Fuzzy Classification on Relational Databases

Fuzzy Classification on Relational Databases

Andreas Meier (University of Fribourg, Switzerland), Günter Schindler (Galexis AG, Switzerland) and Nicolas Werro (University of Fribourg, Switzerland)
Copyright: © 2008 |Pages: 29
DOI: 10.4018/978-1-59904-853-6.ch023
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In practice, information systems are based on very large data collections mostly stored in relational databases. As a result of information overload, it has become increasingly difficult to analyze huge amounts of data and to generate appropriate management decisions. Furthermore, data are often imprecise because they do not accurately represent the world or because they are themselves imperfect. For these reasons, a context model with fuzzy classes is proposed to extend relational database systems. More precisely, fuzzy classes and linguistic variables and terms, together with appropriate membership functions, are added to the database schema. The fuzzy classification query language (fCQL) allows the user to formulate unsharp queries that are then transformed into appropriate SQL statements using the fCQL toolkit so that no migration of the raw data is needed. In addition to the context model with fuzzy classes, fCQL and its implementation are presented here, illustrated by concrete examples.

Key Terms in this Chapter

Fuzzy Classification Database Schema: A fuzzy classification database schema R(A,C,X,T) is a database schema with a set of attributes A, a set of associated contexts C, a set of linguistic variables X, and a set of corresponding terms T. Each linguistic variable Xi has an associated set of terms T(Xi):={T1,…,Tk}. Note that the number of terms depends on the linguistic variable, that is, all linguistic variables must not have the same number of terms.

Merge Operator: The merge operator of two context-redundant tuples t and t’ leads to a new tuple u=(u1,…,un) and is defined as the set theoretic union uj:=tj ? t j’ of all tuple components uj.

Gamma Operator: The operator is used to weigh several attributes, and to calculate the aggregation of membership degrees x1, …, xm: . The ?-operator is composed of the algebraic product operator, a t-norm, and its counterpart the algebraic sum, a t-conorm. The ?-argument ranging from 0 to 1 specifies whether the results should go in the direction of the algebraic product (with ?=0) or toward the algebraic sum (with ?=1). The ?-argument therefore determines the strength of the compensation mechanism.

Linguistic Variable: A linguistic variable is characterized by a quintuple (X,T,U,G,M) where X is the name of the variable, T is the set of terms of X, U is the universe of discourse, G is a syntactic rule for generating the name of the terms, and M is a semantic rule for associating each term with its meaning, that is, a fuzzy set defined on U.

Hierarchical Decomposition: Having a multidimensional fuzzy classification, that is, the classification space has more than two dimensions, leads to a large number of classes whose semantics cannot be derived properly. In order to maintain classes with a meaningful definition, a multidimensional fuzzy classification can be decomposed into a hierarchy of fuzzy classifications. The hierarchical decomposition merges subsets of qualifying attributes to fuzzy subclassifications (composed attributes). The composed attributes are integrated as linguistic variables in classes of higher levels leading to a hierarchy of fuzzy classification. The value v(e) of an element e of a composed attribute can be derived by assigning to each fuzzy class Ck a grade gr(Ck) expressing the meaning of the composed attribute. By aggregating these grades multiplied with the membership degrees of the classified elements, the formula looks like this: .

Database Schema with Contexts: A relational database schema R(A,C) with contexts is a set of attributes A=(A1,…,An) with a associated set of contexts C=(C1(A1),…,Cn(An)). To every attribute Aj defined by a domain D(Aj) there is added a context C(Aj). A context C(Aj) is a partition of D(Aj) into equivalence classes.

Context-Based Selection: For a relation r of a database schema R(A,C) with contexts, a schema R(QA,QC) with a query set of attributes QA ? A, and a set of associated query contexts QC, there exists a context-based selection S [ß(QA,QC)](r) where ß(QA,QC) is a Boolean condition for values of the attribute set QA and corresponding query contexts QC.

Fuzzy Classification Query Language (fCQL): fCQL is a data analysis tool that allows users to query a predefined fuzzy classification of relational databases. In contrast to the fuzzy query languages, the user does not need to deal with a fuzzy SQL or with fuzzy predicates, which could lead to varying semantics and different interpretations of the original data collection. From the user’s point of view, fCQL can be seen as a human-oriented query language as it functions at the linguistic level. The language can be applied without numerical values through the use of predefined linguistic variables and their associated verbal terms. In this way, the user can easily formulate classification queries as they are intuitive; that is, the meaning of the queries is linguistically expressed.

Context Redundancy: Two tuples t and t’ of a relation r with associated schema R(A,C) are context redundant regarding the corresponding set of contexts C=(C1(A1),…,Cn(An)) if all tuple components tj and tj’ belong to the same equivalence class.

Context-Based Relational Algebra: Classical relational algebra consists of five operators, that is, set theoretic union, set theoretic difference, and Cartesian product as well as projection p and selection s. Context-based relational algebra is an extension of classical relational algebra that uses relational database schemas R(A,C) with contexts. For a given set of querying attributes QA and a set of corresponding querying contexts QC, there exists a context-based union, a context-based difference, and a context-based Cartesian product, as well as a context-based projection ? and selection S.

Context-Based Projection: For a relation r of a database schema R(A,C) with contexts and a schema R(QA,QC) with a query set of attributes QA ? A and a set of associated query contexts QC, there exists a context-based projection ?[QA,QC](r). The projection of r regarding R(QA,QC) is a relation qr of R(QA,QC). The tuples in qr are calculated by reducing the tuple components of r to the set of querying attributes QA. Context-redundant tuples regarding QC are merged by the merge operator.

Complete Chapter List

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Editorial Advisory Board
Program Committee
Table of Contents
Maria Amparo Vila, Miguel Delgado
José Galindo
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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