Lectures on Soft Computing and Fuzzy Logic (Advances in Intelligent and Soft Computing Vol.11) (2001. x, 337 S. 55 SW-Abb., 4 Tabellen. 24 cm)

Lectures on Soft Computing and Fuzzy Logic (Advances in Intelligent and Soft Computing Vol.11) (2001. x, 337 S. 55 SW-Abb., 4 Tabellen. 24 cm)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 337 p.
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Full Description

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar- ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re- sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi- fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

Table of Contents

  A Natural Deduction System for Intuitionistic
Fuzzy Logic
Matthias Baaz
Agata Ciabattoni
Christian G. Fermuller
Introduction 1 (1)
Syntax and Semantic of Intuitionistic Fuzzy 2 (2)
A Hypersequent Calculus for IF 4 (3)
Natural Deduction 7 (12)
References 18 (1)
Minimal Ideals and the Socle in MV-algebras
Peter L. Belluce
Salvatore Sessa
Preliminaries 19 (1)
Socle of an MV-algebra 20 (7)
MV-algebras of Continuous Functions 27 (6)
References 31 (2)
Industrial Applications of Soft Computing
Marco Branciforte
Riccardo Caponetto
Mario Lavorgna
Luigi Occhipinti
Introduction 33 (1)
Soft Computing in Control Application 34 (1)
RD-CNNS for Autonomous System Navigation 35 (6)
Conclusion 41 (2)
References 41 (2)
Spatial Diversity in Reaction-Diffusion Fuzzy
Cellular Networks
Maide Bucolo
Maria Chiara Cutuli
Luigi Fortuna
Alessandro Rizzo
Introduction 43 (1)
Preliminaries 43 (1)
Fuzzy Cellular Networks 44 (2)
Reaction-Diffusion Fuzzy Cellular Networks 46 (2)
Experimental Results 48 (7)
Conclusions 55 (2)
References 55 (2)
An Evolutionary View to the Design of
Soft-Computing Agents
Stefano A. Cerri
Vincenzo Loia
Introduction 57 (6)
FuzzyEvoAgent 63 (1)
Evolution 64 (2)
JAVA Implementation 66 (1)
Experimental Results 66 (2)
Conclusions 68 (3)
References 69 (2)
Finiteness and Duality in MV-algebras Theory
Antonio Di Nola
Revaz Grigolia
Preliminaries 71 (2)
MV-algebras 73 (3)
Finite MV-algebras of Words 76 (2)
Duality between Finite MV-algebras and 78 (4)
Finite Posets
Quasi Finite MV (C)-algebras 82 (7)
References 87 (2)
Generalized Pseudo-Effect Algebras
Anatolij Dvurecenskij
Thomas Vetterlein
Introduction 89 (1)
Generalized Pseudo-Effect Algebras 90 (4)
Generalized Pseudo-Effect Algebras with 94 (3)
Riesz Properties
Embedding of Generalized Pseudo-Effect 97 (8)
Algebras into Positive Cones of Groups
Properties of the Representing Group of a 105(3)
Categorical Equivalences of GPE-Algebras 108(5)
and po-Groups
References 111(2)
Extension Principle and Probabilistic
Inferential Process
Giangiacomo Gerla
Domenico Calabro
Luciana Scarpati
Introduction 113(1)
Probability and Boolean Valuations 114(2)
Knowledge Representation System 116(3)
Inferential Process 119(2)
An Extension Principle for Incomplete 121(3)
Incomplete Information 124(5)
References 127(2)
An Algebraic Tool for Classification in Fuzzy
Antonio Gisolfi
Luigi Di Lascio
Enrico Fischetti
Introduction 129(1)
The Fuzzy Algebraic Structure 130(6)
The Linguistic Approximation 136(2)
The Structure as Commutative L-monoid 138(2)
Data Analysis 140(7)
Applications 147(5)
A Case Study 152(4)
Concluding Remarks 156(3)
References 156(3)
Free BLΔ Algebras
Franco Montagna
Introduction 159(1)
Preliminaries about Basic Hoops 160(1)
BLΔ Algebras 161(2)
Free BLΔ Algebras 163(10)
References 171(2)
Natural Duality as a Tool to Study Algebras
Arising from Logics
Philippe Niederkorn
Introduction 173(1)
Boolean Algebras 174(1)
Natural Dualities 175(3)
Dualities for Post Algebras and MV-algebras 178(3)
Special Members of Mn 181(5)
Further Applications 186(3)
References 187(2)
The Principles of Fuzzy Logic: Its
Mathematical and Computational Aspects
Vilem Novak
Irina Perfilieva
Introduction 189(1)
Vagueness, Uncertainty and Fuzzy Logic 189(2)
What is Fuzzy Logic 191(1)
Algebraic Structures for Logical Calculi 192(10)
Fuzzy Logic in Narrow Sense 202(10)
Functional Systems in Fuzzy Logic Theories 212(13)
Fuzzy Logic in Broader Sense 225(11)
Conclusion 236(3)
References 237(2)
Fuzzy Systems and Data Mining
Witold Pedrycz
Introduction 239(1)
Granulation of Information 240(3)
Building Associations in Databases 243(1)
From Associations to Rules in Databases 244(1)
Building Rules in Data Mining Processes 245(5)
Properties of Rules Induced by Associations 250(1)
Linguistic Modifications of Information 251(1)
Granules in the Rules
Growing Rules through Manipulation of 252(3)
Information Granules
Conclusions 255(2)
Flexible Querying in Deductive Database
Maria I. Sessa
Introduction and Previous Works 257(1)
Similarity-based Deductive Database Systems 258(3)
Similarity Relation 261(3)
Interactive Procedures to Define a 264(3)
Similarity Relation
Logic Programming and Abstract 267(3)
Extended and Abstract Deductive Database 270(3)
Fuzzy Least Herbrand Model 273(1)
Conclusion and Future Works 274(3)
References 275(2)
Neural Networks for Pattern Recognition,
Image and Signal Processing
Roberto Tagliaferri
Introduction 277(1)
Neural Networks and the Data 278(2)
Multi-layer Neural Networks 280(2)
Neural Networks for Classification and 282(3)
Neural Networks for the Pre-processing 285(7)
Neural Networks' Applications 292(4)
Conclusions and Perspectives 296(5)
References 297(4)
Computational aspects of probability logics
Sauro Tulipani
Introduction 301(3)
Computational Complexity of the Consistency 304(2)
Decision Problem and Satisfiability Problems
Elimination of Boolean Variables 306(7)
References 310(3)
Survey of Theory and Applications of
Lukasiewicz-Pavelka Fuzzy Logic
Esko Turunen
Introduction 313(1)
The Algebra of Lukasiewicz-Pavelka Logic 314(2)
Lukasiewicz-Pavelka Logic 316(8)
Similarity-based Reasoning 324(12)
References 336