Introduction and Trends to Fuzzy Logic and Fuzzy Databases

Introduction and Trends to Fuzzy Logic and Fuzzy Databases

José Galindo (University of Málaga, Spain)
Copyright: © 2008 |Pages: 33
DOI: 10.4018/978-1-59904-853-6.ch001
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Abstract

This chapter presents an introduction to fuzzy logic and to fuzzy databases. With regard to the first topic, we have introduced the main concepts in this field to facilitate the understanding of the rest of the chapters to novel readers in fuzzy subjects. With respect to the fuzzy databases, this chapter gives a list of six research topics in this fuzzy area. All these topics are briefly commented on, and we include references to books, papers, and even to other chapters of this handbook, where we can find some interesting reviews about different subjects and new approaches with different goals. Finally, we give a historic summary of some fuzzy models, and we conclude with some future trends in this scientific area.

Key Terms in this Chapter

Soft Computing: Computational techniques in computer science and some engineering disciplines, which attempt to study, model, and analyze very complex phenomena: those for which more conventional methods have not yielded low cost, analytic, and complete solutions. Earlier computational approaches could model and precisely analyze only relatively simple systems. More complex systems arising in biology, medicine, the humanities, management sciences, artificial intelligence, machine learning, and similar fields often remained intractable to conventional mathematical and analytical methods. Soft computing techniques include: fuzzy systems (FS), neural networks (NN), evolutionary computation (EC), probabilistic reasoning (PR), and other ideas (chaos theory, etc.). Soft computing techniques often complement each other.

Fuzzy Database: If a regular or classical database is a structured collection of information (records or data) stored in a computer, a fuzzy database is a database which is able to deal with uncertain or incomplete information using fuzzy logic. There are many forms of adding flexibility in fuzzy databases. The simplest technique is to add a fuzzy membership degree to each record, that is, an attribute in the range [0,1]. However, there are other kinds of databases allowing fuzzy values to be stored in fuzzy attributes using fuzzy sets, possibility distributions, or fuzzy degrees associated to some attributes and with different meanings (membership degree, importance degree, fulfillment degree, etc.). Of course, fuzzy databases should allow fuzzy queries using fuzzy or nonfuzzy data and there are some languages that allow this kind of queries, like FSQL or SQLf. In synthesis, the research in fuzzy databases includes the following areas: flexible querying in classical or fuzzy databases, extending classical data models in order to achieve fuzzy databases (fuzzy relational databases, fuzzy object-oriented databases, etc.), fuzzy conceptual modeling, fuzzy data mining techniques, and applications of these advances in real databases.

T-conorm or S-norm: Function s establishing a generic model for the operation of union with fuzzy sets. These functions must comply with certain basic properties: commutative, associative, monotonicity, and border conditions (x s 0 = x, and x s 1 = 1). The most typical is the maximum function, but other widely accepted s-norms exist (Table 2).

Fuzzy Implication: Function computing the fulfillment degree of a rule expressed by IF X THEN Y, where the antecedent and the consequent are fuzzy. These functions must comply with certain basic properties and the most typical is the Kleene-Dienes implication, based on the classical implication definition (x?y = ¬x ? y), using the Zadeh’s negation and the maximum s-norm, but other fuzzy implication functions exist (Table 3).

T-norm: Function t establishing a generic model for the operation of intersection with fuzzy sets. These functions must comply with certain basic properties: commutative, associative, monotonicity, and border conditions (x t 0 = 0, and x t 1 = x). The most typical is the minimum function, but there exists other t-norms widely accepted (Table 1).

Fuzzy Quantifiers: Expressions allowing us to express fuzzy quantities or proportions in order to provide an approximate idea of the number of elements of a subset fulfilling a certain condition or of the proportion of this number in relation to the total number of possible elements. Fuzzy quantifiers can be absolute or relative. Absolute quantifiers express quantities over the total number of elements of a particular set, stating whether this number is, for example, “much more than 10,” “close to 100,” “a great number of,” and so forth. Relative quantifiers express measurements over the total number of elements, which fulfill a certain condition depending on the total number of possible elements. This type of quantifier is used in expressions such as “the majority” or “most,” “the minority,” “little of,” “about half of,” and so on.

Fuzzy Attribute: In a database context, a fuzzy attribute is an attribute of a row or object in a database, with a fuzzy datatype, which allows storing fuzzy information. Sometimes, if a classic attribute allows fuzzy queries, then it is also called fuzzy attribute, because it has only some of the fuzzy attribute characteristics.

Fuzzy Logic: Fuzzy logic is derived from fuzzy set theory by Zadeh (1965), dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. It can be thought of as the application side of fuzzy set theory dealing with well thought out real world expert values for a complex problem.

