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Tables of Contents for Fuzzy Sets in Approximate Reasoning and Information Systems
Chapter/Section Title
Page #
Page Count
Series Foreword
xi
Contributing Authors
xiii
Introduction
1
14
Didier Dubois
Henri Prade
James Bezdek
PART I REASONING
Fuzzy Sets and Possibility Theory in Approximate and Plausible Reasoning
15
176
Bernadette Bouchon-Meunier
Didier Dubois
Lluis Godo
Henri Prade
Introduction
15
3
The Emergence of Fuzzy Set-Based Approximate Reasoning
16
1
Organization of the Chapter
17
1
A Refresher on Possibility Theory and Fuzzy Connectives
18
13
A Short Course on Possibility Theory
18
7
Fuzzy Connectives: Negations, Conjunctions and Disjunctions
25
2
Fuzzy Implications
27
4
Representation of Fuzzy Statements
31
12
Linguistic Variables
32
1
Linguistic Modifiers
33
2
Modelling Elementary Fuzzy Statements
35
4
Compound Fuzzy Statements
39
4
Representation of Qualified and Quantified Fuzzy Statements
43
16
Fuzzy Truth-Values
43
3
Truth Qualified Statements
46
2
Graded Truth Versus Degrees of Uncertainty: The Compositionality Problem
48
3
Certainty and Possibility Qualification
51
3
Probability Qualification
54
1
Fuzzy Quantified Statements
55
4
The Representation of Fuzzy Rules
59
15
The Non Fuzzy Case: Relational and Meta Level Views
59
2
Fuzzy Rules: Implication-Based Models
61
3
Fuzzy Rules: Conjunction-Based Models
64
2
Metalevel Models of Fuzzy Rules
66
1
Comparison Between Fuzzy Rules
66
5
Other Representational Issues on Fuzzy Rules
71
3
Basic Principles of Fuzzy Inference
74
10
Combination and Projection Principles
74
3
Generic Fuzzy Reasoning Techniques
77
7
Elementary Fuzzy Inference: The Generalized Modus Ponens
84
12
Basic Forms of the Generalized Modus Ponens
84
2
Properties of the Generalized Modus Ponens
86
2
Retrieving Modus Ponens as a Particular Case
88
3
Generalized Modus Ponens and Fuzzy Truth-Values
91
2
Inference with Fuzzy Meta-Rules
93
3
Systems of Fuzzy Rules
96
14
Compound Condition Parts
96
1
Systems of Parallel Rules
97
8
Chaining
105
2
Consistency Checking and Redundancy Elimination
107
3
Inference with Certainty Factors and Approximate Reasoning
110
8
The Certainty Factor Approach
110
2
Certainty Factors and Multiple-Valued Logic
112
4
A Possibility-Theoretic View of Certainty Factors
116
2
Specialized Forms of Fuzzy Deductive Reasoning
118
21
A Deductive Approach to Interpolative Reasoning
118
4
Deductive Similarity Reasoning
122
3
Possibilistic Logic
125
2
The Semantic Agreement Between Many-Valued Logics, Uncertain, and Approximate Reasoning
127
2
Reasoning about Preferences
129
4
Fuzzy Temporal Reasoning
133
3
Fuzzy Qualitative Reasoning
136
3
Fuzzy Set-Based Plausible Reasoning
139
21
Plausible Similarity-Based Reasoning
139
4
Reasoning with Fuzzy Quantifiers
143
3
Nonmonotonic Reasoning
146
8
Fuzzy Causal Reasoning
154
6
Conclusion
160
31
References
162
29
Weighted Inference Systems
191
52
Vilem Novak
Introduction
191
2
Formal Inference and its Interpretation
193
3
Truth Values in Many-Valued Logic
196
3
Many-Valued, Fuzzy and Possibilistic Logic
199
26
Historical Remarks
199
2
Lukasiewicz Logic
201
3
Fuzzy Logic in Narrow Sense
204
8
Monoidal Logic as Aggregating View
212
3
Possibilistic Logic
215
8
Some Other Logic Kinds of Weighted Reasoning Systems
223
2
Rule-Based Inference Systems
225
2
Fuzzy Logic Programming
227
7
Theoretical Aspects of Fuzzy Logic Programming
227
6
Attempts at Fuzzy PROLOG
233
1
Summary and Conclusion
234
9
References
235
8
Closure Operators in Fuzzy set Theory
243
36
Loredana Biacino
Giangiacomo Gerla
Introduction
243
1
Closure Operators in a Lattice
244
2
Abstract Logics
246
1
Continuity for Abstract Logics
247
1
Step-by-step Deduction Systems
247
2
Logical Compactness
249
1
Basic Notions in Fuzzy Sets Theory
250
3
Abstract Fuzzy Logic
253
3
Pavelka's Logic
256
3
Logical Compactness and Ultraproducts
259
2
An extension Principle for Deduction Operators
261
3
Extending Compact Deduction Systems
264
2
Similarity Logic
266
1
Ying's Similarity Logic
267
2
Stratified Fuzzy logic
269
3
Graded Consequence Relations
272
7
References
277
2
PART II LEARNING AND FUSION
Learning Fuzzy Decision Rules
279
26
Bernadette Bouchon-Meunier
Christophe Marsala
Introduction
279
1
Fuzzy Decision Rules
