FSQL (Fuzzy SQL)

We have developed a FSQL Server for a Fuzzy Relational Database (FRDB). The FSQL language (Fuzzy SQL) is an extension of the SQL language that allows us to write flexible conditions in our queries. This Server has been depeloped for Oracle, following the model GEFRED, a theoric model for FRDB that includes fuzzy attributes to store vague information in the tables. The FSQL Server allows us to make flexible queries about traditional (crisp) or fuzzy attributes and we can use linguistic labels defined on any attribute.

The FSQL language extends the SQL language to allow flexible queries. We have extended the SELECT command in order for it to express flexible queries and, due to its complex format, we only show here an abstract with the main extensions to this command:

• Linguistic Labels: If an attribute is capable of fuzzy treatment then linguistic labels can be defined on it. These labels will be preceded with the symbol $ to distinguish them easily. There are two types of labels and they will be used in different fuzzy attribute types:
  1. Labels for attributes with an ordered underlined fuzzy domain: Every label of this type has asociated a trapezoidal possibility distribution.
  2. Labels for attributes with an non ordered fuzzy domain. Here, there is a similarity relation defined between each two labels in the domain. The similarity degree is in the interval [0,1].

• Possibility and Necessity Fuzzy Comparators: Besides the typical comparators (=, >...), FSQL includes the fuzzy comparators in the following table. Like in SQL, fuzzy comparators may compare one column with one constant or two columns of the same type.

  Comparator for Possibility	Comparator for Necessity	Significance
  FEQ or F=	NFEQ or NF=	Fuzzy EQual (Possibly/Necessarily Equal)
  FDIF, F!= or F<>	NFDIF, NF!= or NF<>	Fuzzy DIFferent
  FGT or F>	NFGT of NF>	Fuzzy Greater Than
  FGEQ or F>=	NFGEQ or NF>=	Fuzzy Greater or Equal
  FLT or F<	NFLT or NF<	Fuzzy Less Than
  FLEQ or F<=	NFLEQ or NF<=	Fuzzy Less or Equal
  MGT or F>>	NMGT or NF>>	Much Greater Than
  MLT or F<<	NMLT or NF<<	Much Less Than

  Possibility comparators are more general than necessity comparators are. Then, necessity comparators retrieve less tuples and these comply with the conditions necessarily.

• Inclusion Fuzzy Comparators: FSQL includes two comparators for the inclusion operation: FINCL (Fuzzy Included in) and INCL (Included in).

• Fulfilment thresholds (T): For each simple condition a fulfilment threshold may be established (default is 1). with the format: condition THOLD T indicating that the condition must be satisfied with minimum degree T in [0,1] to be considered. The reserved word THOLD is optional and may be substitute for a traditional crisp comparator (=, <...), modifying the query meaning. The word THOLD is equivalent to using the crisp comparator greater or equal. The constant T maybe substituted by a qualifier (a predefined label) like $High or $Low.

  Example: Give me all persons with fair hair (in minimum degree 0.5) that they are possibly taller than label $Tall (in minimum degree 0.8):

  SELECT	* FROM Person
  WHERE	Hair FEQ $Fair THOLD 0.5 AND
  	Height FGT $Tall THOLD 0.8

• Function CDEG(attribute): It shows a column with the fulfilment degree of the condition of the query, for a specific attribute, which is expressed between brackets as the argument. If logic operators appear, the calculation of this compatibility degree is carried out in the following way: We use the minimum T-norm and the maximum T-conorm, but the user may change these values by default modifying only a view (FSQL_NOTANDOR). In this view the user can set the function to use for every logic operator (NOT, AND, OR). Obviously, that function must be implemented in the FSQL Server or may be implemented by the user himself.

  If the argument of the function CDEG is an attribute, then the function CDEG only uses the conditions that includes that attribute. We can use CDEG(*) to obtain the fulfilment degree of each tuple (with all of its attributes, not just one of them) in the condition.

