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| Foreword | |
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| Acknowledgments | |
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| Introduction | |
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| Databases and their Evolution | |
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| Preferences and Fuzzy Sets | |
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| Overview of the Book | |
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| Reminders on Relational Databases | |
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| Basic Notions and Vocabulary | |
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| Algebraic Operations | |
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| Set operations | |
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| Relational operations | |
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| Properties | |
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| An Overview of SQL | |
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| The base block | |
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| Combining base blocks | |
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| Partitioning | |
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| Expressing division and antidivision | |
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| Basic Notions on Fuzzy Sets | |
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| Introduction | |
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| Definitions and Notations | |
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| Composition of Fuzzy Sets | |
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| Intersection and union of fuzzy sets | |
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| Difference between fuzzy sets | |
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| Cartesian product of fuzzy sets | |
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| Trade-off operators | |
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| Nonsymmetric operators | |
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| Inclusions and Implications | |
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| Fuzzy implications | |
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| Inclusions | |
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| Fuzzy Measures and Integrals | |
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| Introduction | |
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| Fuzzy measures | |
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| Fuzzy integrals | |
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| The Extension Principle | |
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| Fuzzy Quantified Propositions | |
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| Fuzzy linguistic quantifiers | |
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| Quantified propositions | |
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| Non-Fuzzy Approaches to Preference Queries: A Brief Overview | |
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| Introduction | |
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| Quantitative Approaches | |
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| Distances and similarity | |
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| Linguistic preferences | |
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| Explicit scores attached to entities | |
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| Top-k queries | |
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| Outranking | |
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| Qualitative Approaches | |
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| Secondary preference criterion | |
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| Pareto-order-based approaches | |
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| CP-nets | |
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| Domain linearization | |
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| Possibilistic-logic-based approach | |
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| Conclusion | |
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| Simple Fuzzy Queries | |
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| Introduction | |
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| An Extended Relational Algebra | |
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| An Overview of a Basic Version of SQLf | |
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| Introduction | |
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| The multiple relation base block | |
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| Subqueries | |
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| Set-oriented operators | |
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| Relation partitioning | |
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| Interface for User-Defined Terms and Operators | |
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| Contextual Queries | |
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| Queries with one level of context | |
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| Queries with several levels of context | |
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| Evaluation of Simple Fuzzy Queries | |
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| Derivation principle | |
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| Derivation-based processing of SQLf queries | |
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| Conclusion | |
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| Fuzzy Queries Involving Quantified Statements or Aggregates | |
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| Introduction | |
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| Quantified Statements | |
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| Introduction | |
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| Quantified statements and fuzzy integral theory | |
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| Interpretation of statements of the type "Q X are A" | |
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| Integration into SQLf | |
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| Evaluation of SQLf queries involving quantified statements | |
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| Aggregates | |
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| Introduction | |
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| The case of monotonic predicates and aggregates | |
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| Dealing with the general case | |
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| SQLf queries involving aggregates | |
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| Evaluation of SQLf queries involving aggregates | |
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| Conclusion | |
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| Division and Antidivision of Fuzzy Relations | |
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| Introduction | |
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| Division of Fuzzy Relations | |
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| Principles | |
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| On the choice of implication | |
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| Primitivity of the extended division operator | |
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| Expressing extended division in SQLf | |
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| Tolerant Division | |
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| Exception-based tolerant division | |
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| Resemblance-based tolerant division | |
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| Stratified Division | |
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| Introduction | |
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| The queries | |
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| Quotient property of the result delivered | |
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| Queries Mixing Division and Antidivision | |
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| Motivation | |
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| Mixed stratified queries | |
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| Evaluation of Division Queries | |
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| Processing the division of fuzzy relations | |
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| Processing the tolerant divisions of fuzzy relations | |
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| Processing the conjunctive stratified division | |
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| Conclusion | |
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| Bipolar Fuzzy Queries | |
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| Introduction | |
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| Preliminaries | |
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| About bipolarity | |
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| Extended Algebraic Operators | |
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| Intersection | |
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| Union | |
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| Cartesian product | |
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| Negation | |
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| Difference | |
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| Selection | |
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| Projection | |
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| Join | |
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| Division | |
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| Implementation Aspects | |
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| Conclusion | |
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| Fuzzy Group By | |
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| Introduction | |
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| An Extended Group By Clause | |
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| Use of a crisp partition | |
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| Use of a fuzzy partition | |
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| Having Clause | |
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| Inclusion constraint | |
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| Aggregate<sub>1</sub> � aggregate<sub>2</sub> | |
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| Aggregate is � | |
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| Application to Association Rule Mining | |
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| Rules of the type A is Li -> B is L | |
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| Rules of the type A is L -> B is L<sub>i</sub> | |
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| Evaluation of a Fuzzy Group By | |
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| Related Work | |
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| Extended group by | |
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| Fuzzy OLAP | |
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| Fuzzy database summarization techniques | |
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| Mining association rules with SQL | |
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| Conclusion | |
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| Empty and Plethoric Answers | |
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| Introduction | |
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| Empty Answer Problem | |
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| Query relaxation | |
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| Relaxation by predicate weakening | |
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| Case-based reasoning approach | |
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| Plethoric Answer Problem | |
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| Introduction | |
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| Approach based on predicate strengthening | |
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| Approach based on query expansion | |
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| Conclusion | |
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| Conclusion | |
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| Bibliography | |
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| Index | |