280
1
Inductive Learning of Fuzzy Rules
281
12
General Inductive Learning Method
282
1
Fuzzy Decision Trees
283
7
Fuzzy Prototypes
290
1
Determination of Fuzzy Modalities
291
1
Other Methods of Inductive Rule Construction
292
1
Applications of Fuzzy Inductive Learning
292
1
Tuning Fuzzy Rules
293
6
Self Learning
294
1
Utilization of a Fuzzy Model of the Process
294
2
Fuzzy Relational Equations
296
1
Clustering Methods
297
1
Optimization
297
1
Genetic Algorithms
298
1
Conclusion
299
6
References
299
6
Neuro-Fuzzy Methods in Fuzzy Rule Generation
305
30
Detlef Nauck
Rudolf Kruse
Introduction
305
2
Structure Learning --- Creating Fuzzy Rules
307
8
Cluster-Oriented Approaches to Learn Fuzzy Rules
308
3
Hyperbox-Oriented Approaches to Learn Fuzzy Rules
311
1
Structure-Oriented Approaches to Learn Fuzzy Rules
312
3
Parameter Learing --- Adapting Fuzzy Sets
315
12
Adapting Fuzzy Sets by Gradient Descent
316
2
Adapting Fuzzy Sets with ANFIS
318
2
Adapting Fuzzy Sets by Simple Heuristics
320
7
Tuning Fuzzy Rules with Adaptive Weights
327
4
Conclusions
331
4
References
332
3
Merging Fuzzy Information
335
68
Didier Dubois
Henri Prade
Ronald Yager
Introduction
335
2
Information Fusion
337
6
Characteristics of the Information Fusion Problem
337
2
Some Limitations of a Pure Probabilistic Approach to Fusion
339
4
The Possibilistic Representation of Incomplete Data
343
7
Possibility Theory: A Refresher
343
2
Building Possibility Distributions
345
5
The Fusion of Possibility Distributions
350
11
Basic Symmetric Combination Modes in the Possibilistic Setting
351
5
Expected Formal Properties of Combination Rules
356
5
Refined Fusion Modes
361
12
Assessment of the Reliability of Sources
361
8
Fusion with Unequally Reliable Sources
Adaptive Fusion
369
4
Fuzzy Estimation
373
7
Fuzzy Extension of Estimation Techniques
373
2
Constrained Merging
375
5
Possibilistic Fusion Under A Priori Knowledge
380
6
Revision with Fuzzy Inputs
381
4
Multisource Fusion under a Priori Knowledge
385
1
Syntactic Combination of Logical Databases in Possibilistic Logic
386
5
From Prioritized Logical Databases to Possibility Distributions
387
1
Syntactic Combination Modes
388
3
Conclusion
391
12
References
392
11
PART III FUZZY INFORMATION SYSTEMS
Fuzzy Databases
403
66
Patrick Bosc
Bill B. Buckles
Frederick E. Petry
O. Pivert
Introduction
403
1
Fuzzy Querying in Relational Databases
404
24
Overview of Relational Databases
405
4
Relations with Weighted Tuples
409
1
Modeling Fuzzy Queries
409
5
Flexible Queries Against Crisp Databases
414
2
A Relational Algebra for Fuzzy Relations
416
3
SQLf, an SQL-Like Fuzzy Query Language
419
3
Implementation Aspects and Query Processing
422
5
Cooperative Answering
427
1
Uncertainty and Incompleteness in Relational Databases
428
12
Non Possibilistic Approaches to Imprecise Values
429
3
The Possibilistic Model for Relational Databases
432
3
Queries in the Possibilistic Framework
435
5
Similarity in Relational Databases
440
12
Introduction
440
2
Similarity Thresholds and Relational Algebra Operations
442
1
Redundancy and Uniqueness Properties
443
3
Query Evaluation in the Similarity Based Framework
446
1
Proximity-Based Models
447
1
Application to Security
448
4
Data Integrity and Dependencies
452
2
Other Data Models
454
6
Fuzzy Extensions for Entity-Relationship Models
454
1
Extended Semantic Model
455
2
Network Data Models
457
1
Object-Oriented Model
457
3
Conclusion
460
9
References
462
7
Fuzzy Set Techniques in Information Retrieval
469
32
Donald H. Kraft
Gloria Bordogna
Gabriella Pasi
Introduction
469
3
Information Retrieval Models
472
2
Fuzzy Information Retrieval Models
474
3
Fuzzy Extended Boolean Models
475
1
Fuzzy Knowledge Based IR Models
476
1
Fuzzy Associative Mechanisms
477
1
The Fuzzy Indexing Procedure
477
5
Issues in Indexing and Retrieval
477
2
Fuzzy Representation of Structured Documents
479
3
Fuzzy Querying
482
7
Query Weights
483
4
Aggregation Operators
487
2
Enhancing Retrieval Through Fuzzy Associations
489
4
Fuzzy Thesauri for Terms
489
3
Fuzzy Clustering for Documents
492
1
Relevance Feedback
493
7
Previous Works on Relevance Feedback
494
2
Relevance Feedback Based on Naive Learning
496
4
Evaluation of Information Retrieval Systems
500
1
Summary
501
1
References
502