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| Foreword | |
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| Preface | |
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| Theory | |
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| From Classical (Crisp) Sets to Fuzzy Sets: A Grand Paradigm Shift | |
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| Introduction | |
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| Crisp Sets: An Overview | |
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| Fuzzy Sets: Basic Types | |
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| Fuzzy Sets: Basic Concepts | |
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| Characteristics and Significance of the Paradigm Shift | |
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| Notes | |
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| Exercises | |
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| Fuzzy Sets versus Crisp Sets | |
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| Additional Properties of -Cuts | |
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| Representations of Fuzzy Sets | |
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| Extension Principle for Fuzzy Sets | |
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| Notes | |
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| Exercises | |
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| Operations on Fuzzy Sets | |
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| Types of Operations | |
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| Fuzzy Complements | |
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| Fuzzy Intersections: t- Norms | |
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| Fuzzy Unions: t-Conorms | |
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| Combinations of Operations | |
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| Aggregation Operations | |
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| Notes | |
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| Exercises | |
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| Fuzzy Arithmetic | |
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| Fuzzy Numbers | |
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| Linguistic Variables | |
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| Arithmetic Operations on Intervals | |
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| Arithmetic Operations on Fuzzy Numbers | |
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| Lattice of Fuzzy Numbers | |
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| Fuzzy Equations | |
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| Notes | |
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| Exercises!2<l>5</l> | |
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| Crisp versus Fuzzy Relations | |
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| Projections and Cylindric Extensions | |
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| Binary Fuzzy Relations | |
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| Binary Relations on a Single Set | |
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| Fuzzy Equivalence Relations | |
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| Fuzzy Compatibility Relations | |
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| Fuzzy Ordering Relations | |
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| Fuzzy Morphisms | |
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| Sup-i Compositions of Fuzzy Relations | |
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| Inf- Compositions of Fuzzy Relations | |
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| Notes | |
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| Exercises | |
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| Fuzzy Relation Equations | |
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| General Discussion | |
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| Problem Partitioning | |
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| Solution Method | |
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| Fuzzy Relation Equations Based on Sup-i Compositions | |
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| Fuzzy Relation Equations Based on Inf-Compositions | |
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| Approximate Solutions | |
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| The Use of Neural Networks | |
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| Notes | |
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| Exercises | |
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| Possibility Theory | |
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| Fuzzy Measures | |
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| Evidence Theory | |
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| Possibility Theory | |
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| Fuzzy Sets and Possibility Theory | |
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| Possibility Theory versus Probability Theory | |
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| Notes | |
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| Exercises | |
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| Fuzzy Logic | |
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| Classical Logic: An Overview | |
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| Multivalued Logics | |
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| Fuzzy Propositions | |
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| Fuzzy Quantifiers | |
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| Linguistic Hedges | |
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| Inference from Conditional Fuzzy Propositions | |
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| Inference from Conditional and Qualified Propositions | |
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| Inference from Quantified Propositions | |
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| Notes | |
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| Exercises | |
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| Uncertainty-Based Information | |
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| Information and Uncertainty | |
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| Nonspecificity of Crisp Sets | |
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| Nonspecificity of Fuzzy Sets | |
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| Fuzziness of Fuzzy Sets | |
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| Uncertainty in Evidence Theory | |
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| Summary of Uncertainty Measures | |
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| Principles of Uncertainty | |
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| Notes | |
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| Exercises | |
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| Applications | |
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| Constructing Fuzzy Sets and Operations on Fuzzy Sets | |
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| General Discussion | |
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| Methods of Construction: An Overview | |
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| Direct Methods with One Expert | |
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| Direct Methods with Multiple Experts | |
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| Indirect Methods with One Expert | |
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| Indirect Methods with Multiple Experts | |
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| Constructions from Sample Data | |
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| Notes | |
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| Exercises | |
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| Approximate Reasoning | |
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| Fuzzy Expert Systems: An Overview | |
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| Fuzzy Implications | |
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| Selection of Fuzzy Implications | |
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| Multiconditional Approximate Reasoning | |
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| The Role of Fuzzy Relation Equations | |
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| Interval-Valued Approximate Reasoning | |
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| Notes | |
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| Exercises | |
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| Fuzzy Systems | |
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| General Discussion | |
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| Fuzzy Controllers: An Overview | |
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| Fuzzy Controllers: An Example | |
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| Fuzzy Systems and Neural Networks | |
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| Fuzzy Neural Networks | |
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| Fuzzy Automata | |
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| Fuzzy Dynamic Systems | |
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| Notes | |
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| Exercises | |
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| Pattern Recognition | |
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| Introduction | |
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| Fuzzy Clustering | |
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| Fuzzy Pattern Recognition | |
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| Fuzzy Image Processing | |
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| Notes | |
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| Exercises | |
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| Fuzzy Databases and Information Retrieval Systems | |
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| General Discussion | |
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| Fuzzy Databases | |
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| Fuzzy Information Retrieval | |
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| Notes | |
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| Exercises | |
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| Fuzzy Decision Making | |
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| General Discussion | |
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| Individual Decision Making | |
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| Multiperson Decision Making | |
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| Multicriteria Decision Making | |
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| Multistage Decision Making | |
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| Fuzzy Ranking Methods | |
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| Fuzzy Linear Programming | |
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| Notes | |
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| Exercises | |
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| Engineering Applications | |
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| Introduction | |
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| Civil Engineering | |
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| Mechanical Engineering | |
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| Industrial Engineering | |
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| Computer Engineering | |
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| Rel | |