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

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 ,

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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

$37.50

Chapter 2

Slawomir Zadrozny, Guy de Tré, Rita de Caluwe, Janusz Kacprzyk

$37.50

$37.50

Chapter 4

Handling Bipolar Queries in Fuzzy Information Processing
(pages 97-114)

Didier Dubois, Henri Prade

$37.50

Chapter 5

Noureddine Mouaddib, Guillaume Raschia, W. Amenel Voglozin, Laurent Ughetto

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Chapter 6

On the Versatility of Fuzzy Sets for Modeling Flexible Queries
(pages 143-166)

P Bosc, A Hadjali, O Pivert

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Chapter 7

Flexible Querying Techniques Based on CBR
(pages 167-190)

Guy De Tré, Marysa Demoor, Bert Callens, Lise Gosseye

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Chapter 8

Customizable Flexible Querying in Classical Relational Databases
(pages 191-217)

Bordogna Bordogna, Guiseppe Psaila

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Chapter 9

Qualifying Objects in Classical Relational Database Querying
(pages 218-245)

Cornelia Tudorie

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Chapter 10

Evaluation of Quantified Statements Using Gradual Numbers
(pages 246-269)

Ludovic Liétard, Daniel Rocacher

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Chapter 11

FSQL and SQLf: Towards a Standard in Fuzzy Databases
(pages 270-298)

Angélica Urrutia, Leonid Tineo, Claudia Gonzalez

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Chapter 12

Hierarchical Fuzzy Sets to Query Possibilistic Databases
(pages 299-324)

Rallou Thomopoulos, Patrice Buche, Ollivier Haemmerlé

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Chapter 14

Mohamed Ali Ben Hassine, Amel Grissa Touzi, José Galindo, Habib Ounelli

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Chapter 16

Data Model of FRDB with Different Data Types and PFSQL
(pages 407-434)

Aleksandar Takaci, Srdan Škrbic

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Chapter 17

Towards a Fuzzy Object-Relational Database Model
(pages 435-461)

Carlos D. Barranco, Jesús R. Campaña, Juan M. Medina

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Chapter 18

Relational Data,Formal Concept Analysis, and Graded Attributes
(pages 462-489)

Radim Belohlavek

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Chapter 19

Markus Schneider

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Chapter 20

Fuzzy Classification in Shipwreck Scatter Analysis
(pages 516-537)

Yauheni Veryha, Jean-Yves Blot, Joao Coelho

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Chapter 21

Yan Chen, Graham H. Rong, Jianhua Chen

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Chapter 22

Applying Fuzzy Data Mining to Tourism Area
(pages 563-584)

R. A. Carrasco, F. Araque, A. Salguero, M. A. Vila

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Chapter 23

Fuzzy Classification on Relational Databases
(pages 586-614)

Andreas Meier, Günter Schindler, Nicolas Werro

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Chapter 24

Incremental Discovery of Fuzzy Functional Dependencies
(pages 615-633)

Shyue-Liang Wang, Ju-Wen Shen, Tuzng-Pei Hong

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Chapter 25

Data Dependencies in Codd's Relational Model with Similarities
(pages 634-657)

Radim Belohlavek, Vilem Vychodil

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Chapter 26

Fuzzy Inclusion Dependencies in Fuzzy Databases
(pages 658-684)

Awadhesh Kumar Sharma, A. Goswami, D. K. Gupta

$37.50

Chapter 27

Wai-Ho Au

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Chapter 30

Hamid Haidarian Shahri

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Chapter 33

Fuzzy Imputation Method for Database Systems
(pages 805-821)

J. I. Peláez, J. M. Doña, D. La Red

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