A Fuzzy Valid-Time Model for Relational Databases Within the Hibernate Framework

A Fuzzy Valid-Time Model Contents
Motivation

for Relational Databases Context
Proposal
Example

Within the Hibernate Comparison
Conclusions and . . .

Framework Home Page

Title Page
Jos´ Enrique Pons
e Olga Pons Capote
Ignacio Blanco Medina
Department of Computer Science and Artiﬁcial Intelligence
University of Granada, Spain
{jpons,opc,iblanco}@decsai.ugr.es Page 1 of 37

October 22, 2011 Go Back

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1. Contents Contents
Motivation
Context
The structure of the presentation is: Proposal
Example

• Motivation. Comparison

• Context: Home Page

– Fuzzy relational databases. Title Page

– Temporal databases.
– Fuzzy temporal databases.
– Hibernate. Page 2 of 37

• Proposal: Fuzzy Valid-Time model for relational Go Back

databases. Full Screen

• Conclusions and future work. Close

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Contents
Motivation

2. Motivation Context
Proposal
Example

• Time-related attributes are considered to have Comparison
an impact on the consistency of the object set Home Page
modelled by the database.
Title Page

• A true standard for fuzzy temporal databases
does not exist.
• General model to represent and querying fuzzy Page 3 of 37
temporal types in any relational database.
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• Portable implementation within the Hibernate Full Screen
Framework.
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3. Context Contents
Motivation
Context
• 3.1 Fuzzy relational databases (FBD): Proposal
Example
– Representation: fuzzy data types. Comparison
– Querying: ﬂexible querying. Home Page

• 3.2 Temporal databases: Title Page

– Time models (valid-time, transaction time,
decision time... )
– Temporal operators. Page 4 of 37

• 3.3 Fuzzy temporal databases: Go Back

– Fuzzy Validity Period. Full Screen

• Hibernate. Close

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Contents

3.1. Fuzzy relational databases Motivation
Context
Proposal
Two main features: Example
Comparison
• Fuzzy representation Conclusions and . . .

”The restaurant X in the database is cheap in Home Page

average.” Title Page

”The restaurant X in the database is a ham-
burguer bar.”
• Flexible querying: Page 5 of 37
”The user wants to obtain a list with cheap
restaurants.” Go Back

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3.1.1. Fuzzy data types
Two main types:
Contents
• Ordered underlying domain: Motivation
possibility
Context
Cheap Middle-price Expensive
1 Proposal
Example
Comparison

Home Page
Price
0
16 18 24 26
Title Page
This data type may be represented as a trapezoid
in the form: [α, β, γ, δ].
E.g. Middle-price = [16, 18, 24, 26]
Page 6 of 37
• Non-ordered underlying domain:
Fast food Hamburger Chinese Go Back

Fast food 1 0.8 0.6 Full Screen

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3.1.2. Flexible Querying
The user may query with vagueness in the database: Contents

”The user want to obtain a list of cheap restau- Motivation
Context
rants.” Proposal
Example

ID Name AVG Quality Comparison
001 Amadeus [15,10,20,5] 5 Home Page

002 Atlantis [11,5,17,6] 3 Title Page
003 Cafe Theatre [20,10,30,10] 2
004 De Graslei [23,18,28,5] 5
005 Pakhuis [13,11,15,2] 3
006 De 3 Biggetjes [45,25,65,20] 4 Page 7 of 37
possibility
Cheap Middle-price Expensive
1
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Price Close
0
16 18 24 26

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Contents
Motivation
Context
Proposal
Example

The selected restaurants are: Comparison

Home Page
ID Name AVG Quality
001 Amadeus [15,10,20,5] 5 Title Page

002 Atlantis [11,5,17,6] 3
005 Pakhuis [13,11,15,2] 3
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Operators for fuzzy querying:
Contents
Possibility Necessity Possibly / Necessarily Motivation

FEQ NFEQ Fuzzy = Context
Proposal
FGT NFGT Fuzzy > Example

FGEQ NFGEQ Fuzzy ≥ Comparison
FLT NFLT Fuzzy.< Home Page
FLEQ NFLEQ Fuzzy ≤
Title Page
MGT NMGT Much >
MLT NMLT Much <
F EQ(p1, p2) = sup min(πp1(d), πp2(d)) (1)
d∈U Page 9 of 37

