ppi 201502ZU4659
This scientific digital publication is
continuance of the printed journal
p-ISSN 0254-0770 / e-ISSN 2477-9377 / Legal Deposit pp 197802ZU38
UNIVERSIDAD DEL ZULIA
An international refereed Journal
indexed by:
• SCOPUS
• SCIELO
• LATINDEX
• DOAJ
• MIAR
• REDIB
• AEROSPACE DATABASE
• CIVIL ENGINEERING ABTRACTS
• METADEX
• COMMUNICATION ABSTRACTS
• ZENTRALBLATT MATH, ZBMATH
• ACTUALIDAD IBEROAMERICANA
• BIBLAT
• PERIODICA
• REVENCYT
DE LA FACULTAD DE INGENIERÍA
REVIST
A TÉCNICAREVISTA TÉCNICA
“Post nubila phoebus”
“After the clouds, the sun”
“Post nubila phoebus”
“After the clouds, the sun”
LUZ in its 130th
anniversary
Established since
1891
LUZ in its 130th
anniversary
Established since
1891
VOLUME 44
JANUARY - APRIL 2021
NUMBER 1
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, January-April, 2021, 36-43
An Implementation for SQL Fuzzy Grouping
Ana Isabel Aguilera Faraco
*1
, Marlene Goncalves Da Silva
2
1
Escuela de Ingeniería Informática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, C.P.
2340000, Chile
2
Departamento de Computación y Tecnología de la Información, Universidad Simón Bolívar, Caracas,
Venezuela, Apartado 89000, Caracas, Venezuela.
*Corresponding author: ana.aguilera@uv.cl
https://doi.org/10.22209/rt.v44n1a05
Received: 13 de abril de 2020 | Accepted: 20 de octubre de 2020 | Available: 01 de enero de 2021
Abstract
Also, some DBMS extensions based on fuzzy logic have been proposed to improve the expressiveness of query languages.
Among which SQLf is an extension of SQL that supports fuzzy conditions. Separately, the Group-By is a database operator
widely used in data analysis and decision support systems. In many cases, it seems useful to group values according to their
similarity to a certain concept rather than establishing grouping on the basis of equal values. In this context, a new SQLf
structure called Fuzzy Group By (FGB) has been proposed to support a grouping based on fuzzy partitions. In this work, we
incorporated the fuzzy grouping in PostgreSQLf, which is an extension of the PostgreSQL DBMS for the handling of fuzzy
queries using the SQLf language on the basis of a tight coupled architecture, i.e., directly into the DBMS. We have proposed
an algorithm based on a hash to evaluate the FGB operator and also empirically assessed the performance of PostgreSQLf
over the TPC Benchmark™ -H (TPC-H).
Keywords: Fuzzy Group By; PostgreSQLf; tight coupled architecture
Una Implementación para el Agrupamiento Difuso en SQL
Resumen
Los sistemas de gestión de bases de datos (SGBD) relacionales tienen una gran utilidad en el almacenamiento
la lógica difusa, para mejorar la expresividad de los lenguajes de consulta, entre ellos, el lenguaje SQLf (extensión de SQL
que soporta condiciones difusas). Por otra parte, el Group-By es un operador de base de datos ampliamente utilizado en el
su similitud con un determinado concepto en lugar de establecer la agrupación sobre la base de valores iguales. En este
contexto, se ha propuesto una nueva estructura de SQLf denominada Fuzzy Group By (FGB), para apoyar una agrupación
basada en particiones difusas. En este trabajo, se incorporó la agrupación difusa en PostgreSQLf, que es una extensión
del SGBD PostgreSQL, para el manejo de consultas difusas utilizando el lenguaje SQLf con una arquitectura fuertemente
acoplada (directamente en el SGBD). Se pronone un algoritmo basado en un hash para evaluar el operador FGB y también se
Palabras clave: Fuzzy Group By; PostgreSQLf; arquitectura fuertemente acoplada.
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
37
An Implementation for SQL Fuzzy Grouping
Introduction
Despite the dizzying development of database
technology, common DataBase management systems
(DBMSs) do not allow the expression of gradual users’
requirements because they suffer from the problem of
rigidity [1], [2], [3]. In a classic system, users’ requirements
must be expressed in a precise manner. In this sense, the
rigidity of classical systems has two main consequences
[4]. There is no discrimination of responses according to
users’ preferences and the borderline responses can leave
out results. Fuzzy logic offers new tools for accessing and
processing data that may have applicability in systems
where users’ requirements are not precise by nature [5],
[6], [7].
