Fuzzy Relational Database Model Research Articles

An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations

This paper introduces an extended type-2 fuzzy relational database model (ET-2FRDB) for aggregate and grouping operations that can represent and query uncertain and imprecise information in the real world applications. In ET-2FRDB, each fuzzy relation is represented by a type-2 fuzzy set whose membership degree of each tuple is a fuzzy number on [0, 1], the fuzzy aggregate functions, the fuzzy relational algebraic, aggregate and grouping operations are defined as extensions of those in the classical relational database model thereby the membership degree of tuples associated by using the minimum and maximum of fuzzy numbers. Also, some properties of the fuzzy relational algebraic, aggregate and grouping operations in ET-2FRDB are formulated and proven.

A relational database model and algebra integrating fuzzy attributes and probabilistic tuples

Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed.

FUZZY RELATIONAL DATABASE MODEL AND MANAGEMANT SYSTEM FOR IMPRECISE INFORMATION

This paper introduces a fuzzy relational database model (FRDB) and the management system for it. FRDB is built by extending the classical relational database model with the fuzzy membership degree of tuples in relations. The management system for FRDB with the querying language like SQL is built by using a classical open-source management system.

Modeling fuzzy data with RDF and fuzzy relational database models

Modeling fuzzy data with RDF and fuzzy relational database models

Class dependency of fuzzy relational database using relational calculus and conditional probability

In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as ’projection’, ’selection’, ’injection’ and ’natural join’. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.

A Type-2 Fuzzy Relational Database Model

This paper introduces a type-2 fuzzy relational database model (T-2FRDB) as an extension of type-1 fuzzy relational database models with a full set of basic fuzzy relational algebraic operations that can represent and query uncertain and imprecise information in real world applications. In this model, the membership degree of tuples in a fuzzy relation is represented by fuzzy numbers on [0,1], and fuzzy relational algebraic operations are defined by using the extension principle for computing minimum and maximum values of such fuzzy numbers. Some properties of the type-2 fuzzy relational algebraic operations in T-2FRDB are also formulated and proven as extensions of their counterpart in the type-1 fuzzy relational database models. DOI: 10.32913/rd-ict.vol3.no14.352

F-perceptory: an approach for handling fuzziness of spatiotemporal data in geographical databases

In the literature, several studies have focused on introducing fuzzy extensions to the relational and/or object database models in order to store the imprecision. Indeed, on one hand, fuzzy EER and fuzzy UML are both applied for fuzzy object-oriented database modelling. On the other hand, Fuzzy ER is adapted for fuzzy relational database models. All these previous fuzzy conceptual modelling methods are not adapted to fuzzy spatiotemporal data. In this paper, we propose an approach for modelling imprecise data in object and relational databases based on the representation of data using connected and normalised fuzzy sets stored via α-cuts. The approach is applied to geographical information systems in order to handle imprecise spatiotemporal data.

Một mô hình cơ sở dữ liệu quan hệ mờ

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.

An Ontology as a Tool for Representing Fuzzy Data in Relational Databases

Abstract Several applications to represent classical or fuzzy data in databases have been developed in the last two decades. However, these representations present some limitations specially related with the system portability and complexity. Ontologies provides a mechanism to represent data in an implementation-independent and web-accessible way. To get advantage of this, in this paper, an ontology, that represents fuzzy relational database model, has been redefined to communicate users or applications with fuzzy data stored in fuzzy databases. The communication channel established between the ontology and any Relational Database Management System (RDBMS) is analysed in depth throughout the text to justify some of the advantages of the system: expressiveness, portability and platform heterogeneity. Moreover, some tools have been developed to define and manage fuzzy and classical data in relational databases using this ontology. Even an application that performs fuzzy queries using the same technology is ...

Functional Dependencies Analyse in Fuzzy Relational Database Models

This paper presents a literature overview of Fuzzy Relational Database Models with emphasis on the role of functional dependencies in logical designing and modeling. The aim is the analysis of recent results in this field. Fuzzy set theory is widely applied for the classical relational database extensions resulting in numerous contributions. This is because fuzzy sets and fuzzy logic are powerful tool for manilupating imprecise and uncertain information. A significant body of research in efficient designing FRDM has been developed over the last decades. Knowing the set of functional dependencies, database managers have a chance to normalize the same eliminating redundancy and data anomalies. In this paper we have considered the most important results in this field.

Normalization and lossless join decomposition of similarity-based fuzzy relational databases

Fuzzy relational database models generalize the classical relational database model by allowing uncertain and imprecise information to be represented and manipulated. In this article, we introduce fuzzy extensions of the normal forms for the similarity-based fuzzy relational database model. Within this framework of fuzzy data representation, similarity, conformance of tuples, the concept of fuzzy functional dependencies, and partial fuzzy functional dependencies are utilized to define the fuzzy key notion, transitive closures, and the fuzzy normal forms. Algorithms for dependency preserving and lossless join decompositions of fuzzy relations are also given. We include examples to show how normalization, dependency preserving, and lossless join decomposition based on the fuzzy functional dependencies of fuzzy relation are done and applied to some real-life applications. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 885–917, 2004.

