The study of joins in fuzzy relational databases

Extending the fuzzy database with fuzzy numbers

Fuzzy relations and fuzzy relational databases

The Extensible Markup Language (XML) is emerging as the dominant data format for data exchange between applications. Many translation techniques have been devised to publish large amounts of existing conventional relational data in XML format. There also exists a need to be able to represent imprecise data in both relational databases and XML. This paper describes a fuzzy XML schema model for representing a fuzzy relational database in XML format. It also outlines a translation algorithm to include fuzzy relations and similarity matrices with their associated conventional relations. We also describe how the proposed fuzzy XML schema and the conversion process from fuzzy relational data into fuzzy XML have been integrated into VIREX, which is a prototype with powerful visual tool for transforming relational data into XML.KeywordsFuzzy XMLFuzzy Relational DatabaseSchema ConversionVisual Interface

This paper reports on the architecture of a Fuzzy Relational DBMS (FRDBMS) with deduction capabilities, whose main characteristics are: 1) It is built on the basis of a theoretical model for fuzzy relational databases and a theoretical model for logic fuzzy databases; 2) It is implemented entirely on classical RDBMS, using their resources; 3) It conserves all the operations of the host RDBMS and gives them more power, adding new capabilities for dealing with ”fuzzy” and ”intensive” information; 4) It provides a deductive fuzzy language, DFSQL, and a processor which permits the translation of each DFSQL statement into one or more SQL statements, which can be used by the host RDBMS; 5) It offers a relational representaion of the rules that define an intensive table, in such a way that all necessary information to perform deduction is stored in tables. 6) This system needs to interact with a deduction module which performs the computation of intensive tables.KeywordsIntelligent Information SystemsFuzzy relational databaseDeductive database

Recently, new applications have emerged that require database management systems with uncertainty capabilities. Many of the existing approaches to modeling uncertainty in database management systems are based on the theory of fuzzy sets. This paper introduces basic parallelism in fuzzy relational databases and its queries. Article describes basic characteristics of fuzzy relational databases and their properties, compares fuzzy logic with Boolean one in connection with fuzzy relational databases. Deal with data classification and form of storage fuzzy data in database systems. Paper describes fuzzy queries and parallelism in queries from view of today's systems and their connection to SQL language and its extension fuzzy SQL. Discuss about pipeline parallelism of query operators and its benefits.

Functional dependency is the basis of database normalization. Various types of fuzzy functional dependencies have been proposed for fuzzy relational database and applied to the process of database normalization. However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models. To resolve the problem, this study defined fuzzy functional dependency based on a notion of approximate equality for extended possibility-based fuzzy relational databases. Examples show that the notion is more applicable than other similarity concept to the research related to the extended possibility-based data model. We provide a decomposition method of using the proposed fuzzy functional dependency for database normalization and prove the lossless join property of the decomposition method.

Information imprecision and uncertainty exist in many real-world applications and for this reason fuzzy ontologies have been extensively investigated and increasingly created. Therefore, it is critical to develop scalable and efficient fuzzy ontology storage mechanism. The fuzzy relational database may be a good candidate for storing fuzzy ontologies because of the widespread use and mature techniques. In this paper, we propose an approach for storing fuzzy ontologies in fuzzy relational databases. The elements of fuzzy ontologies are introduced first, where most of constructors of fuzzy ontologies are considered. On this basis, we propose an approach for storing all of these elements of fuzzy ontologies in fuzzy relational databases, and an example is provided throughout the paper to well explain the approach.

Following the development of fuzzy logic theory by Lotfi Zadeh, its applications were investigated by researchers in different fields. Presenting and working with uncertain data is a complex problem. To solve for such a complex problem, the structure of relationships and operators dependent on such relationships must be repaired. The fuzzy database has integrity limitations including data dependencies. In this paper, first fuzzy multivalued dependency based semantic proximity and its problems are studied. To solve these problems, the semantic proximity's formula is modified, and fuzzy multivalued dependency based on the concept of extension of semantic proximity with \alpha degree is defined in fuzzy relational database which includes Crisp, NULL and fuzzy values, and also inference rules for this dependency are defined, and their completeness is proved. Finally, we will show that fuzzy functional dependency based on this concept is a special case of fuzzy multivalued dependency in fuzzy relational database.

Fuzzy set theory was introduced by L.A. Zadeh in 1965. Immediately, it has many applications in practice and in building databases, one of which is the construction of a fuzzy relational database based on similar relationship. The study of cases of fuzzy relations in different environments will help us understand its applications. In this paper, the rough fuzzy relation on Cartesian product of two universe sets is defined, and then the algebraic properties of them, such as the max, min, and composition of two rough fuzzy relations are examined. Finally, reflexive, αreflexive, symmetric and transitive rough fuzzy relations on two universe sets are also defined.

In this paper we consider all possible dependencies that can be built upon similarity-based fuzzy relations, that is, fuzzy functional and fuzzy multivalued dependencies. Motivated by the fact that the classical obtaining of new dependencies via inference rules may be tedious and uncertain, we replace it by the automated one, where the key role is played by the resolution principle techniques and the fuzzy formulas in place of fuzzy dependencies. We prove that some fuzzy multivalued dependency is actively correct with respect to given fuzzy relation instance if and only if the corresponding fuzzy formula is in line with the attached interpretation. Additionally, we require the tuples of the instance to be conformant (up to some extent) on the leading set of attributes. The equivalence as well as the conclusion are generalized to sets of attributes. The research is conducted by representing the attributes and fuzzy dependencies in the form of fuzzy formulas, and the application of fuzzy implication operators derived from carefully selected Frank’s classes of additive generators

This paper introduces a fuzzy relational data base model (FRDB) that extends the conventional relational data base model with two key features: (1) the relations represent the set of data tuples to be the fuzzy relations; (2) selection conditions are associated with fuzzy set values to be able to query the fuzzy, imprecise information of objects in relations. An interpretation of the membership degree of tuples for fuzzy relations is proposed on the basis of the fuzzy set theory to develop the data model and data manipulating model of FRDB that consist of schemas, fuzzy relations and algebraic operations. Some properties of the fuzzy relational algebraic operations are also formulated and proven as extensions of the properties of relational algebraic operations in the conventional relational data base model.

Multivalued dependencies in fuzzy relational databases

A new definition of Fuzzy Relational Database is given by using logical concepts. With this definition it is possible to consider several kinds of fuzziness for the database attributes. A Domain Calculus-based query language is also established for the model. It allows us to formulate several types of queries with different lack of precision levels. © 1994 John Wiley & Sons, Inc.

Many flexible approaches allow users to query the relational database with vague or imprecise terms similar to natural language; most of these proposals are based on the fuzzy set theory which provides an environment for working with the uncertainty described by the linguistic terms. This paper presents an overview of the most important proposals, to highlight important models concerning fuzzy query databases we consider two classifications: the first classification deals with flexible queries in crisp relational databases and the second deals with flexible queries in fuzzy relational databases. This paper aims to help researchers understand these approaches for further research in this area.

We discuss the idea of a linguistic quantifier and fuzzy set representations of these objects. We describe two formalisms for evaluating the truth of linguistically quantified propositions such as Most winter days are cold. the first approach is based upon a probabilistic interpretation and the second is based upon a logical interpretation, and uses a generalization of the “and” and “or” operations via OWA operators. We suggest an application of these quantified statements for the representation of the quotient operator in fuzzy relational data bases. © 1994 John Wiley & Sons, Inc.