Granular computing: at the junction of rough sets and fuzzy sets

✍ Scribed by Rafael Bello

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 352
• Series: Studies in Fuzziness and Soft Computing
• Edition: 1
• Category: Library

✦ Synopsis

This volume is a compilation of the best papers presented at the First International Symposium on Fuzzy and Rough Sets (ISFUROS 2006) held in Santa Clara, Cuba. They contain valuable contributions both in the theoretical field and in several application domains such as intelligent control, data analysis, decision making and machine learning, just to name a few. Together, they capture the huge potential of the aforementioned methodologies.

✦ Table of Contents

Studies in Fuzziness and Soft Computing......Page 3
Granular Computing: At the Junction of Rough Sets and Fuzzy Sets......Page 4
Preface......Page 8
Contents......Page 10
List of Contributors......Page 14
Part I: Fuzzy and Rough Sets. Teoretical and Practical Aspects......Page 18
Introduction......Page 20
Tolerance Relations and Non-symmetric Similarity Relations......Page 21
Object-Oriented Rough Sets......Page 23
Missing Value Semantics in the Object--Oriented Rough Sets......Page 28
Well-Defined Structures with Null Value Objects......Page 29
Tolerance Relations in Object--Oriented Rough Sets......Page 30
Characterization of Absence of Values" Based on IS-A Relationship......Page 32<br>Non-symmetric Similarity Relations in Object-Oriented Rough Sets......Page 35<br>Conclusion......Page 36<br>References......Page 37<br>Introduction......Page 40<br>Probabilistic Valuations of the Formulas in Classical Logic......Page 42<br>Formal Contexts, Statistical Inferential Bases and Indiscernibility......Page 43<br>Vague Properties and Similarities......Page 47<br>Probabilistic Logic in Fuzzy Framework......Page 50<br>Fuzzy Statistical Inferential Bases......Page 51<br>The Actual Case and Its Similar Past Cases......Page 53<br>Fuzzy Statistical Inferential Bases Induced by a Piece of Information and the Step-by-Step Inferential Process......Page 54<br>Conclusions and Future Work......Page 57<br>References......Page 58<br>Introduction......Page 60<br>Multi-dimensional Index Structure......Page 62<br>Similarity Measurement......Page 63<br>Querying the M-Tree......Page 66<br>Performance Experiments......Page 68<br>References......Page 70<br>Abstract Rough Approximation Spaces......Page 72<br>Topological Rough Approximation Spaces......Page 74<br>The Partition Approach to Rough Set Theory......Page 75<br>Entropy (as Measure of Average Uncertainty) and Co--entropy (as Measure of Average Granularity) of Partitions......Page 76<br>The Lattice of Partitions and the Monotonic Behavior of Entropy and Co--entropy......Page 79<br>Local Rough Granularity Measure in the Case of Partitions......Page 81<br>Application to Complete Information Systems......Page 84<br>Entropy and Co--entropy of Coverings: The Global Approach......Page 87<br>Quasi--orderings for Coverings......Page 89<br>ThePointwise'' Quasi--orderings on Coverings......Page 90
Pointwise Lower and Upper Entropy and Co--entropy from Coverings......Page 91
Conclusions......Page 92
References......Page 93
Introduction......Page 96
The Description of the RSDS System......Page 97
Adding New Data to the System......Page 98
Searching for Information......Page 99
The RSDS Data and the Construction of the Collaboration Graph......Page 102
The Properties of the Collaboration Graph......Page 103
The Evolution of the Collaboration Graph over Time......Page 106
Open Questions and Directions for Future Work......Page 107
References......Page 109
Introduction......Page 110
Background......Page 111
Bayesian Networks......Page 112
Possibilistic Networks......Page 113
The Quantitative Component: Visualization......Page 114
The Possibilistic Case......Page 117
Real-Life Dataset......Page 118
Conclusion and Future Work......Page 120
References......Page 121
Introduction......Page 122
Concept Modifiers......Page 123
The $Reference Frame$ Model......Page 127
A Two-Level Approach......Page 130
Comparison Between the Two Models......Page 132
Case of Study......Page 133
Conclusions......Page 136
References......Page 137
Introduction......Page 138
Fuzzy Sets and Games......Page 139
Nonzero-Sum Games......Page 140
Coevolutionary Algorithm to Solve Fuzzy Games......Page 141
Numerical Experiments......Page 144
Conclusions......Page 146
References......Page 147
Introduction......Page 148
Rough Set Theory: Fundamental Ideas......Page 149
Conventional Deinterlacing Methods......Page 151
