page 557
Multidimensional U-Scoring......Page 559
Application of the Method......Page 560
Conclusions......Page 561
Introduction......Page 563
Paper Structure......Page 564
Objectiveness, Subjectiveness and Vagueness......Page 565
Similarity Spaces......Page 566
Approximations and Vagueness......Page 567
Examples......Page 569
Relation to Other Approaches and Conclusion......Page 571
Introduction......Page 573
Measuring Problem Solving Performance: Optimization Under Bounded Resources......Page 574
The $-Calculus Algebra of Bounded Rational Agents......Page 576
The $-Calculus Syntax......Page 577
The $-Calculus Semantics: The $k\Omega$-Search......Page 578
Probabilistic, Fuzzy Sets and Rough Sets Performance Measure......Page 579
The $-Calculus Support for Intractability: Optimization Under Bounded Resources and Total Optimality......Page 581
Conclusions......Page 582
Introduction......Page 583
The Preliminaries......Page 585
The Entropy and Partitions......Page 586
The Graph-Theoretical Representation of Partitions and Entropy......Page 590
Conclusions......Page 591
Introduction......Page 593
Data Preparation......Page 595
Method for Comparison......Page 596
Experimental Result......Page 597
Discussion......Page 601
Introduction......Page 603
Background......Page 604
Computational Complexity of Exact Inference: The Consensus......Page 605
Inconsistency in the Consensus......Page 606
Exploring the Inconsistency......Page 607
A Variant of the 3SAT Problem......Page 608
The Complexity of Exact Inference in Singly Connected BNs......Page 610
Concluding Remarks......Page 611
Introduction......Page 613
The Semantics of Processes......Page 614
An Example: Pendulum and Balls Scenario......Page 615
An Axiomatization of Pendulum and Balls Scenario......Page 616
Soundness and Completeness Theorem......Page 618
Implementation......Page 621
References......Page 622
Introduction......Page 623
Goyal and Egenhofer's Model......Page 624
Mathematical Morphological Model......Page 625
Fuzzy Set Theory......Page 628
Modeling and Refining Cardinal Directional Relationships Between Fuzzy Regions......Page 629
Computational Problems......Page 630
Simulation Experiment......Page 631
Conclusions......Page 632
Introduction......Page 634
Data Structure......Page 635
Target Series Selection......Page 636
Data Cleansing and Interpretation......Page 637
Multiscale Comparison of Pass Sequences......Page 638
Grouping of Sequences by Rough Clustering......Page 640
Experimental Results......Page 641
Conclusions......Page 642
Introduction......Page 644
Basic Definitions......Page 645
Information Maps of Data Tables......Page 646
Spatio-temporal Modelling of Objects......Page 647
Hierarchical Information Maps......Page 649
Constructing Higher Levels of Hierarchical Maps by Information Granulation......Page 651
Conclusions......Page 652
Introduction......Page 654
Direct Fusion in Epistemic Logic......Page 655
Ordered Fusion in Epistemic Logic......Page 656
Direct Fusion in Possibilistic Logic......Page 658
Level Cutting Fusion in Possibilistic Logic......Page 659
Level Skipping Fusion in Possibilistic Logic......Page 660
Concluding Remarks......Page 662
Introduction......Page 664
A Quick Overview of First-Order Modal Logic......Page 665
Fuzzy First-Order Modal Logic with Believable Degrees......Page 666
Fuzzy Reasoning and Satisfiability......Page 669
Conclusion and Further Works......Page 672
Introduction......Page 673
Decision Logic......Page 674
Arrow Logic......Page 675
Pairwise Comparison Table......Page 676
Formulas and Semantics of ADL......Page 677
An Example......Page 678
Conclusions......Page 679
Introduction......Page 682
P-Systems, Classification and Approximation......Page 683
From Information Systems to Information Quantum Relational System......Page 685
Comparing Information Systems......Page 686
Transforming Perception Systems......Page 688
Example......Page 689
Dichotomic, Functional and Nominal Systems......Page 690
Conclusions......Page 691
Introduction......Page 693
EVALPSN Overview......Page 694
EVALPSN Stable Model......Page 696
Cat and Mouse Example......Page 697
Cat and Mouse Control in EVALPSN......Page 698
Examples......Page 701
Conclusion......Page 702
Introduction......Page 704
Tolerance Relation System......Page 705
The Nested Tolerance Covering System......Page 706
The Construction of Tolerance Relation Based Granular Space......Page 708
Decision Granular Lattice......Page 710
Conclusion......Page 712
Introduction......Page 714
Reduction and Partition......Page 715
Discernible Granularity......Page 717
Evaluation of Granularity......Page 718
Experiments......Page 719
Conclusion......Page 721
Introduction......Page 723
Positive Approximation......Page 724
Application......Page 726
Case Study......Page 727
Conclusions......Page 729
Introduction......Page 731
A Granular Logic with Closeness Relation $ im_\lambda$......Page 732
Closeness Relation $ im_\lambda$ and Its Relative Properties......Page 734
Reasoning Rules......Page 735
Reasoning in Granular Logic with Closeness Relation $ im_\lambda$......Page 736
Conclusion......Page 737
Introduction......Page 740
Approximation Spaces......Page 741
Rough Information Granules and Transducers......Page 742
Approximation of Concepts and Dependencies from Ontology......Page 743
Models of Real World Entities......Page 750
Geometric and Algebraic Views......Page 751
Knowledge Representations......Page 752
Relational Tables - Representations of Partitions......Page 753
Granular Tables......Page 754
Topological Tables......Page 756
Conclusions......Page 758
Back matter......Page 760