The standard Group-By operator has great
importance for data warehouses and analysis techniques
such as OLAP and data mining, and it has relatively good
runtime and scalability properties. Even though, the
semantics of Group-By is simple, it is limited to equality
(all tuples in a group have exactly the same values as the
grouping attributes). To overcome these shortcomings,
Bosc and Pivert [8] propose to extend the Group-By
clause in SQLf by means of the Fuzzy Group-By (FGB)
fuzzy partitions in the domain attributes instead of data
equality. A Group-By clause in SQL builds a partition
in that clause, e.g., “GROUP BY A” constructs a partition
where every group is associated with a value of A present
in the relationship. Bosc and Pivert’s idea is to extend
this mechanism in order to build partitions in terms of
intervals or fuzzy sets of values. In addition, they add a
variant of the count aggregation function called count-rel,
which calculates the relative cardinality (e.g., the average
satisfaction degree) associated with a group.
Emerging applications such as biological databases
approximate values. In addition, business applications
from SQLf statements that identify groups of similar
values. The implementation of fuzzy grouping within a
database engine can have the advantage that the execution
time of Fuzzy Group-By is comparable to the conventional
Group-By. Thus, this work comprises the development of
an extension of the PostgreSQL DBMS for the management
of fuzzy grouping on the basis of a tight coupled
architecture. In a tight coupled architecture [9], [10], [8],
all tasks, components and functionalities corresponding
to the database paradigm to be integrated are part of
the respective DBMS as a primitive operation. The main
advantage of this architecture is that all scalability and
performance problems that may present themselves in
other types of architectures are solved.
Motivating example
Consider the Billboard Chart data shown in Table
1, where an item is characterized by a title, year, artist and
sales in millions. Also, consider a user’s query to determine
the mean of sales by decade (sixties, seventies, eighties,
nineties, etc.). In SQL, this query can be expressed as [8],
[11]: SELECT label(year), avg(sales) FROM billboard_
chart GROUP BY label(year) USING p(year) = {[1960,
1969], [1970, 1979], [1980, 1989], [1990, 1999], [2000,
2009], [2010,2019]}; The result of this query is presented
in Table 2.
Table 1. The billboard chart data.
Title Year Artist
Sales
(millions)
Can’t Help Falling In
Love
1962 Elvis Presley 28
Carnegie Hall Concert 1966 Buck Owens 54
Aretha Franklin: Soul
‘69
1969
Aretha
Franklin
32
Something Better To
Do
1975
Olivia
Newton-John
22
Thriller 1983
Michael
Jackson
65
This Is The Time 1987 Billy Joel 12
Ballerina Girl 1987 Lionel Richie 53
My Heart Will Go On 1998 Celine Dion 8
Hard Candy 2008 Madonna 34
No Line On The
Horizon
2009 U2 31
Someone Like You 2011 Adele 41
Love Yourself 2016 Justin Bieber 23
Cozy Little Christmas 2018 Katy Perry 12
Table 2. Mean sales of titles by year range.
Label (year)
[1960, 1969] [1970, 1979] [1980, 1989] [1990, 1999] [2000, 2009] [2010, 2019]
mean
38.00 22.00 43.33 8.00 32.50 25.33
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
38
Aguilera and Goncalves
A classical query with a GROUP BY clause is as
follows [3], [9]: SELECT label(A) [, agg, …] FROM R WHERE
GROUP BY label (A) USING p (a)={L
1
, …, L
n
}; Where p (A)
tag L
i
of p (A), and is a Boolean or fuzzy condition. If the
WHERE clause has a fuzzy condition, COUNT can be only
used as an aggregation function in the clause since the
sets. For a given Li belonging to p(A) and a relationship r,
count(Li) is computed. Additionally, in this work, we use
a count variant named count-rel which calculates relative
cardinality associated to a group, e.g. average degree of
satisfaction [8], [11]:
To illustrate the count-rel use, consider the
following query: SELECT label(year), count, count-rel
FROM billboard_chart WHERE sales=medium GROUP
BY label(year) USING p(year) = {[1960, 1969], [1970,
1979], [1980, 1989], [1990, 1999], [2000, 2009],
[2010,2019]};
by means of the trapezium shown in Figure 1(b), the
calculations are in Table 3 and the results of the query are
in Table 4; n represents . Partitioned queries
may be extended by means of fuzzy logic. To exemplify
fuzzy partitioned queries, consider the trapeziums in
Figure 1 and the following query that determines the
volume of sales for all titles newer than 1990 for each sales
class (low, medium, high): SELECT label(sales), count
FROM billboard_chart WHERE year > 1990 GROUP BY
label(sales) USING p(sales) = {low, medium, high}.
