Fuzzy Preference Queries to Relational Databases 1st Edition by Olivier Pivert, Patrick Bosc 9781848168701 1848168705

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ISBN 10: 1848168705
ISBN 13: 9781848168701 
Author: Olivier Pivert, Patrick Bosc 

The manipulation of databases is an integral part of a world which is becoming increasingly and pervasively information-focused. This book puts forward a suggestion to advocate preference queries and fuzzy sets as a central concern in database queries and offers an important contribution to the design of intelligent information systems. It provides a comprehensive study on fuzzy preference queries in the context of relational databases. Preference queries, a recent hot topic in database research, provide a basis for rank-ordering the items retrieved, which is especially valuable for large sets of answers.This book aims to show that fuzzy set theory constitutes a highly expressive framework for modeling preference queries. It presents a study of the algorithmic aspects related to the evaluation of such queries in order to demonstrate that this framework offers a good trade-off between expressivity and efficiency. Numerous examples and proofs are liberally and lucidly demonstrated throughout, and greatly enhance the detailed theoretical aspects explored in the book.Researchers working in databases will greatly benefit from this comprehensive and up-to-date study of fuzzy preference queries, and it will also become an invaluable reference point for postgraduate students interested in advanced database techniques.The only other books which deal with this topic are edited books or conference proceedings which include a few contributions about some specific aspects of the question. This book provides a comprehensive view of the issue, starting with basic notions related to relational databases and fuzzy set theory, up to the detailed study of complex fuzzy queries and the way they can be efficiently processed. It is the compendium of more than 20 years of research by the authors who benefit from a great international recognition in the domain of intelligent information systems, on the subject.

Fuzzy Preference Queries to Relational Databases 1st Table of contents:

1. Introduction

1.1 Databases and their Evolution

1.2 Preferences and Fuzzy Sets

1.3 Overview of the Book

2. Reminders on Relational Databases

2.1 Basic Notions and Vocabulary

2.2 Algebraic Operations

2.2.1 Set operations

2.2.2 Relational operations

2.2.3 Properties

2.3 An Overview of SQL

2.3.1 The base block

2.3.2 Combining base blocks

2.3.3 Partitioning

2.3.4 Expressing division and antidivision

3. Basic Notions on Fuzzy Sets

3.1 Introduction

3.2 Definitions and Notations

3.3 Composition of Fuzzy Sets

3.3.1 Intersection and union of fuzzy sets

3.3.2 Difference between fuzzy sets

3.3.3 Cartesian product of fuzzy sets

3.3.4 Trade-off operators

3.3.5 Nonsymmetric operators

3.3.5.1 “And if possible”

3.3.5.2 “Or else”

3.3.5.3 “All the more as”