Handling indefinite and maybe information in logical fuzzy relational databases

In this article, fuzzy set theory uses an extension of the classical logical relational database model. A logical fuzzy relational database model was developed with the aim of manipulating imprecise information and adding deduction capabilities to the database system. The essence of this work is the detailed discussion on fuzzy definite, fuzzy indefinite, and fuzzy maybe information and the development of an information theoretical approach of query evaluation on the logical fuzzy relational database. We define redundancies among fuzzy tuples and the operator of their removal. A complete set of fuzzy relational operations in relational algebra and the calculus of linguistically quantified propositions are included also. © 2004 Wiley Periodicals, Inc.

A fuzzy knowledge based method for maintenance planning in a power system

The inspection planning in electric power industry is used to assess the safety and reliability of system components and to increase the ability of failure situation identification before it actually occurs. It reflects the implications of the available information on the operational and maintenance history of the system. The output is a ranked list of components, with the most critical ones at the top, which indicates the selection of the components to be inspected. In this paper, we demonstrate the use of a fuzzy relational database model for manipulating the data required for the criticality component ranking in thermal power systems inspection planning, incorporating criteria concerning aspects of safety and reliability, economy, variable operational conditions and environmental impacts. Often, qualitative thresholds and linguistic terms are used for the component criticality analysis. Fuzzy linguistic terms for criteria definitions along with fuzzy inference mechanisms allow the exploitation of the operators' expertise. The proposed database model ensures the representation and handling of the aforementioned fuzzy information and additionally offers to the user the functionality for specifying the precision degree by which the conditions involved in a query are satisfied. In order to illustrate the behavior of the model, a case study is given using real inspection data.

On extended fuzzy relational database model with proximity relations

In this paper, Shenoi and Melton's model of fuzzy relational database is considered. Proximity relation, being an important tool of the model, is characterized theoretically. An optimal α-distribution in [0, 1] and consequently the domain partition are defined, and studied with examples on fuzzy queries.

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.

Proximity relations in the fuzzy relational database model

Proximity relations in the fuzzy relational database model

Proximity relations in the fuzzy relational database model

The fuzzy relational model of Buckles and Petry is a rigorous scheme for incorporating non-ideal or fuzzy information in a relational database. In addition to providing a consistent scheme for representing fuzzy information in the relational structure, the model possesses two critical properties that hold for classical relational databases. These properties are that no two tuples have identical interpretations and each relational operation has a unique result. The fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database. These relations are reflexive, symmetric, and max-min transitive. In addition to introducing fuzziness into the relational model, each similarity relation induces equivalence classes in its domain. It is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases. In this paper, we extend the fuzzy relational database model of Buckles and Petry to deal with proximity relations for scalar domains. Since reflexivity and symmetry are the only constraints placed on proximity relations, they generalize the notion of similarity relations. We show that it is possible to induce equivalence classes from proximity relations; thus, the ‘nice’ properties of the fuzzy relational model of Buckles and Petry are preserved. Furthermore, the removal of the max-min transitivity restriction also provides database users with more freedom to express their value structures.

Analyzing FD inference in relational databases

This paper deals with the general problem of analyzing fuzzy inference based on functional dependencies (FDs) in database relations. Fuzzy inference, the ability to infer fuzzy set values, generalizes imprecise (set-valued) inference and precise inference. Likewise, fuzzy relational databases generalize their classical and imprecise counterparts by supporting fuzzy information storage and retrieval. Inference analysis is performed using a special abstract model which maintains vital links to classical, imprecise and fuzzy relational database models. These links increase the utility of the inference formalism in practical applications involving “catalytic inference analysis”, including knowledge discovery and database security.

Towards the implementation of a generalized fuzzy relational database model

This paper shows the necessary elements for the effective implementation of the generalized fuzzy relational database model. From the model described in Medina et al. (1994) some criteria for representation and handling of imprecise information are introduced, the most important aspect being the simplicity of the implementation. The paper shows a series of mechanisms to implement imprecise information in a classical RDBMS. Having the information represented in a classical RDBMS data structure and having the implementation of procedural knowledge about such information, we will be able to build a FRDBMS on a host RDBMS.

Fuzzy functional dependencies and independencies in extended fuzzy relational database models

In this paper we have considered data dependencies, more specifically (restricted) fuzzy functional dependencies, in the framework of extended fuzzy relational database model. A formal system is presented for the derivation of fuzzy functional dependencies, which is both sound and complete. The problem of lossless join decomposition is discussed in the framework of extended fuzzy relational model. Then we introduce a formal statement, of fuzzy functional independency, which expresses the fact that the corresponding restricted fuzzy functional dependency is not a legitimate constraint of the real world. A formal system is presented for the derivation of restricted fuzzy functional dependencies and independencies. The various problems such as the membership problem, the contradiction problem, and the problem of canonical represents are discussed. A cover, called minimal cover, of restricted fuzzy functional independencies is shown to be unique.