On the basis of data in Table 1, the result of this
query is presented in Table 5. That is, for the label(sales)=
high the count corresponds to sum of the membership
degree of each tuple that has a year greater than 1990,
they are: {My Heart Will Go On/0, Hard Candy/0.7, No
Line On The Horizon/0.55, Someone Like You/1, Love
Yourself/0.15, Cozy Little Christmas/0}, similarly for
label(sales)= medium and label(sales)= low.
It is important to note that for those cases
count and count-rel as follows [8], [11]:
(1)
(2)
Figure 1.
medium (c) high
Table 3. Computed satisfaction degrees for the fuzzy
partitioned query.
Label
(year)
I Title sales
[1960-
1969]
1
Can’t Help Falling
In Love
28 1.00
2
Carnegie Hall
Concert
54 0.08 2.08 0.69
3
Aretha Franklin:
Soul ‘69
32 1.00
[1970-
1979]
1
Something Better
To Do
22 1.00 1.00 1.00
[1980-
1989]
1 Thriller 65 0.00
1.15 0.382 This Is The Time 12 0.60
3 Ballerina Girl 53 0.55
[1990-
1999]
1
My Heart Will
Go On
8 0.45 0.45 0.45
[2000-
2009]
1 Hard Candy 34 1.00
2.00 1.00
2
No Line On The
Horizon
31 1.00
[2010-
2019]
1
Someone Like
You
41 0.95
2.55 0.852 Love Yourself 23 1.00
3
Cozy Little
Christmas
12 0.6
Table 4.
label
(ventas)
[1960,
1969]
[1970,
1979]
[1980,
1989]
[1990,
1999]
[2000,
2009]
[2010,
2019]
count
2,08 1,00 1,15 0,45 2,00 2,55
count-rel
0,69 1,00 0,38 0,45 1,00 0,85
Table 5. Query results using a fuzzy partition on sales.
Label (sales)
High Medium low
count
2.40 4.95 3.45
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
39
An Implementation for SQL Fuzzy Grouping
Experimental
PostgreSQLf
In this work, we extended PostgreSQL based us
on a tightly coupled integration architecture, which takes
advantages of the internal characteristics of DBMS [12],
[13], [14]. Unfortunately, more effort can be required due
to the complexity of open source system and additionally
the portability to new version is completely lost. Even
if the portability was compromised, our interesting is
focused in the performance and to show the feasibility
of implementation as a proof of concept. This work is
part of another big project called PostgreSQLf started in
2006 [15]. Figure 2 shows the modules of PostgreSQL
by PostgreSQL must pass through three modules: i) the
builds the execution plan for the query; iii) the Executor
Catalog
The DBMS catalog is a repository where the
metadata of the database schema is stored (information of
tables, columns, indexes, operators, aggregate functions,
among others). PostgreSQL manages these metadata
as system tables. Particularly, in this work, the catalog
was extended to add the new aggregation functions of
the Fuzzy Grouping as part of the standard PostgreSQL
functions.
Figure 2. PostgreSQL modules
Parser
The parser comprises two processes: the
syntactic and semantic analysis, and the transformation
process that takes the query sentence and converts it to
data structures operable by PostgreSQL. The query trees
are managed by means of linked lists. The lexical analyzer
Fuzzy Grouping, a new type of node called A_Partition was
created with all the relevant data of the partition such as its
domain, its labels, among others. A pointer (usingClause)
is added to the SelectStmt node in a list of partition nodes.
Planner
The task of this module is to create a fuzzy
execution plan. Thus, it combines possible access paths of
the relationships (index scan, sequential scan or bitmap
index scan) and joins them if it is necessary (nested loop
join, hashed join or merge sort join). The task of this module
is to estimate the execution costs of each access path and
choose the cheapest one. In this work, the received query
query tree. Additional plan nodes are built to calculate the
cardinalities necessary for the aggregate functions of the
fuzzy grouping.
