E-raamat: Lectures on Soft Computing and Fuzzy Logic

A Natural Deduction System for Intuitionistic Fuzzy Logic Matthias Baaz Agata Ciabattoni Christian G. Fermuller Introduction 1(1) Syntax and Semantic of Intuitionistic Fuzzy Logic 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 Finite Posets 78(4) 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 Riesz Properties 94(3) Embedding of Generalized Pseudo-Effect Algebras into Positive Cones of Groups 97(8) Properties of the Representing Group of a GPE-algebra 105(3) Categorical Equivalences of GPE-Algebras and po-Groups 108(5) 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 Information 121(3) Incomplete Information 124(5) References 127(2) An Algebraic Tool for Classification in Fuzzy Environments 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 Granules in the Rules 251(1) Growing Rules through Manipulation of Information Granules 252(3) 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 Similarity Relation 264(3) Logic Programming and Abstract Interpretations 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 Regression 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 Decision Problem and Satisfiability Problems 304(2) 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