Where U is the underlying domain, p1, p2 are two Go Back

values of a given fuzzy type (e.g. fuzzy type 2) and Full Screen

πp1(d), πp2(d) are the associated possibility distribu- Close
tions.
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Context:
Contents
Motivation
Context
• 3.1 Fuzzy relational databases (FBD): Proposal
Example

– Representation: fuzzy data types. Comparison
– Querying: ﬂexible querying. Home Page

• 3.2 Temporal databases: Title Page

decision time... )
– Temporal operators. Page 10 of 37



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Contents
Motivation
Context
Proposal
Example

3.2. Temporal Databases: Comparison

Home Page
A temporal database is a database that manages the
time in its schema. Title Page

Time-related attributes have an impact on the con-
sistency of the database.
Page 11 of 37

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Contents
Motivation
Context
Example: Proposal
Example
Comparison
ID Name Year Works for Start Year End Year
1 Peter 1987 John 2010 -
Home Page
2 Maria 1978 John 2001 -
3 John 1954 - 1999 - Title Page
4 Sarah 1982 Maria 2005 2009

Consider that ID is the primary key.
Problem: If Sarah is hired in 2010, we can not
insert the new tuple. Page 12 of 37

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Example: Motivation
Context
Proposal
New primary key: Example
Comparison
{ ID ∪[ Start Year, End Year ]} Home Page

Title Page
1 Peter 1987 John 2010 -
2 Maria 1978 John 2001 -
3 John 1954 - 1999 -
4 Sarah 1982 Maria 2005 2009
Page 13 of 37
4 Sarah 29 Maria 2010 -
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Also a consistence mechanism must be deﬁned...
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Example: Motivation
Context
Proposal

Some spurious values might be inserted: Example
Comparison
Home Page
1 Peter 1987 John 2010 -
2 Maria 1978 John 2001 - Title Page
3 John 1954 - 1999 -
4 Sarah 1982 Maria 2005 2009
4 Sarah 29 Maria 2001 2007
4 Sarah 1982 Maria 2010 -
Page 14 of 37
Usually, DML sentences (insert, update, delete) are
re-deﬁned to ensure consistency. Go Back

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Contents
3.2.1. Temporal models Motivation
Context

• Valid-Time: The time when the fact is true in Proposal
Example
the modelled reality. Comparison
• Transaction time: The time when the fact is Home Page
stored in the database.
Title Page

• Decision-time: The time when an event was
decided to happen.
• Bi-temporal: Valid and transaction time. Page 15 of 37

• Tri-temporal: Valid, transaction and decision Go Back

time. Full Screen

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Contents
Motivation
Context
3.2.2. Temporal operators: Proposal
Example

Allen’s temporal relation between intervals: Comparison
Operator Inverse Representation
Home Page
X Before Y After XXX YYY
XXX
X Equal Y Equal YYY Title Page
X Meets Y Meet by XXXYYY
XXX
X Overlaps Y Overlap by YYY
XXX
X During Y Contains YYYYYY
XXX
X Starts Y Start by YYYYYY
XXX Page 16 of 37
X Finishes Y Finished by YYYYYY
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Context:
Contents
Motivation

• 3.1 Fuzzy relational databases (FBD): Context
Proposal

– Representation: fuzzy data types. Example
Comparison
– Querying: ﬂexible querying. Conclusions and . . .

Home Page
• 3.2 Temporal databases:
Title Page

decision time... )
– Temporal operators.
Page 17 of 37



– Fuzzy temporal operators. Close

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Contents
Motivation
Context
Proposal
Example
Comparison

Home Page

3.3. Fuzzy temporal databases: Title Page

Page 18 of 37

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3.3.1. Fuzzy Validity Period:
possibility VET Contents
VST
Initial data values
1 Motivation
Context
Proposal
S1 Example
0 time Comparison
ds-as ds ds+bs de-ae de de+be

possibility Home Page
1

Title Page

S2

time
0
α=d1-a β= d1 γ= d2 δ= d2+b

(ds + bs ) − (ds − as ) d1 − (d1 − a) Page 19 of 37
S1 = S2 ⇒ = (2)
2 2
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Where d1 = ds + bs and d2 = de + ae. Full Screen

The FVP is [d1 − a, d1, d2, d2 + b]. Close

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Contents
Motivation
Context
Proposal
Example
Underlying domain: Julian Day Number (JDN): A Comparison

counter which value is incremented in one unit every Conclusions and . . .

day since 1 January 4713 B.C noon. Home Page

Reasons: Title Page

• Representation as unique number
• Simpliﬁcation of calculations.
Page 20 of 37

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3.3.2. Fuzzy temporal operators:
• BEFORE (I,J) =
Contents

1, if Iβ ≤ Jα
 Motivation
Iα −Jβ
(Jα −Jβ )−(Iβ −Iα )
, if
Iβ > Jα and Iα < Jβ Context

0, otherwise (Iα ≥ Jβ ) Proposal

Example
Comparison
• OVERLAPS (I, J) = Conclusions and . . .