• Character %: It is similar to the character * of SQL but this one also includes the columns for the fulfilment degrees of the attributes in which they are relevant. In the result you will also find the function CDEG applied to each and every one of the fuzzy attributes which appear in the condition. If we wanted to obtain in previous example two more columns with the degrees of CDEG(Hair) and CDEG(Height), we would only have to replace * by %. Of course, this character may be also used with the format [[scheme.]table.]%, as for example: Person.%.

• Basic Fuzzy Constants: Firstly, FSQL defined the syntax for some fuzzy constants. These fuzzy constants that we can use in FSQL are detailed in the following table:

  Fuzzy Constant	Significance
  UNKNOWN	Unknown value but the attribute is applicable
  UNDEFINED	The attribute is not applicable or it is meaningless
  NULL	Total ignorance: We know nothing about it
  $[a,b,c,d]	Fuzzy trapezium (a<=b<=c<=d)
  $label	Linguistic Label: It may be a trapezium or a scalar (defined in FMB).
  [n,m]	Interval "Between n and m" (a=b=n and c=d=m).
  #n	Fuzzy value "Approximately n" (b=c=n and n-a=d-n=margin).

• Extended Fuzzy Constants: In FSQL we can also use the following fuzzy constants:

  Fuzzy Constant	Significance
  $[a,b,c,d,P1/N1,…,Pn/Nn]	Extended fuzzy trapezoid (with some points Pi/Ni where all the Ni are between a and b or between c and d). Values b and c are both optional. If they do not exist, then this constant is a fuzzy value without kernel.
  n+-m	Fuzzy value “Approximately n”: triangle n ± m.
  {P1/L1, P2/L2,…, Pn/Ln}	Non-continuous possibility distribution on labels, where P1, P2, …, Pn are the possibility values and L1, L2, …,Ln are the labels.
  {L1, L2,…, Ln}	Non-continuous possibility distribution on labels, where L1, L2, …, Ln are the labels, with possibility degrees 1 for all of them: {1/L1, …, 1/Ln}.
  {P1/N1, P2/N2,…, Pn/Nn}	Non-continuous possibility distribution on numbers, where P1, P2, …, Pn are the possibility values and N1, N2, …, Nn are the numbers.
  {N1, N2,…, Nn}	Non-continuous possibility distribution on numbers, where N1, N2, …, Nn are the numbers, with possibility 1 for all of them: {1/N1, …, 1/Nn}.

• Condition with IS: Another kind of condition we can use has the next format: IS [NOT] (UNKNOWN | UNDEFINED | NULL) Remarks concerning the condition with IS:
  • This condition (without NOT) will be true if the left fuzzy attribute value (Fuzzy_Attribute) is the fuzzy constant situated on the right.
  • If the attribute is not fuzzy and the constant is NULL, this constant will be understood in the way given by the DBMS.
  • If FEQ is used instead of IS, the compatibility degree between attribute and constant is compared and not only when the attribute is equal to the constant.

• More characteristics: fuzzy quantifiers in queries, dynamic change of functions in logic operations, fuzzy set operators (FUNION, FINTERSECT and FMINUS), the ALTER FSQL statement, some useful functions to handle fuzzy attributes and fuzzy values (cardinality, normalization, concentration or dilatation, contrast intensification or fuzzification...), some DDL statements of FSQL and fuzzy comparators for fuzzy time in FSQL (F_BEFORE, NF_BEFORE, F_AFTER, NF_AFTER, F_MUCH_BEFORE, NF_MUCH_BEFORE, F_OVERLAPS...).

