Fuzzy Inclusion Dependencies in Fuzzy Databases

Fuzzy Inclusion Dependencies in Fuzzy Databases

Awadhesh Kumar Sharma (MMM Engg College, Gorakhpur, UP, India), A. Goswami (I.I.T., Kharagpur, India) and D. K. Gupta (I.I.T., Kharagpur, India)
Copyright: © 2008 |Pages: 27
DOI: 10.4018/978-1-59904-853-6.ch026
OnDemand PDF Download:


In this chapter, the concept of fuzzy inclusion dependencies (FIDas) in fuzzy databases is introduced and inference rules on such FIDas are derived. These FIDas may arise while putting efforts to integrate fuzzy relational databases into a fuzzy relational multidatabase. Since the concept of FIDas itself is new, no work has been done as yet for its discovery in fuzzy relational databases. Hence, an algorithm has been proposed for the discovery of FIDas that may exist between two given fuzzy relations stored in one or more fuzzy relational databases. The existence of such an FIDa will indicate that the two relations are relevant for integration during the course of integration of fuzzy databases.

Key Terms in this Chapter

Partial Fuzzy Inclusion Dependency (FIDa): Let and be (projections on) two fuzzy relations. Let X be a sequence of k distinct fuzzy attribute names from R, and Y be a sequence of k distinct fuzzy attribute names from S, with . Then, a partial fuzzy inclusion dependency is an assertion of the form , such that the fuzzy subset-hood, where is specified in the interval [0,1] and most of the Fuzzy Values under all the attribute names in are Fuzzy Value Equivalent to some Fuzzy Values under respective attribute names in , however, the vice versa may not hold.

Valid FID: A is valid between two relations and if the sets of fuzzy tuples in and satisfy the assertion given by . Otherwise, is called invalid for R and S. In other words, is said to be valid if holds.

Fuzzy Inclusion Dependency (FID): Let and be (projections on) two fuzzy relations. Let X be a sequence of k distinct fuzzy attribute names from R, and Y be a sequence of k distinct fuzzy attribute names from S, with . Then, fuzzy inclusion dependency FID is an assertion of the form , where all the Fuzzy Values under all the attribute names in are Fuzzy Value Equivalent to some Fuzzy Values under respective attribute names in, however, the vice versa may not hold.

Fuzzy Value Equivalent (FVEQ): Fuzzy Value Equivalent (FVEQ): Let A and B be two fuzzy sets with their membership functions and respectively. A fuzzy value is said to be equivalent to some other fuzzy value , for some , where is the set of crisp values that are returned by , where is the inverse of the membership function of fuzzy set A.

Derived FID: A valid FID can be derived from a set of valid FIDs, denoted by ¦, if can be obtained by repeatedly applying the above axioms on some set of FIDs taken from . Similarly, a valid partial inclusion dependency can be derived from a fuzzy set of valid denoted by¦, if can be obtained by repeatedly applying the axioms on some set of FIDs taken from . The membership function of the fuzzy set may be given as follows:, where and, n and m are the cardinality of sets of fuzzy attribute names belonging to fuzzy relations R and S respectively. For example a fuzzy set of valid of arity k may be given as,

Generating Set of FIDa: Consider a fuzzy set of valid partial fuzzy inclusion dependencies:. A generating set of , denoted by, and is a set of valid with the following properties: 1.¦, 2.¦).where the symbol ’’ stands for “fuzzy set-difference”.

Equality of FIDs: Two FIDs and are equal iff there is a sequence () of distinct integers , such that ,. A similar definition holds for the equality of partial fuzzy inclusion dependencies too.

Fuzzy Relational Database of Type-2: A type-2 fuzzy relation r is a fuzzy subset of D, where must satisfy the condition where .

Fuzzy Relational Database of Type-1: In type-1 fuzzy relations, may be a classical subset or a fuzzy subset of . Let the membership function of be denoted by , for . Then from the definition of Cartesian product of fuzzy sets, is a fuzzy subset of . Hence a type-1 fuzzy relation r is also a fuzzy subset of with membership function.

a-Cut: Given a fuzzy set defined on and any number, the -cut , and the strong -cut, , are the crisp sets ,

Complete Chapter List

Search this Book:
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
About the Editor
About the Contributors