3.4 Inclusions and Implications

3.4.1 Fuzzy implications

3.4.1.1 Introduction

3.4.1.2 S-implications

3.4.1.3 R-implications

3.4.1.4 Contraposition of R-implications

3.4.1.5 Some characteristics of fuzzy implications

3.4.1.6 Semantic aspects of fuzzy implications

3.4.2 Inclusions

3.4.2.1 Introduction

3.4.2.2 Regular inclusion between fuzzy sets

3.4.2.3 Graded inclusion

3.4.2.4 Graded equality of fuzzy sets

3.4.2.5 Tolerant inclusion

3.5 Fuzzy Measures and Integrals

3.5.1 Introduction

3.5.2 Fuzzy measures

3.5.3 Fuzzy integrals

3.6 The Extension Principle

3.7 Fuzzy Quantified Propositions

3.7.1 Fuzzy linguistic quantifiers

3.7.2 Quantified propositions

4. Non-Fuzzy Approaches to Preference Queries: A Brief Overview

4.1 Introduction

4.2 Quantitative Approaches

4.2.1 Distances and similarity

4.2.2 Linguistic preferences

4.2.3 Explicit scores attached to entities

4.2.4 Top-k queries

4.2.5 Outranking

4.3 Qualitative Approaches

4.3.1 Secondary preference criterion

4.3.2 Pareto-order-based approaches

4.3.3 CP-nets

4.3.4 Domain linearization

4.3.5 Possibilistic-logic-based approach

4.4 Conclusion

5. Simple Fuzzy Queries

5.1 Introduction

5.2 An Extended Relational Algebra

5.3 An Overview of a Basic Version of SQLf

5.3.1 Introduction

5.3.2 The multiple relation base block

5.3.3 Subqueries

5.3.3.1 Nesting with “in”

5.3.3.2 Nesting with “exists”

5.3.3.3 Nesting with “all” and “any”

5.3.3.4 Nesting and scalar comparison

5.3.4 Set-oriented operators

5.3.5 Relation partitioning

5.3.5.1 Qualification of partitions by means of aggregate functions

5.4 Interface for User-Defined Terms and Operators

5.5 Contextual Queries

5.5.1 Queries with one level of context

5.5.2 Queries with several levels of context

5.6 Evaluation of Simple Fuzzy Queries

5.6.1 Derivation principle

5.6.1.1 Transformation of base predicates

5.6.1.2 Single-block projection–selection–join queries

5.6.1.3 Nested queries

5.6.2 Derivation-based processing of SQLf queries

5.6.2.1 General strategy

5.6.2.2 Single-block selection–projection–join queries

5.6.2.3 Nested queries

5.6.2.4 Efficiency of the derivation-based processing strategy

5.7 Conclusion

6. Fuzzy Queries Involving Quantified Statements or Aggregates

6.1 Introduction

6.2 Quantified Statements

6.2.1 Introduction

6.2.2 Quantified statements and fuzzy integral theory

6.2.2.1 Introduction

6.2.2.2 Fuzzy integrals and increasing quantifiers

6.2.3 Interpretation of statements of the type “Q X are A”

6.2.3.1 Interpretation according to Zadeh

6.2.3.2 Interpretation according to Prade

6.2.3.3 Yager’s competitive type aggregation

6.2.3.4 Interpretation based on the OWA operator

6.2.3.5 Interpretation of quantifiers of the type “about S”

6.2.4 Integration into SQLf

6.2.4.1 Horizontal quantification

6.2.4.2 Nested queries (extension of any and all)

6.2.4.3 Quantified statement in the having clause

6.2.5 Evaluation of SQLf queries involving quantified statements

6.2.5.1 Zadeh’s interpretation

6.2.5.2 Interpretation based on Sugeno’s integral

6.2.5.3 Interpretation based on Choquet’s integral

6.3 Aggregates

6.3.1 Introduction

6.3.2 The case of monotonic predicates and aggregates

6.3.3 Dealing with the general case

6.3.3.1 A straightforward interpretation

6.3.3.2 The proposed interpretation

6.3.3.3 Algebraic properties related to negation

6.3.4 SQLf queries involving aggregates

6.3.4.1 Aggregates in the having clause

6.3.4.2 Nested queries

6.3.5 Evaluation of SQLf queries involving aggregates

6.3.5.1 Queries involving aggregates over fuzzy sets

6.4 Conclusion

7. Division and Antidivision of Fuzzy Relations

7.1 Introduction