Possibility Theory: This theory is based on the idea that we can evaluate the possibility of a determinate variable X being (or belonging to) a determinate set or event A. Here, fuzzy sets are called possibility distributions and instead of measuring the membership degrees, they measure the possibility degrees. All the tools and properties defined for fuzzy sets are also applicable to possibility distributions.

Complete Chapter List

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Editorial Advisory Board
Program Committee
Table of Contents
Foreword
Maria Amparo Vila, Miguel Delgado
Preface
José Galindo
Acknowledgment
Chapter 1
José Galindo
This chapter presents an introduction to fuzzy logic and to fuzzy databases. With regard to the first topic, we have introduced the main concepts in... Sample PDF
Introduction and Trends to Fuzzy Logic and Fuzzy Databases
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Chapter 2
Slawomir Zadrozny, Guy de Tré, Rita de Caluwe, Janusz Kacprzyk
In reality, a lot of information is available only in an imperfect form. This might be due to imprecision, vagueness, uncertainty, incompleteness... Sample PDF
An Overview of Fuzzy Approaches to Flexible Database Querying
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Chapter 3
Balazs Feil, Janos Abonyi
This chapter aims to give a comprehensive view about the links between fuzzy logic and data mining. It will be shown that knowledge extracted from... Sample PDF
Introduction to Fuzzy Data Mining Methods
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Chapter 4
Didier Dubois, Henri Prade
The chapter advocates the interest of distinguishing between negative and positive preferences in the processing of flexible queries. Negative... Sample PDF
Handling Bipolar Queries in Fuzzy Information Processing
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Chapter 5
Noureddine Mouaddib, Guillaume Raschia, W. Amenel Voglozin, Laurent Ughetto
This chapter presents a discussion on fuzzy querying. It deals with the whole process of fuzzy querying, from the query formulation to its... Sample PDF
From User Requirements to Evaluation Strategies of Flexible Queries in Databases
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Chapter 6
P Bosc, A Hadjali, O Pivert
The idea of extending the usual Boolean queries with preferences has become a hot topic in the database community. One of the advantages of this... Sample PDF
On the Versatility of Fuzzy Sets for Modeling Flexible Queries
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Chapter 7
Guy De Tré, Marysa Demoor, Bert Callens, Lise Gosseye
In case-based reasoning (CBR), a new untreated case is compared to cases that have been treated earlier, after which data from the similar cases (if... Sample PDF
Flexible Querying Techniques Based on CBR
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Chapter 8
Bordogna Bordogna, Guiseppe Psaila
In this chapter, we present the Soft-SQL project whose goal is to define a rich extension of SQL aimed at effectively exploiting flexibility offered... Sample PDF
Customizable Flexible Querying in Classical Relational Databases
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Chapter 9
Cornelia Tudorie
The topic presented in this chapter refers to qualifying objects in some kinds of vague queries sent to relational databases. We want to compute a... Sample PDF
Qualifying Objects in Classical Relational Database Querying
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Chapter 10
Ludovic Liétard, Daniel Rocacher
This chapter is devoted to the evaluation of quantified statements which can be found in many applications as decision making, expert systems, or... Sample PDF
Evaluation of Quantified Statements Using Gradual Numbers
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Chapter 11
Angélica Urrutia, Leonid Tineo, Claudia Gonzalez
Actually, FSQL and SQLf are the main fuzzy logic based proposed extensions to SQL. It would be very interesting to integrate them with a standard... Sample PDF
FSQL and SQLf: Towards a Standard in Fuzzy Databases
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Chapter 12
Rallou Thomopoulos, Patrice Buche, Ollivier Haemmerlé
Within the framework of flexible querying of possibilistic databases, based on the fuzzy set theory, this chapter focuses on the case where the... Sample PDF
Hierarchical Fuzzy Sets to Query Possibilistic Databases
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Chapter 13
Troels Andreasen, Henrik Bulskov
The use of taxonomies and ontologies as a foundation for enhancing textual information base access has recently gained increased attention in the... Sample PDF
Query Expansion by Taxonomy
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Chapter 14
Mohamed Ali Ben Hassine, Amel Grissa Touzi, José Galindo, Habib Ounelli
Fuzzy relational databases have been introduced to deal with uncertain or incomplete information demonstrating the efficiency of processing fuzzy... Sample PDF
How to Achieve Fuzzy Relational Databases Managing Fuzzy Data and Metadata
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Chapter 15
Geraldo Xexéo, André Braga
We present CLOUDS, which stands for C++ Library Organizing Uncertainty in Database Systems, a tool that allows the creation of fuzzy reasoning... Sample PDF
A Tool for Fuzzy Reasoning and Querying
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Chapter 16
Aleksandar Takaci, Srdan Škrbic
This chapter introduces a way to extend the relational model with mechanisms that can handle imprecise, uncertain, and inconsistent attribute values... Sample PDF