References

• The most international publications about FSQL are:

  

  • Galindo, J. (Editor). Handbook of Research on Fuzzy Information Processing in Databases. Information Science Reference, Hershey, PA, USA (www.igi-pub.com) 2008.
    • Editorial Advisory Board: J.M. Medina, P. Bosc, J. Kacprzyk, T. Andreasen, W. Pedrycz, R.R. Yager, R. De Caluwe, I. Bloch, D. Dubois, H. Prade, G. De Tré, J. Abonyi & O. Pons.
    • ISBN: 978-1-59904-853-6 (hardcover), 978-1-59904-854-3 (ebook).
    • This book includes two volumes, 926 pages, and 34 chapters with different topics like, fuzzy relational databases, fuzzy object-oriented databases, fuzzy dependencies, fuzzy queries, fuzzy languages (FSQL, SQLf...), Data Mining, indexing, bipolar queries...
    • Some authors of these chapters are: Bosc, Pivert, Dubois, Prade, Kacprzyk, Zadrozny, de Tré, de Caluwe, Medina, Mouaddib, Raschia, Takaci, Wang, Meier, Werro, Bordogna, Psaila, Belohlavek, Buche, Sharma, Urrutia, Tineo, Carrasco, Vila, Abonyi, Andreasen...
    • Handbook web: http://www.igi-pub.com/reference/details.asp?id=7568.
    • Recommendation Form: to Library (web) or to a collegue (also in PDF).
    • Information Science Reference, Catalog 2008.
    • Exclusive Contributing Author Offer.
    • Read more detailed information and the list of chapters (references for all of them).

  • J. Galindo, R.A. Carrasco, A.M. Almagro. Fuzzy Quantifiers with and without Arguments for Databases: Definition, Implementation and Application to Fuzzy Dependencies. 12th Int. Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU'2008, pp. 227-234. Málaga (Spain), June 2008.
    - L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay (eds.)

    Abstract: This paper studies how fuzzy quantifiers may be defined and implemented in a fuzzy database context. Fuzzy quantifiers are very useful for fuzzy queries, fuzzy constraints and fuzzy data mining applications. Besides, this paper shows different kind of fuzzy quantifiers with and without arguments. Finally, we show how fuzzy dependencies may use these fuzzy quantifiers.

    

  • Galindo, J., Urrutia, A., Piattini, M., "Fuzzy Databases: Modeling, Design and Implementation". Idea Group Publishing Hershey, USA, 2006.
    • ISBN: 1-59140-325-1 (soft cover) and 1-59140-324-3 (hard cover).
    • Look the Idea Group web to see an abstract, the table of contents, book excerpt, preface and authors' bio.
    • Contact with Idea Group Inc.: cust@idea-group.com.
    • Order form (Special 30% Discount Offer).
    • Recommendation Form: to Library (web) or to a collegue

  • J. Galindo, "New Characteristics in FSQL, a Fuzzy SQL for Fuzzy Databases". WSEAS Transactions on Information Science and Applications 2, Vol. 2, pp. 161-169, February 2005 (World Scientific and Engineering Academy and Society, www.wseas.org, ISSN: 1790-0832).

  • J. Galindo, J.M. Medina, O. Pons, J.C. Cubero, "A Server for Fuzzy SQL Queries". In "Flexible Query Answering Systems", T. Andreasen, H. Christiansen and H.L. Larsen (Eds.). Lecture Notes in Artificial Intelligence (LNAI) 1495, pp. 164-174. Ed. Springer, 1998.

    Abstract: The client-server model is being used mostly in the actual DataBase Management Systems (DBMS). However, these DBMS do not allow either to make flexible queries to the database or to store vague information in it. We have developed a FSQL Server for a Fuzzy Relational Database (FRDB). The FSQL language (Fuzzy SQL) is an extension of the SQL language that allows us to write flexible conditions in our queries. This Server has been developed for Oracle, following the model GEFRED, a theoric model for FRDB that includes fuzzy attributes to store vague information in the tables. The FSQL Server allows us to make flexible queries about traditional (crisp) or fuzzy attributes and we can use linguistic labels defined on any attribute.

  • J. Galindo, J.M. Medina, J.C. Cubero, M.T. García, "Relaxing the Universal Quantifier of the Division in Fuzzy Relational Databases". International Journal of Intelligent Systems, Vol. 16-6, pp. 713-742, 2001.