Home Page
sup (min (I (t) , J (t)))
t
Title Page

• CONTAINS (I, J) =
inf {max (1 − I (t) , J (t))}
t
Page 21 of 37

• EQUALS (I, J) = Go Back

min (CON T AIN S (I, J) , CON T AIN S (J, I)) = Full Screen

min(inf {max (1 − I (t) , J (t))},
t Close
inf {max (1 − J (t) , I (t))})
t
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Contents
Motivation
Context
Proposal

Fuzzy temporal operators implemented in FSQL: Example
Comparison

Operator Name FSQL implementation Home Page

BEFORE (I, J) I FGEQ J Title Page
OVERLAPS (I, J) I FEQ J
EQUALS (I, J) min(I NFEQ J, J NFEQ I)
CONTAINS (I, J) I NFEQ J
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Contents
Motivation
Context

3.4. Hibernate Framework Proposal
Example

The Hibernate Framework is a collection of open Comparison
source projects that enable developers to make Home Page

object-relational mapping. Features: Title Page

• Database independent by means of dialects.
• HQL: an object-oriented query language.
• Open source. Page 23 of 37

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3.4.1. Architecture Contents
Motivation
An application working with Hibernate has 3 layers: Context
Proposal

1. Application layer: CRUD (CReate,Update Example
Comparison
and Delete) operations: Conclusions and . . .

(a) Persistent Objects: A current database state. Home Page

(b) Transient Objects: These objects do not rep- Title Page

resent a current database state.
2. Hibernate layer: An abstraction layer be-
tween the DBMS and the application. Page 24 of 37

3. The database: The running DBMS: MySQL, Go Back

PostgreSQL, Oracle...etc. Full Screen

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Contents
Motivation
Context
Proposal
Hibernate Architecture: Example
Comparison
Application
Home Page
Persistent Objects

HIBERNATE Title Page
hibernate. XML mapping
properties

Database
Page 25 of 37

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3.4.2. Querying in Hibernate
1. Query by criteria: Contents
createCriteria(Person.class). Motivation

Add(Restrictions.eq(”login”,”lmmn”)); Context
Proposal
Example
Comparison

2. Query by example: Conclusions and . . .

Person p.login = ”lmmn”; Home Page

Title Page

3. HQL:
Select p from Personal p where p.login =
”lmmn”; Page 26 of 37

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4. SQL: Full Screen

Select * from Person as p where p.login = Close
’lmmn’;
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Contents
Motivation
Context
Proposal
Example
Comparison

4. Proposal Conclusions and . . .

Home Page

• Architecture for the general framework for: Title Page

– Fuzzy representation.
– Fuzzy querying.
Page 27 of 37

• Implementation within the Hibernate frame-
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work.
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Contents
Motivation
Context

4.1. Fuzzy Representation Proposal
Example

Conditions for portability: Comparison

1. The SQL standard is the interface. Home Page

Title Page
2. The fuzzy types are represented in the database
by basic SQL types.
3. The meta-data for managing properly the ex-
tended types relies outside the database catalog. Page 28 of 37

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Contents
4.1.1. Architecture for the general model Motivation
Context

The architecture for a generalized object-oriented Proposal
Example
model needs the following elements: Comparison
Object-Oriented Layer.
O1 ON (OORL) Home Page

Object-Oriented to Relational. Title Page
(OO2RL).

RN Relational Layer.
R1
(RRL)

Conversion Layer. (CL)
Page 29 of 37

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MySQL PostgreSQL Oracle

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Contents
Motivation
4.1.2. Implementation Context
Proposal

The model has the following layers: Example
Comparison
Application
Home Page
Fuzzy Data Types Fuzzy Domains Fuzzy Representation
Constraint
Values Labels Constraint Layer (OORL) F Title Page
Validator
S
Fuzzy Data Fuzzy Domain Q
Types Adaptor Adaptor Adaptation L
Layer (OO2RRL)
Type 2 Type 3 & (RRL)

Hibernate Core
Conversion
Page 30 of 37
Layer (CL)
Database
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Architecture with the FVP support: Contents
Motivation
Context
Proposal
Application
Example
Comparison
Hibernate FVP

Hibernate FSQL Home Page

Hibernate Title Page

Database

The Hibernate FSQL allows the representation and
querying of objects with fuzzy attributes. Page 31 of 37

The Hibernate FVP layer allows the use of Fuzzy Go Back

Validity Periods. Full Screen

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4.2. Fuzzy Querying
The model uses the following elements:
Contents

• Declarative implementation for each fuzzy Motivation
Context
operator. This implementation should be done Proposal

in the SQL language. Example
Comparison

• Abstract syntax tree (AST) representa- Conclusions and . . .