Rough Set-Based Deinterlacing: Attributes Definition......Page 153
Experimental Results......Page 161
References......Page 163
Part II: Fuzzy and Rough Sets in Machine Learning and Data Mining......Page 166
Introduction......Page 168
By Using the Measurement Theory and Interpolation......Page 169
By Means of Evolutionary Algorithms......Page 170
A New Approach to Create Membership Functions......Page 171
Building the Membership Functions......Page 172
The Associative Fuzzy Neural Network......Page 174
Experimental Results and Discussion......Page 175
References......Page 177
Introduction......Page 180
Agglomerative Clustering Method (AddC)......Page 182
Evolving--Agglomerative Clustering Method (eACM)......Page 183
Quantitative Analysis of Clustering Algorithms......Page 185
Takagi-Sugeno Fuzzy System......Page 188
Algorithm for Structure Identification and Parameters Determination......Page 189
Mackey--Glass Time Series Data Set......Page 191
References......Page 194
Introduction......Page 196
Information Retrieval Methods Based on Concepts......Page 200
Fuzzy Model for Synonymy and Polysemy......Page 204
Adjusting the Vector Space Model......Page 206
Query Expansion......Page 210
Conclusions......Page 211
References......Page 213
Introduction......Page 216
A Look into the Problem......Page 217
Rough Set Theory......Page 218
Basic Concepts of Rough Set Theory......Page 219
RST-Based Measures for Decision Systems......Page 220
A Study on the Estimation Capability of the RST Measures......Page 221
Building the Dataset......Page 222
Machine Learning Techniques to Rule Generation......Page 223
Appraising the Performance of the Fittest Classifier......Page 225
References......Page 226
Introduction......Page 228
Dataset Description......Page 231
Rough Sets......Page 232
Methods......Page 235
Results......Page 237
Discussion......Page 240
References......Page 242
Introduction......Page 246
Rough Set Theory......Page 247
Measures for Decision Systems Using Rough Set Theory......Page 249
Rough Text Definition......Page 252
Rough Text and Clustering Validity Measures......Page 253
The Application of Rough Text in Clustering Validity......Page 255
Illustrating the Use of Rough Text in Clustering Validity......Page 256
Evaluating the New Method Using Rough Text for Clustering Validity......Page 258
Other Applications of Rough Text in Text Mining......Page 261
Conclusions......Page 263
References......Page 264
Introduction......Page 266
HIV Biology and Lifecycle......Page 267
Data Material and Methods......Page 268
Results......Page 271
Discussion......Page 272
References......Page 274
Part III: Fuzzy and Rough Sets in Decision-Making......Page 276
Introduction......Page 278
Information System with Ambiguous Decisions in Evaluation Problems......Page 279
Numerical Example......Page 280
Removal of Unnecessary Divisions Between Decision Values......Page 282
References......Page 283
Introduction......Page 286
Region Classifier Based on Fuzzified Edge Detector......Page 287
Expanded Cubic Curve Fitting (ECCF) Method......Page 290
Case 1 - $R_1$ Region: $90\circ$ (Vertical) Direction......Page 291
Case 3 - $R_3$ Region: $45\circ$ Direction......Page 293
Case 5 - $R_5$ Region: $30\circ$ Direction......Page 295
Case 6 - $R_6$ Region: $−30\circ$ Direction......Page 296
Case 8 - $R_8$ Region: $−60\circ$ Direction......Page 297
Experimental Results......Page 298
References......Page 301
Introduction......Page 304
Reverse Prediction......Page 305
Coverage and Certainty......Page 307
Electronic Purchasing Application......Page 308
Evaluation of Reverse Prediction Algorithm......Page 311
Algorithms for Ordinary Prediction......Page 313
RSES, Rosetta and RSGUI......Page 316
RSES......Page 318
Rosetta......Page 319
Comparison with RSGUI......Page 320
Conclusion......Page 321
References......Page 322
Introduction......Page 324
Fuzzy Numbers......Page 326
Proposed Algorithm......Page 327
Description of the Algorithm......Page 328
Computational Results......Page 329
Implemented Order Relations......Page 330
Illustrative Example......Page 331
Conclusions......Page 335
References......Page 336
Introduction......Page 338
The Influence of the Temperature in the Reduction Process......Page 339
Description of the Combustion Process with Secondary Air in Hearth 4......Page 340
The Process Model......Page 341
Linear Local Controllers......Page 342
Adaptive Control......Page 343
Fuzzy Operators......Page 345
Simulation Results......Page 346
Conclusions......Page 348
References......Page 349
Index......Page 350
Author Index......Page 352