  • J. Galindo, M.C. Aranda, J.L. Caro, A.Guevara, A.Aguayo, "Applying Fuzzy Databases and FSQL to the Management of Rural Accommodation". Tourism Management, Vol. 23-6, pp. 623-629, 2002.

  • Barranco C.D. , Campaña J., Medina J.M. , Pons O. (2004): "ImmoSoftWeb: a Web Based Fuzzy Application for Real Estate Management". In Lecture Notes in Computer Science Volume 3034 "Advances in Web Intelligence: Second International Atlantic Web Intelligence Conference, AWIC 2004", pp. 196-206. Springer-Verlag Heidelberg. ISSN: 0302-9743. ISBN: 3-540-22009-7.

• More References (search and download papers and related links).

Download

• Software:
  1. FSQL Server (only for Oracle).
     • It only implements the first defined characteristics of FSQL. Extended fuzzy constants and others characteristics are not included yet.
     • Author: J. Galindo and J.M. Medina.
     • One FSQL client: FQ, a SQL/FSQL client application (for Windows, 3.2MB):
       • Version 1.2 (for Oracle 7).
       • Version 1.3 (for Oracle 8).

  2. Others FSQL Clients (all in spanish language):
     • Visual FSQL: Gestión Visual de Bases de Datos Difusas en ORACLE a través de Internet usando FSQL (Visual FSQL: Visual Fuzzy Database Management in ORACLE through Internet):
       • Download: Resumen (abstract), Documentación (documentation) and Programa Visual FSQL (application).
       • Author: Rafael Francisco Oliva Moreno.
     • Recuperación de Imágenes Usando Atributos Difusos (Image Retrieval using Fuzzy Attributes):
       • Download: Resumen (abstract), Documentación (documentation), Instalación (application) and Fuente (source).
       • Author: Jorge Eloy-García Vargas-Machuca.

  3. FSQL Server for PostgreSQL (in spanish language): Last version.
     • Previous version: Instalation scripts and brief tutorial.
     • FSQL Client (for PostgreSQL).
     • Authors: Roxana Maraboli, Alejandro Sepúlveda and Angélica Urrutia.

• Documentation:
  1. PhD Thesis (in spanish language) by José Galindo: "Tratamiento de la Imprecisión en Bases de Datos Relacionales: Extensión del Modelo y Adaptación de los SGBD Actuales" (Managing Uncertainty in Relational Databases: Extending the Model and Adapting the Current DBMS). University of Granada (Spain), 1999 (PostScript: 988KB).
     • Definition of fuzzy relational division, fuzzy relational calculus, FSQL (Fuzzy SQL) and the implementation for fuzzy databases.
  2. PhD Thesis (in spanish language) by Angélica Urrutia: "Definición de un Modelo Conceptual para Bases de Datos Difusas" (Defining a Conceptual Model for Fuzzy Databases). University of Castilla la Mancha (Spain), 2003.
     • Definition of FuzzyEER: Fuzzy Case tool for fuzzy database modeling using FuzzyEER.
  3. Diplome De Mastère (in french language) by Mohamed Ali Ben Hassine: "Contribution A L'implémentation D'une Base De Données Floue Sous Un Système De Gestion De Base De Données Relationnel" (Diplome De Mastère en Automatique et Traitement du Signal), Universite de Tunis El Manar, 2005.
     • Software implementing the Fuzzy CREATE TABLE (and exemple.txt).
  4. Curso Introductorio de Conjuntos y Sistemas Difusos (Lógica Difusa y Aplicaciones), por el Dr. José Galindo G., Universidad de Málaga (España).
  5. Information in the Wikipedia (The Free Encyclopedia, La Enciclopedia Libre): http://es.wikipedia.org/wiki/FSQL (español), http://en.wikipedia.org/wiki/FSQL (english).