Executor
This module takes the Planner execution plan and
processes it recursively to obtain the required set of rows;
it uses a progressive demand pipeline mechanism. Each
time a plan-type node is called, it must dispatch one or
rows. To evaluate the Fuzzy Group By operator, we propose
an algorithm based on a hash. Each partition represents a
bucket (a fuzzy set) and the hash function discriminates to
which bucket a tuple belongs and its membership degree.
hash table for
fuzzy grouping.
Algorithm 1. Filling the hash table for fuzzy grouping
NewTuple Ø;
for each Partition in Query do
for each Label in Partition do
if Tuple is in Label domain then
NewTuple copyTuple(Tuple); M
SatisfactionDegreeFGB(Tuple, Label);
HashTableEntry
insertInHashTable(NewTuple);
if Query has count_rel then
N LabelCardinality(Label); Advance
Aggregates(HashTableEntry, M, N);
elseAdvanceAggregates(HashTableEntry, M);
First, the executor calculates the membership
grades for the predicates that represent the partition labels
in the fuzzy grouping. For queries with fuzzy or classic
nodeAgg.c
the way in which the system groups the tuples must be
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
40
Aguilera and Goncalves
23, others by age= 31, etc. In other words, the groups are
disjoint sets, where there are no elements found in more
means of a Hash table that is then extracted for each group
difference in fuzzy grouping is that each tuple can belong
to one or more groups (Figure 3b), this happens when
overlapping tags (classic or fuzzy) are used within the
the agg_fill_hash_table
in the query. If the tuple belongs to more than one label,
it is duplicated and introduced into the hash table. If it
is a fuzzy partition or there are fuzzy predicates in the
query, its membership grade is calculated and used for
the calculations of the count_p and count_prel aggregate
functions. For the latter, it will be necessary to calculate
the cardinality of each label.
Figure 3. Difference between standard and proposed
groupings
The implementation of the function
advanceAgregates is exactly the same as the default
function of PostgreSQL, except that the count_p aggregate
function is a sum function that adds the membership
degrees as parameters and the function count_prel is
equal to a sum function but adds the division between the
membership degree and cardinality passed as parameters.
Experimental study
In this section, we study the performance of fuzzy
grouping queries inside PostgreSQL. First, we describe the
benchmark, the metrics and implementation details for
our experimental study.
Benchmark
TPC-H™ provides a database schema, a data
generator, and queries to evaluate the performance of a
system under standard conditions. The dataset sizes were
1 and 5 GB. In this experimental study, the tables part
(200,000/1,000,000 rows), partsupp (800,000/4,000,000
rows), and supplier (10,000/50,000 rows) were
considered. Only the data generator was used because
we evaluate our own queries with fuzzy grouping. Thus,
condition and classical partition; ii) six queries with fuzzy
condition and classical partition; iii) six queries with
Boolean condition and fuzzy partition; iv) six queries with
fuzzy condition and fuzzy partition. Also, six equivalent
Evaluation metrics
Performance is reported and measured as total
execution time (the elapsed time in milliseconds between
the submission of a query to PostgreSQL and the delivery
of the answers). Time was measured using the SQL
EXPLAIN ANALYZE.
Implementation
Experiments were executed using PostgreSQL
8.2 on Ubuntu Desktop 10.10, architecture AMD64,
equipped with an Intel Core 2 Duo T6400 and 4 GB RAM.
Results and discussion
Afterwards, exploratory analysis of the data
was performed using descriptive statistics. For this
purpose, a histogram of time (ms) was plotted in Figure
4. According to the dataset, the highest frequency is in
data distribution resembles a log-normal function (Figure
4 left). As a measure of location, we have the mean, in
this case was 1,034.76739 ms. There is also a very high
variability of the data since the standard deviation was
959.035129 ms. With respect to measure of dispersion,
the difference between the minimum and maximum
values was high (101.477 and 3,900.827 ms).
Figure 4 (center) contains a boxplot for the total
execution time. Considering the type of query in Figure
4 (right), it showe that the classic Boolean queries have
the highest times. Although the classic queries return
the same tuples and are grouped in the same way as the
extension, they use the UNION operator which generates
an additional workload increasing the execution time.
Thus, our solution experimentally shows that it is more
which is related to the returned high data volume.
Subsequently, an ANOVA was performed to
the database size or the type of queries. That is, the
affect the execution time of the query.
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
41
An Implementation for SQL Fuzzy Grouping
Figure 4. Histogram of total execution time (left).
Histogram of total execution time boxplot (center).