Home Page
tion for the query. These representation allows
a customization process done by the conversion Title Page

layer (CL).
• Conversion Layer: This layer customizes the
AST for the running database. Page 32 of 37

The implementation of the fuzzy querying is done by Go Back

modifying the HQL language. The fuzzy operators Full Screen

are implemented in a declarative way in the SQL Close

language. Quit

Query translation:
Contents
SQL sentence
SELECT Motivation
"SELECT *
HQL sentence:
c,c1
FROM Customer as c, Context
"SELECT c
Translation FROM Customization Customer as c1
FROM Customer c, WHERE 1 < CASE WHEN Proposal
Customer c1 (c.fvp.gamma <= beta2)
WHERE c.fvp Customer WHERE OR (c.fvp.beta >= gamma2) THEN 0 Example
contains c1.fvp" WHEN (c.fvp.alpha = alpha2) THEN 1
WHEN (c.fvp.gamma > beta2) AND
Comparison
contains (c.fvp.alpha < alpha2)
THEN (c.fvp.gamma - beta2) /
( c.fvp.delta - delta2 )
c.fvp c1.fvp
ELSE (gamma2 - c.fvp.beta) /
( c.fvp.delta + delta2 );" Home Page

• The framework builds an abstract syntax tree Title Page

(AST) once the query passed lexical and syntac-
tical analysis.
• The AST represents tokens as nodes. The se- Page 33 of 37

mantic analyzer renders the tree in the into SQL Go Back

sentences. Then the dialect customizes the SQL Full Screen
sentence.
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Example:
Contents
ID Name Salary BossID FVP Motivation
001 Josh 1200 C [10/10/2009,27/10/2009,19/10/2010,27/10/2010] Context
001 Josh 1500 B [19/10/2010,27/10/2010,-,-]
Proposal
002 Robert 800 A [14/05/2007,25/05/2007,17/01/2008,30/01/2008]
002 Robert 1200 A [17/01/2008,30/01/2008,24/05/2009 ,30/05/2009] Example

002 Robert 1400 A [24/05/2009,30/05/2009,28/10/2010,30/10/2010] Comparison
003 Alex 2100 - [02/05/2007,15/05/2007,-,-] Conclusions and . . .
004 Tyna 1300 002 [25/07/2009,30/7/2009,15/10/2009,25/10/2009]
005 Rose 2300 003 [25/09/2010,30/09/2010,25/02/2011,30/02/2011] Home Page

”Find all the employees with the boss 002 during the same period of Title Page
time.”

SELECT e,f FROM Employee e, Employee f WHERE e.ID="002"
AND e.ID<>f.ID AND e.fvp EQUALS f.fvp; Page 34 of 37

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e.ID e.name f.ID f.name Comp. Full Screen
001 Josh 004 Tyna 0, 55
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Contents
Motivation
Context

5. Conclusions and Future Proposal
Example

Work Comparison

Home Page

• We introduced a framework for the representa- Title Page
tion of fuzzy types and for fuzzy querying.
• The implementation within Hibernate is based
on the portability.
Page 35 of 37

• The drawback for the portability is the depen- Go Back
dency between the application and the frame-
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work.
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Contents
Motivation

Future work: Context
Proposal

• Fuzzy querying: bipolar speciﬁcation in the Example
Comparison
queries Conclusions and . . .

• Applications in historical databases: the time is Home Page

usually not precisely known. Title Page

• New fuzzy temporal representation: representa-
tion for Fuzzy Validity Periods and implementa-
tion of temporal comparisons within the Allen’s Page 36 of 37

relations. Go Back

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Contents
Motivation
Context
Proposal
Example
Thank you! Comparison

Home Page
Questions?
Title Page

Contact:
jpons@decsai.ugr.es
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A Fuzzy Valid-Time Model for Relational Databases Within the Hibernate Framework

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