Fuzzy Relational Algebra Research Articles

Modeling fuzzy relational database in HBase

With the increase of massive data, a large number of business applications began to seek effective and scalable frameworks for data storages and processing. Under this background, emerging technologies for big data, such as Hadoop- based systems that use scalable distributed storage system HBase, become available. Since most of business data nowadays are stored in relational databases, and information imprecision and uncertainty widely exist in real-world applications, there is an increasing willingness to manage large-scale fuzzy relational data in the Hadoop-based platform. This paper concentrates on fuzzy information modeling in HBase. In particular, we investigate the formal transformation from the fuzzy relational data model to the HBase model and develop a set of mapping rules to assist in the transformation process. In addition, we present a generic approach to transform the fuzzy relational algebra into the fuzzy HBase manipulation language.

On a fuzzy bipolar relational algebra

This paper presents an extension of relational algebra suitable for the handling of bipolar concepts. The type of queries considered involves two parts: a first one which expresses a (possibly flexible) constraint, and a second one that corresponds to a (possibly flexible) wish. The framework considered is that of bipolar fuzzy relations where each tuple is associated with a pair of satisfaction degrees.

Fuzzy rough set techniques for uncertainty processing in a relational database

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy rough relational algebra for querying. Comparisons of theoretical properties of operators in this model with those in the standard relational model are discussed. An example application is used to illustrate other aspects of this model, including a fuzzy entity–relationship type diagram for database design, a fuzzy rough data definition language, and an SQL-like query language supportive of the fuzzy rough relational database model. This example also illustrates the ease of use of the fuzzy rough relational database, which often produces results that are better than those of conventional databases since it more accurately models the uncertainty of real-world enterprises than do conventional databases through the use of indiscernibility and fuzzy membership values. ©2000 John Wiley & Sons, Inc.

Querying fuzzy relational databases through fuzzy domain calculus

In this paper we present a definition of a domain relational calculus for fuzzy relational databases using the GEFRED model as a starting point. It is possible to define an equivalent fuzzy tuple relational calculus and consequently we achieve the two query language levels that Codd designed for relational databases but these are extended to fuzzy relational databases: Fuzzy relational algebra (defined in the GEFRED model) and the fuzzy relational calculus which is put forward in this paper. The expressive power of this fuzzy relational calculus is demonstrated through the use of a method to translate any algebraic expression into an equivalent expression in fuzzy domain relational calculus. Furthermore, we include a useful system so that the degree to which each value has satisfied the query condition can be measured. Some examples are also included in order to clarify the definition. ©1999 John Wiley & Sons, Inc.

Fuzzy information in extended fuzzy relational databases

The queries on type-2 fuzzy relational databases may get non-reasonable answers, and as pointed out by Buckles, a tuple's membership value is not static but is a measure of the appropriateness of that tuple to a given query. Here, we use two supplementary attributes μ r and I e to model the concepts of fuzziness and uncertainty, respectively. We also use these two attribute values to compute the appropriateness of a tuple to a given query. In this paper, the proposed fuzzy relational model is defined by first-order logical. In our proposed model, the classical properties of the database, which are (1) database interpretation being redundant-free, being uniquely-determined and (2) the well-definedness of relational algebra, are preserved for the fuzzy relational algebra. Therefore, the proposed fuzzy relational model can capture more meaning than the conventional approaches and is more suitable to handle the real-life application.

Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data

In the real world, there exist a lot of fuzzy data which cannot or need not be precisely defined. We distinguish two types of fuzziness: one in an attribute value itself and the other in an association of them. For such fuzzy data, we propose a possibility-distribution-fuzzy-relational model, in which fuzzy data are represented by fuzzy relations whose grades of membership and attribute values are possibility distributions. In this model, the former fuzziness is represented by a possibility distribution and the latter by a grade of membership. Relational algebra for the ordinary relational database as defined by Codd includes the traditional set operations and the special relational operations. These operations are classified into the primitive operations, namely, union, difference, extended Cartesian product, selection and projection, and the additional operations, namely, intersection, join, and division. We define the relational algebra for the possibility-distribution-fuzzy-relational model of fuzzy databases.

