Publication: Bases de datos relacionales con conjuntos intervalo-valorados difusos
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2018
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Abstract
Cuando se habla de bases de datos relacionales, se piensa en una colección de elementos de datos organizados, definidos y estructurados en un conjunto de tablas con columnas y filas. Además, las tablas pueden relacionarse con otras a través de claves foráneas, así como también debe existir una consistencia e integridad en los datos de la misma. Se entiende que en una base de datos relacional, los atributos están basados en las restricciones de su dominio, donde además, el concepto de dominio sigue los principios de teoría de conjuntos clásico, es decir, se basa en la hipótesis de que un valor de un atributo debe ser un elemento que pertenece al conjunto especificado en su dominio. Por su parte, cuando se habla de bases de datos relacionales difusas, se habla esencialmente de lo anterior mencionado, pero empleando las propiedades de la lógica y conjuntos difusos en en el dominio de integridad de los datos; se habla del tratamiento flexible de los datos de una base de datos.
Para explotar el hecho de que la membresía de un elemento a un conjunto difuso es relativo y parcial, y para flexibilizar aún más las condiciones y consultas hechas sobre una base de datos, se introduce en este trabajo los cimientos de las bases de datos relacionales con conjuntos intervalo-valorados difusos, dando origen a IVFSQL (Interval-Valued Fuzzy SQL). Para ello, se comenzarán a estudiar los conceptos básicos de conjuntos difusos y bases de datos difusas. Posteriormente, se introduce la noción de conjuntos intervalo-valorados difusos para luego relacionar estos con SQL, dando origen a FSQL, para por último dar paso a IVFSQL. Lo que se busca es que los datos puedan ser tratados de una forma más tolerante de lo que ya se tratan si se siguen los principios de conjuntos difusos sobre una base de datos. La idea es, esencialmente, aumentar y permitir la incertidumbre en los datos lo más posible. Es precisamente por este motivo que los conjuntos intervalo-valorados difusos buscan tratar la incertidumbre de la información gradual y establecer criterios que midan el grado de pertenencia de un elemento a un conjunto intervalo-valorado difuso.
When talking about relational databases, we think of a collection of organized, defined and structured data elements in a set of tables with columns and rows. In addition, the tables can be related to others through foreign keys, as well as there must be a consistency and integrity in the data. It is well known that in a relational database, the attributes are based on the restrictions of their domain, where in addition, the concept of domain follows the principles of classical set theory, which is based on the hypothesis that a value of an attribute must be an element that belongs to the set specified in its domain. On the other hand, when talking about fuzzy relational databases, we essentially talk about the aforementioned, but using the properties of the logic and fuzzy sets in the data integrity domain, that is, we talk about the flexible treatment of the data of a database and the representation of a set of fuzzy data in it. To take advantage of the fact that the membership of an element to a fuzzy set is relative and partial, and to further lighten up the queries and conditions, the foundations of the relational databases with interval-valued fuzzy sets are introduced, giving rise to IVFSQL (Interval-Valued Fuzzy SQL). For this, we will study the basic concepts of fuzzy sets and fuzzy databases. Subsequently, the notion of interval-valued fuzzy sets are introduced in order to make a relationship between this and SQL, giving rise to FSQL, to finally open to IVFSQL. What is sought is that the data can be treated in a more tolerant way than they are already treated if the principles of fuzzy sets are followed on a database, as well as allowing the expansion of being able to fulfill with certain conditions partially. The idea is, essentially, to increase and allow uncertainty in the data as much as possible. It is precisely for this reason that the interval-valued fuzzy sets seek to deal with the uncertainty of the gradual information and establish criteria that could measure the degree of belonging of an element to an interval-valued fuzzy set.
When talking about relational databases, we think of a collection of organized, defined and structured data elements in a set of tables with columns and rows. In addition, the tables can be related to others through foreign keys, as well as there must be a consistency and integrity in the data. It is well known that in a relational database, the attributes are based on the restrictions of their domain, where in addition, the concept of domain follows the principles of classical set theory, which is based on the hypothesis that a value of an attribute must be an element that belongs to the set specified in its domain. On the other hand, when talking about fuzzy relational databases, we essentially talk about the aforementioned, but using the properties of the logic and fuzzy sets in the data integrity domain, that is, we talk about the flexible treatment of the data of a database and the representation of a set of fuzzy data in it. To take advantage of the fact that the membership of an element to a fuzzy set is relative and partial, and to further lighten up the queries and conditions, the foundations of the relational databases with interval-valued fuzzy sets are introduced, giving rise to IVFSQL (Interval-Valued Fuzzy SQL). For this, we will study the basic concepts of fuzzy sets and fuzzy databases. Subsequently, the notion of interval-valued fuzzy sets are introduced in order to make a relationship between this and SQL, giving rise to FSQL, to finally open to IVFSQL. What is sought is that the data can be treated in a more tolerant way than they are already treated if the principles of fuzzy sets are followed on a database, as well as allowing the expansion of being able to fulfill with certain conditions partially. The idea is, essentially, to increase and allow uncertainty in the data as much as possible. It is precisely for this reason that the interval-valued fuzzy sets seek to deal with the uncertainty of the gradual information and establish criteria that could measure the degree of belonging of an element to an interval-valued fuzzy set.
Description
Máster en Ingeniería Informática, Facultad de Informática, Departamento de Sistemas Informáticos y Computación, curso 2017-2018