Histogram of query type boxplot (right)
Table 6. ANOVA results.
Origin Type III sum of squares df Quadratic mean F Sig.
Corrected model 40.534.397.077 11 3.684.945.189 8.927 0,000
Volume 31.168.599.521 1 31.168.599.521 75.506 0,000
Volume*query type 861.253.945 2 430.626.972 1.043 0,359
Númber* query type 2.321.883.863 2 1.160.941.931 2.812 0,068
Error 24.767.737.862 60 412.795.631
Total 142.395.670.474 72
Corrected total 65.302.134.939 71
Related work
using fuzzy set theory, presented by Rosenfeld [16]. It has
also been utilized for several domains of application such
decision making and database clustering. Zhang and Huang
[17] proposed some SQL instructions to allow grouping in
the context of spatial data. Basically, these instructions
act as wrappers of conventional grouping algorithms,
but no further integration with databases is studied. Li
[18] extended the operator GROUP BY to group all tuples
This framework makes use of conventional grouping
algorithms, e.g. K-means, and utilizes bitmap indexes to
et al. [19] proposed a Group-By based on a similarity
principle in PostgreSQL. Laverde [20] introduced a new
operator capable of producing higher quality groups for
several data domains. In this work, we focus on fuzzy
grouping based on vague concepts instead of grouping
based on similarity. We also do not rely on discovering
the query by means of fuzzy partitions. Additionally, the
authors of these works did not consider an extension
of fuzzy queries such as SQLf, but only extension of a
particular SQL functionality.
Based on the similarity-based-group-by
construct, Bosc and Pivert [8] proposed how to introduce
the grouping of data in terms of vague concepts (fuzzy
predicates) within the SQLf statements [8], [11]. Lastly,
some other implementations of fuzzy grouping have been
developed. A windows program called fuzzy grouping
offers three methods of fuzzy clustering to community
ecologists [21]. The fuzzy grouping transformation is
a technique used to perform data cleaning tasks while
eliminating duplicate data [22] and it is part of Microsoft
SQL Server [23].
Conclusions
In this work, the PostgreSQL DBMS was
extended to execute fuzzy grouping queries within a tight
coupled architecture. To the best of our knowledge, it is
fuzzy grouping, the catalog was extended to add the new
aggregation functions for Fuzzy Grouping as a part of
standard PostgreSQL functions. The new functions added
were count_p and count_prel. The proposed extension
database manager, they were the parser, the planner
and the executor. It should be noted that this method
can be applied to other extensions that want to be made
beyond the fuzzy paradigm. The changes involve the
incorporation of new structures and the implementation
of new operators to manage these new structures and the
operations associated with them. In particular, to evaluate
the Fuzzy Group-By (FGB) operator, we proposed a new
hash-based algorithm. The algorithm implemented the
new keywords were added to the syntax and new nodes
were added to the Parser tree, a new way of grouping tuples
using partition tags (classic or fuzzy) was introduced.
This work focused on fuzzy grouping based on
vague concepts, rather than similarity-focused grouping.
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
42
Aguilera and Goncalves
It did not focus on the discovery of groups since they are
The experimental study shows that the proposed
clustering mechanism, integrated into a database engine,
the case of the count_prel function, in which it is necessary
to execute additional queries for cardinality calculations.
Therefore, the greater the volume of records that the table
has, the more load is added to the execution time.
As future work, two key points are to be
considered in order to enable more complete fuzzy
aggregation functions: the implementation of the Fuzzy
of the HAVING clause for the fuzzy query evaluation,
in addition to implementing the count-g aggregation
function.
Acknowledgement
We thank professor Ralph Grove, a friend in
Norfolk, VA who helped us with the editing of this paper.
References
[1] Bosc P. and Pivert O.: “SQLf: a relational database
language for fuzzy querying”. IEEE Transactions
on Fuzzy Systems, 3(1), (1995)1-17. https://doi.
org/10.1109/91.366566.
[2] Bosc P. and Pivert O.: “SQLf Query Functionality on
Top of a Regular Relational Database Management
System”. Studies in Fuzziness and Soft Computing,
(2000), 171-190.
[3] George R., Petry F. E., Buckles B. P. and Srikanth
R.: “Fuzzy database systems—challenges and
opportunities of a new era”. Int J of Intelligent
Systems, Vol. 11, No. 9, (1996), 649-659.
de bases de données: expression et évaluation de
Université de Rennes 1.