Accommodating subjective vagueness through a fuzzy extension to the relational data model

Expression and processing of vagueness, which has many real world applications, are not handled effectively in the conventional relational data model. In this paper we investigate a fuzzy extension to the relational data model and propose three fuzzy relational query languages. Two of them are the Level-1 Fuzzy Relational Algebra and Level-1 Fuzzy Relational Calculus. They are fundamental query languages and serve as a theoretical framework for the fuzzy relational database. Finally, the Fuzzy Selective Relational Algebra is presented to express fuzzy constants and fuzzy comparators, which are more effective to represent vagueness in user queries. We show that the three proposed query languages have the same expressive powers. We also present various aspects of the proposed model and its functional advantages over the conventional relational data model.

Functional dependencies and normal forms in the fuzzy relational database model

The fuzzy relational database model as defined by Buckles and Petry employs sets in place of atomic values for components of tuples in database relations. This technique for dealing with imprecision in relational databases is intuitively appealing. Moreover, the model preserves several important properties of classical relational databases. In recent works we have demonstrated that the existence of partitions on scalar domains is the key to ensuring conformity with the classical relational model. Specifically, by restricting the components of fuzzy tuples to be nonempty subsets of equivalence classes from domain partitions, it is possible to define the notions of redundant tuples and consistent database relations and to specify a well-defined fuzzy relational algebra. Since these properties are obtained by working only with equivalence classes, the fuzzy relational model of Buckles and Petry is generalized to an equivalence classes model of relational databases. In this work, additional properties of the fuzzy relational database model are presented. By employing equivalence classes from domain partitions, we define functional dependencies and normal forms for the fuzzy relational model. These definitions extend the corresponding classical definitions. Moreover, our definitions of functional dependencies and normal forms provide valuable guidelines for designing fuzzy relational databases.

A domain calculus for fuzzy relational databases

A complete relational calculus is introduced for similarity-based fuzzy relational databases. The ordinary domain calculus is chosen as the basis from which to develop the fuzzy counterpart because it tends to be closer to natural language than tuple calculus. A constructive proof is used to show that the fuzzy relational algebra can be mapped into the calculus. The proof is significant from the standpoint of demonstrating implementability of the calculus as a query language.

Extending the fuzzy database with fuzzy numbers

The fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete, finite universe. The model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra. Where equivalence is required in an ordinary relational database, similarity is employed in a fuzzy relational database. For discrete, finite universes, similarity between atomic elements is described via a fuzzy similarity relation with max-min transitivity. Two or more fuzzy numbers are defined to be α-similar if their union forms a continuous α-level set over the real line. This convention effects the partitioning of fuzzy number domains that is necessary to assure the well-definedness of the fuzzy relational algebra.

Retrieval From Fuzzy Database by Fuzzy Relational Algebra

The real world data may have two types of ambiguity, one is in a data value itself and the other in an association between values. For representing such data, we propose a possibility-distribution fuzzy-relational model. In this model, the former ambiguity is represented by a possibility distribution and the latter by a grade of membership. The relational algebra for such fuzzy data model is defined. The traditional operations, namely, the union, intersection, difference and extended Cartesian product are similarly defined as those in fuzzy set theory. And the special relational operations, namely, the projection, join, restriction and division, are newly defined for fuzzy databases.

Extension of the Fuzzy Database with Fuzzy Arithmetic

The fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete, finite universe. The model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra. Where equivalence is required in an ordinary relational database, similarity is employed in a fuzzy relational database. For discrete, finite universes, similarity between atomic elements is described via a fuzzy similarity relation with max-min transitivity. Two or more fuzzy numbers are defined to be α-similar if their union forms a continuous α-level set over the real line. This convention effects the partitioning of fuzzy number domains that is necessary to assure the well-definedness of the fuzzy relational algebra.