ISBN: 3790813966
TITLE: Lectures on Soft Computing and Fuzzy Logic
AUTHOR: Di Nola
TOC:

A Natural Deduction System for Intuitionistic Fuzzy Logic
Matthias Baaz, Agata Ciabattoni, Christian G. Fermller
1 Introduction 1
2 Syntax and Semantic of Intuitionistic Fuzzy Logic 2
3 A Hypersequent Calculus for IF 4
4 Natural Deduction 7
References 18
Minimal Ideals and the Socle in MV-algebras
Peter L. Belluce, Salvatore Sessa
1 Preliminaries 19
2 Socle of an MV-algebra 20
3 MV-algebras of Continuous Functions 27
References 31
Industrial Applications of Soft Computing
Marco Branciforte, Riccardo Capanetto, Mario Lavorgna, Luigi Occhipinti
1 Introduction 33
2 Soft Computing in Control Application 34
3 RD-CNNS for Autonomous System Navigation 35
4 Conclusion 41
References 41
Spatial Diversity in Reaction-Diffusion Fuzzy Cellular Networks
Maide Bucolo, Maria Chiara Cutuli, Luigi Fortuna, Alessandro Rizzo
1 Introduction 43
2 Preliminaries 43
3 Fuzzy Cellular Networks 44
4 Reaction-Diffusion Fuzzy Cellular Networks 46
5 Experimental Results 48
6 Conclusions 55
References 55
An Evolutionary View to the Design of Soft-Computing Agents
Stefano A. Gerri, Vincenzo Loia
1 Introduction 57
2 FuzzyEvoAgent 63
3 Evolution 64
4 JAVA Implementation 66
5 Experimental Results 66
6 Conclusions 68
References 69
Finiteness and Duality in MV-algebras Theory
Antonio Di Nola, Revaz Grigolia
1 Preliminaries 71
2 MV-algebras 73
3 Finite MV-algebras of Words 76
4 Duality between Finite MV-algebras and Finite Posets 78
5 Quasi Finite MV(C)-algebras 82
References 87
Generalized Pseudo-Effect Algebras
Anatolij Dvurecenskij and Thomas Vetterlein
1 Introduction 89
2 Generalized Pseudo-Effect Algebras 90
3 Generalized Pseudo-Effect Algebras with Riesz Properties 94
4 Embedding of Generahzed Pseudo-Effect Algebras into Positive Cones of Groups 97
5 Properties of the Representing Group of a GPE-algebra 105
6 Categorical Equivalences of GPE-Algebras and po-Groups 108
References 111
Extension Principle and Probabilistic Inferential Process
Giangiacomo Gerla, Domenico Calabr, Luciana Scarpati
1 Introduction 113
2 Probability and Boolean Valuations 114
3 Knowledge Representation System 116
4 Inferential Process 119
5 An Extension Principle for Incomplete Information 121
6 Incomplete Information 124
References 127
An Algebraic Tool for Classification in Fuzzy Environments
Antonio Gisolfi, Luigi Di Lascio, Enrico Fischetti
1 Introduction 129
2 The Fuzzy Algebraic Structure 130
3 The Linguistic Approximation 136
4 The Structure as Commutative L-monoid 138
5 Data Analysis 140
6 Applications 147
7 A Case Study 152
8 Concluding Remarks 156
References 156
Free BL_Delta Algebras
Franco Montagna
1 Introduction 159
2 Preliminaries about Basic Hoops 160
3 BL_Delta Algebras 161
4 Free BL_Delta Algebras 163
References 171
Natural Duality as a Tool to Study Algebras Arising from Logics
Philippe Niederkorn
1 Introduction 173
2 Boolean Algebras 174
3 Natural Dualities 175
4 Dualities for Post Algebras and MV-algebras 178
5 Special Members of M_n 181
6 Further Applications 186
References 187
The Principles of Fuzzy Logic: Its Mathematical and Computational Aspects
Vilm Novk, Irina Perfilieva
1 Introduction 189
2 Vagueness, Uncertainty and Fuzzy Logic 189
3 What is Fuzzy Logic 191
4 Algebraic Structures for Logical Calculi 192
5 Fuzzy Logic in Narrow Sense 202
6 Functional Systems in Fuzzy Logic Theories 212
7 Fuzzy Logic in Broader Sense 225
8 Conclusion 236
References 237
Fuzzy Systems and Data Mining
Witold Pedrycz
1 Introduction 239
2 Granulation of Information 240
3 Building Associations in Databases 243
4 From Associations to Rules in Databases 244
5 Building Rules in Data Mining Processes 245
6 Properties of Rules Induced by Associations 250
7 Linguistic Modifications of Information Granules in the Rules 251
8 Growing Rules through Manipulation of Information Granules 252
9 Conclusions 255
Flexible Querying in Deductive Database
Maria I. Sessa
1 Introduction and Previous Works 257
2 Similarity-based Deductive Database Systems 258
3 Similarity Relation 261
4 Interactive Procedures to Define a Similarity Relation 264
5 Logic Programming and Abstract Interpretations 267
6 Extended and Abstract Deductive Database 270
7 Fuzzy Least Herbrand Model 273
8 Conclusion and Future Works 274
References 275
Neural Networks for Pattern Recognition, Image and Signal Processing
Roberto Tagliaferri
1 Introduction 277
2 Neural Networks and the Data 278
3 Multi-layer Neural Networks 280
4 Neural Networks for Classification and Regression 282
5 Neural Networks for the Pre-processing 285
6 Neural Networks' Applications 292
7 Conclusions and Perspectives 296
References 297
Computational aspects of probability logics
Sauro Tulipani
1 Introduction 301
2 Computational Complexity of the Consistency Decision Problem and Satisfiability Problems 304
3 Elimination of Boolean Variables 306
References 310
Survey of Theory and Applications of Lukasiewicz-Pavelka Fuzzy Logic
Esko Turunen
1 Introduction 313
2 The Algebra of Lukasiewicz-Pavelka Logic 314
3 Lukasiewicz-Pavelka Logic 316
4 Similarity-based Reasoning 324
References 336
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