7.2 Division of Fuzzy Relations

7.2.1 Principles

7.2.2 On the choice of implication

7.2.3 Primitivity of the extended division operator

7.2.4 Expressing extended division in SQLf

7.3 Tolerant Division

7.3.1 Exception-based tolerant division

7.3.1.1 Quantitative tolerant division

7.3.1.2 Qualitative tolerant division

7.3.2 Resemblance-based tolerant division

7.4 Stratified Division

7.4.1 Introduction

7.4.2 The queries

7.4.2.1 Conjunctive queries (CJ)

7.4.2.2 Disjunctive queries (DJ)

7.4.2.3 Full discrimination-based queries (FD)

7.4.3 Quotient property of the result delivered

7.5 Queries Mixing Division and Antidivision

7.5.1 Motivation

7.5.2 Mixed stratified queries

7.6 Evaluation of Division Queries

7.6.1 Processing the division of fuzzy relations

7.6.2 Processing the tolerant divisions of fuzzy relations

7.6.2.1 Quantitative exception-tolerant division

7.6.2.2 Qualitative exception-tolerant division

7.6.2.3 Resemblance-based tolerant division

7.6.3 Processing the conjunctive stratified division

7.6.3.1 Principle of the algorithms

7.6.3.2 Experiments and results

7.7 Conclusion

8. Bipolar Fuzzy Queries

8.1 Introduction

8.2 Preliminaries

8.2.1 About bipolarity

8.3 Extended Algebraic Operators

8.3.1 Intersection

8.3.2 Union

8.3.3 Cartesian product

8.3.4 Negation

8.3.4.1 Approach inspired by twofold fuzzy sets

8.3.4.2 Counter-example

8.3.4.3 From “and if possible” to “or else”

8.3.4.4 An approach based on product and division

8.3.4.5 Negation based on antonymy

8.3.5 Difference

8.3.5.1 A logical view of di.erence

8.3.5.2 A non-logical view of the difference

8.3.5.3 Counter-example (first property)

8.3.5.4 Conclusion

8.3.6 Selection

8.3.6.1 Counter-example

8.3.7 Projection

8.3.8 Join

8.3.9 Division

8.3.9.1 Reminder about “classical” division

8.3.9.2 Reminder about the division of fuzzy relations

8.3.9.3 Bipolar division of bipolar fuzzy relations

8.3.9.4 About the quotient property

8.3.9.5 About the non-primitivity of the operator

8.4 Implementation Aspects

8.5 Conclusion

9. Fuzzy Group By

9.1 Introduction

9.2 An Extended Group By Clause

9.2.1 Use of a crisp partition

9.2.2 Use of a fuzzy partition

9.3 Having Clause

9.3.1 Inclusion constraint

9.3.2 Aggregate1 θ aggregate2

9.3.3 Aggregate is ψ

9.4 Application to Association Rule Mining

9.4.1 Rules of the type A is Li B is L

9.4.1.1 Computation of the support

9.4.1.2 Computation of the confidence

9.4.2 Rules of the type A is L B is L

9.5 Evaluation of a Fuzzy Group By

9.6 Related Work

9.6.1 Extended group by

9.6.2 Fuzzy OLAP

9.6.3 Fuzzy database summarization techniques

9.6.4 Mining association rules with SQL

9.7 Conclusion

10. Empty and Plethoric Answers

10.1 Introduction

10.2 Empty Answer Problem

10.2.1 Query relaxation

10.2.2 Relaxation by predicate weakening

10.2.2.1 Principle

10.2.2.2 Dilation mechanism

10.2.2.3 Relaxing an atomic criterion

10.2.2.4 Relaxing a conjunctive query

10.2.3 Case-based reasoning approach

10.2.3.1 Introduction and principle

10.2.3.2 Predicate substitution

10.2.3.3 Conjunctive query replacement strategy

10.3 Plethoric Answer Problem

10.3.1 Introduction

10.3.2 Approach based on predicate strengthening

10.3.2.1 Principle

10.3.2.2 Erosion operation

10.3.2.3 Erosion of an atomic query

10.3.2.4 Intensifying a conjunctive query

10.3.3 Approach based on query expansion

10.3.3.1 Fuzzy cardinalities and association rules

10.3.3.2 Shared vocabulary

10.3.3.3 Strengthening steps

10.3.3.4 Strengthening process

10.3.3.5 Experimentation

10.4 Conclusion

11. Conclusion

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Relational Databases,Olivier Pivert,Patrick Bosc