Data Model of FRDB with Different Data Types and PFSQL
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Chapter 17
Carlos D. Barranco, Jesús R. Campaña, Juan M. Medina
This chapter introduces a fuzzy object-relational database model including fuzzy extensions of the basic object-relational databases constructs, the... Sample PDF
Towards a Fuzzy Object-Relational Database Model
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Chapter 18
Radim Belohlavek
Formal concept analysis is a particular method of analysis of relational data. Also, formal concept analysis provides elaborate mathematical... Sample PDF
Relational Data,Formal Concept Analysis, and Graded Attributes
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Chapter 19
Markus Schneider
Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with crisp... Sample PDF
Fuzzy Spatial Data Types for Spatial Uncertainty Management in Databases
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Chapter 20
Yauheni Veryha, Jean-Yves Blot, Joao Coelho
There are many well-known applications of fuzzy sets theory in various fields of science and technology. However, we think that the area of maritime... Sample PDF
Fuzzy Classification in Shipwreck Scatter Analysis
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Chapter 21
Yan Chen, Graham H. Rong, Jianhua Chen
A Web-based fabric database is introduced in terms of its physical structure, software system architecture, basic and intelligent search engines... Sample PDF
Fabric Database and Fuzzy Logic Models for Evaluating Fabric Performance
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Chapter 22
R. A. Carrasco, F. Araque, A. Salguero, M. A. Vila
Soaring is a recreational activity and a competitive sport where individuals fly un-powered aircrafts known as gliders. The soaring location... Sample PDF
Applying Fuzzy Data Mining to Tourism Area
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Chapter 23
Andreas Meier, Günter Schindler, Nicolas Werro
In practice, information systems are based on very large data collections mostly stored in relational databases. As a result of information... Sample PDF
Fuzzy Classification on Relational Databases
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Chapter 24
Shyue-Liang Wang, Ju-Wen Shen, Tuzng-Pei Hong
Mining functional dependencies (FDs) from databases has been identified as an important database analysis technique. It has received considerable... Sample PDF
Incremental Discovery of Fuzzy Functional Dependencies
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Chapter 25
Radim Belohlavek, Vilem Vychodil
This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational... Sample PDF
Data Dependencies in Codd's Relational Model with Similarities
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Chapter 26
Awadhesh Kumar Sharma, A. Goswami, D. K. Gupta
In this chapter, the concept of fuzzy inclusion dependencies (FIDas) in fuzzy databases is introduced and inference rules on such FIDas are derived.... Sample PDF
Fuzzy Inclusion Dependencies in Fuzzy Databases
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Chapter 27
Wai-Ho Au
The mining of fuzzy association rules has been proposed in the literature recently. Many of the ensuing algorithms are developed to make use of only... Sample PDF
A Distributed Algorithm for Mining Fuzzy Association Rules in Traditional Databases
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Chapter 28
Yi Wang
This chapter applies fuzzy logic to a dynamic causal mining (DCM) algorithm and argues that DCM, a combination of association mining and system... Sample PDF
Applying Fuzzy Logic in Dynamic Causal Mining
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Chapter 29
Céline Fiot
The explosive growth of collected and stored data has generated a need for new techniques transforming these large amounts of data into useful... Sample PDF
Fuzzy Sequential Patterns for Quantitative Data Mining
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Chapter 30
Hamid Haidarian Shahri
Entity resolution (also known as duplicate elimination) is an important part of the data cleaning process, especially in data integration and... Sample PDF
A Machine Learning Approach to Data Cleaning in Databases and Data Warehouses
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Chapter 31
Malcolm Beynon
The general fuzzy decision tree approach encapsulates the benefits of being an inductive learning technique to classify objects, utilising the... Sample PDF
Fuzzy Decision-Tree-Based Analysis of Databases
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Chapter 32
Malcolm Beynon
Outranking methods are a family of techniques concerned with ranking the preference for alternatives based on the criteria values that describe... Sample PDF
Fuzzy Outranking Methods Including Fuzzy PROMETHEE
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Chapter 33
J. I. Peláez, J. M. Doña, D. La Red
Missing data is often an actual problem in real data sets, and different imputation techniques are normally used to alleviate this problem.... Sample PDF
Fuzzy Imputation Method for Database Systems
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Chapter 34
Safìye Turgay
In this chapter, an agent-based fuzzy data mining structure was developed to process and evaluate data with an enlargement in the knowledge... Sample PDF
Intelligent Fuzzy Database Management Systems
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