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Bibliografická citace

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BK
Boston : Kluwer Academic Publishers, 1999
xiii,320 s.

objednat
ISBN 0-7923-8595-0 (váz.)
The Kluwer international series in engineering and computer science ; [vol.] 517
Obsahuje předmluvu, rejstřík
Bibliografie: s. 305-313
Fuzzy logika - studie
000058682
Preface xi // 1. FUZZY LOGIC: WHAT, WHY, FOR WHICH? I // 1.1 Vagueness and Uncertainty 2 // 1.2 Vagueness and Fuzzy Sets 6 // 1.3 What Is Fuzzy Logic 9 // 1.4 Outline of the Agenda of Fuzzy Logic 12 // 2. ALGEBRAIC STRUCTURES FOR LOGICAL CALCULI 15 // 2.1 Algebras for Logics 16 // 2.1.1 Boolean algebras 16 // 2.1.2 Residuated lattices and MV-algebras 23 // 2.2 Filters and Representation Theorems 35 // 2.3 Elements of the theory of t-norms 41 // 2.4 Introduction to Topos Theory 52 // 2.4.1 Topos theory 52 // 2.4.2 Lattice of subobjects in topos 56 // 3. LOGICAL CALCULI AND MODEL THEORY 61 // 3.1 Classical Logic 61 // 3.1.1 Propositional logic 62 // 3.1.2 Predicate logic 67 // 3.1.3 Many-sorted predicate logic 73 // 3.2 Classical Model Theory 74 // 3.3 Formal Logical Systems 77 // 3.4 Model Theory in Categories 83 // 4. FUZZY LOGIC IN NARROW SENSE 95 // 4.1 Graded Formal Logical Systems 97 // 4.2 Truth Values 106 // 4.2.1 Intuition on truth values and operations with them 106 // 4.2.2 Truth values as algebras 111 // 4.2.3 Why Lukasiewicz algebra 112 // 4.2.4 Enriching structure of truth values 113 // 4.3 Predicate Fuzzy Logic of First-Order 114 // viii MATHEMATICAL PRINCIPLES OF FUZZY LOGIC // 4.3.1 Syntax and semantics 115 // 4.3.2 Basic properties of fuzzy theories 120 // 4.3.3 Consistency of fuzzy theories 129 // 4.3.4 Extension of fuzzy theories 132 // 4.3.5 Henkin fuzzy theories 139 // 4.3.6 Complete fuzzy theories 140 // 4.3.7 Lindenbaum algebra of formulas and its properties 142 // 4.3.8 Completeness theorems 147 // 4.3.9 Sorites fuzzy theories 150 // 4.3.10 Partial inconsistency and the consistency threshold 151 // 4.3.11 Additional connectives 153 // 4.3.12 Disposing irrational logical constants 154 // 4.4 Fuzzy Theories with Equality and Open Fuzzy Theories 158 // 4.4.1 Fuzzy theories with equality 159 // 4.4.2 Consistency theorem in fuzzy logic 160 //
4.4.3 Herbrand theorem in fuzzy logic 166 // 4.5 Model Theory in Fuzzy Logic 168 // 4.5.1 Basic concepts of fuzzy model theory 169 // 4.5.2 Chains of models 171 // 4.5.3 Ultraproduct theorem 172 // 4.6 Recursive Properties of Fuzzy Theories 176 // 5. FUNCTIONAL SYSTEMS IN FUZZY LOGIC THEORIES 179 // 5.1 Fuzzy Logic Functions and Their Representation by Formulas 181 // 5.1.1 Formulas and their relation to fuzzy logic functions 181 // 5.1.2 Piecewise linear functions and their representation by formulas 185 // 5.2 Normal Forms for FL-Functions and Formulas of Propositional Fuzzy Logic 189 // 5.2.1 Normal forms for L-valued FL-functions 190 // 5.2.2 Normal forms for functions represented by formulas 195 // 5.3 FL-Relations and Their Connection with Formulas of Predicate Fuzzy Logic 201 // 5.3.1 FL-Relations and Their Representation by Formulas 201 // 5.3.2 Normal Forms and Approximation Theorems 204 // 5.3.3 Representation of FL-relations and Consistency of Fuzzy Theories 208 // 5.4 Approximation of Continuous Functions by Fuzzy Logic Normal Forms 210 // 5.4.1 Approximation of continuous functions through FL- relations 210 // 5.4.2 Approximation of continuous functions determined by a defuzzification // operation 213 // 5.5 Representation of Continuous Functions by the Conjunctive Normal Form 218 // 6. FUZZY LOGIC IN BROADER SENSE 223 // 6.1 Partial Formalization of Natural Language 224 // 6.1.1 Evaluating and simple conditional linguistic syntagms 224 // 6.1.2 Translation of evaluating syntagms and predications into fuzzy logic 227 // 6.1.3 The meaning of simple evaluating syntagms 231 // 6.2 Formal Scheme of FLb 239 // 6.3 Special Theories in FLb 242 // 6.3.1 Independence of formulas 243 // 6.3.2 Deduction on simple linguistic descriptions 247 // 6.3.3 Fuzzy approximation based on simple linguistic descriptions 249 //
7. TOPOI AND CATEGORIES OF FUZZY SETS 259 // 7.1 Category of A-sets as generalization of fuzzy sets 261 // 7.2 Category of A-fuzzy sets 275 // 7.2.1 -fuzzy sets over MV-algebras 275 // 7.3 Interpretation of formulas in the category CQ - Set 286 // 8. FEW HISTORICAL AND CONCLUDING REMARKS 299 // References 305 // Index 315 // I

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