[5] Galindo J., Urrutia A. and Piattini M.:
“Representation of Fuzzy Knowledge in Relational
Databases”. Fuzzy Databases: Modeling, Design
and Implementation, (2006), 145-170.
[6] Goncalves M. and Tineo L.: “SQLf3: an extension of
SQLf with SQL3 features”. In Proceedings of 10th
IEEE International Conference on Fuzzy Systems,
(2001), 477-480.
[7] Sanchez, H.R., Sarango, D.E. and Cucuri, M.I.:
“Evaluación de un sistema de alimentación avícola
basado en lógica difusa”. Revista Técnica de
Ingeniería Universidad del Zulia, Vol. Especial, No.
1, (2020), 3-10.
[8] Bosc P. and Pivert O.: “On a fuzzy group-by clause in
SQLf”. International Conference on Fuzzy Systems,
(2010), 1-6.
[9] Aguilera A., Cadenas J.T. and Tineo L.: “Fuzzy
Querying Capability at Core of a RDBMS”.
In Advances in Data Mining and Database
Management, IGI Global. Hershey, 2011, 160-184.
[10] Bosc P. and Galibourg M.: “Indexing principles for
a fuzzy database”. J. Information Systems, Vol. 14,
No. 6, (1989), 493-499.
[11] Pivert O. and Bosc P.: “Fuzzy Group By”. In: Fuzzy
preference queries to relational databases. World
[12] Timarán R.: “Arquitecturas de Integración del
Proceso de Descubrimiento de Conocimiento con
Sistemas de Gestión de Bases de Datos: un Estado
del Arte, Ingeniería y Competitividad”, Vol. 3, No. 2,
(2001), 45-55.
[13] Smits G., Pivert O. and Girault T.: “ReqFlex: fuzzy
queries for everyone”. Proc. VLDB Endow., Vol. 6,
No. 12, (2013), 1206-1209.
[14] Aguilera A., Cadenas J. and Tineo L.: “Rendimiento
de Consultas SQLf en arquitecturas débil y
fuertemente acopladas”. Revista Multiciencias,
Latindex Venezuela, Vol. 11, No 4, (2011), 410-415.
[15] Cadenas. J.: “Una contribución a la interrogación
USB, Caracas, Venezuela.
[16] Rosenfeld A.: “Fuzzy groups”. Journal of
mathematical analysis and applications, Vol. 35,
No. 3, (1971), 512-517.
[17] Zhang C. and Huang Y.: “Cluster By: a new
sql extension for spatial data aggregation”. In
Proceedings of the 15th annual ACM International
Symposium on Advances in Geographic
Information Systems, (2007), 1-4.
[18] Li C., Wang M., Lim L., Wang H. and Chang K. C.:
“Supporting ranking and clustering as generalized
order-by and group-by”. In Proceedings of the ACM
SIGMOD International Conference on Management
of data, (2007), 127-138.
[19] Silva Y. N., Aref W. G. and Ali M. H.: “Similarity group-
by”. In Proceeding of 2009 IEEE 25th International
Conference on Data Engineering, (2009), 904-915.
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 1, 2021, January-April, pp. 04-58
43
An Implementation for SQL Fuzzy Grouping
[20] Laverde N. A., Cazzolato M. T., Traina A. J. and Traina
C.: “Semantic Similarity Group By Operators for
Metric Data”. In Similarity Search and Applications
(SISAP), (2017), Vol. 10609, 247-261.
[21] Henderson P.A., Seaby R.M.H. and Somes J.R.:
“Fuzzy Grouping”. Pisces Conservation Ltd.,
Lymington, Hampshire, UK., Vol. 2, (2014).
Quality improvement methods in Management
Information Systems”. Information Systems in
Management II, Wyd. SGGW, (2008), 124-133.
[23] Zhang J., Guyer C., Milener G. and Petersen T.: “Fuzzy
Grouping Transformation”. Available at https://
docs.microsoft.com/en-us/sql/integration-
grouping-transformation?view=sql-server-2017,
(2017).
REVISTA TECNICA
www.luz.edu.ve
www.serbi.luz.edu.ve
www.produccioncientica.luz.edu.ve
OF THE FACULTY OF ENGINEERING
UNIVERSIDAD DEL ZULIA
This Journal was edited and published in digital format
on December 2020 by Serbiluz Editorial Foundation
Vol. 44. N°1, January - April 2021_________________
