Fuzzy Relational Database Research Articles

Designing PostGIS Database System with Fuzzy Theory to Support Accessibility Tools for Urban Pedestrians

The combination of fuzzy logic and crowdsourcing can be a powerful tool for generating geospatial data for pedestrians with mobility challenges in urban areas. Although potentially useful, information about the accessibility of paths that is generated through crowdsourcing is susceptible to a high degree of imprecision. Spatial data management is required for such systems, which supports the management of uncertain data. Fuzzy theory allows us to model ambiguous information. To fill this gap, an improved method based on a fuzzy relational PostGIS database (FPostGIS) is proposed. The method includes extensions to represent imprecise data within an entity-relationship (ER) data model specifically tailored for path accessibility, and a set of steps for the derivation of FPostGIS from this extended ER model. According to the case study, this methodology has been applied in the design and development of decision support application within the Maps for Easy Paths (MEP) project. This application stores and retrieves accessibility information about a particular path and allows performing spatial operations and analysis inside the database.

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.

A case-base fuzzification process: diabetes diagnosis case study

Medical case-based reasoning (CBR) systems require the handling of vague or imprecise data. The fuzzy set theory is particularly suitable for this purpose. This paper proposes a case-base preparation framework for CBR systems, which converts the electronic health record medical data into fuzzy CBR knowledge. It generates fuzzy case-base knowledge by suggesting a standard crisp entity–relationship data model for CBR case-base. The resulting data model is fuzzified using a proposed relational data model fuzzification methodology. The performances of this methodology and its resulting fuzzy case-base structure are evaluated. Diabetes diagnosis is used as a case study. A set of 60 real diabetic cases is used in the study. A fuzzy CBR system is implemented to check the diagnoses accuracy. It combines the resulting fuzzy case-base with a proposed fuzzy similarity measure. Experimental results indicate that the proposed fuzzy CBR method is superior to traditional CBR and other machine-learning methods. Our fuzzy CBR achieves an accuracy of 95%, a precision of 96%, a recall 97.96%, an f-measure of 96.97%, a specificity of 81.82%, and good robustness for dealing with vagueness. The resulting fuzzy case-base relational database enhances the representation of case-base knowledge, the performance of retrieval algorithms, and the querying capabilities of CBR systems.

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

Relational Representation of Uncertain and Imprecise Time Assessments: An Application to Artworks Dating

Imprecision and uncertainty appear together in many situations of real life and therefore soft computing techniques must be studied to tackle this problem. Imprecise and uncertain values are usually expressed by means of linguistic terms, especially when they have been provided by a human being. This is also the case of temporal information where, in addition to handling time constraints, we may also have both uncertainty and imprecision in the description, like in the sentence “It is very possible that Giotto's Crucifix was painted by 1289.” To manage both uncertainty (very possible) and imprecision (by 1289) in a separate way would lead to a quite complicated computation and a lack of comprehension by the users of the system. Because of these reasons, it is very desirable that both sources of imperfection of time values are combined into a single value that appropriately describes the intended information. In this work, we extend our previous research on this topic and we study how to adapt it to relational systems in order to be useful. The final goal is obtaining normalized fuzzy values that provide an equivalent information about the described temporal fact than the original ones, for making it possible to store and manage them in a fuzzy relational database. On the other hand, there will be some situations where more than one expert opinion about a time period must be taken into account and we need to find a representative value of them all in order to be stored and managed. For the sake of simplicity, comprehensibility, and the efficiency in computation (when using trapezoidal representation), the fuzzy average is used to find such a representative value.

Storing fuzzy description logic ontology knowledge bases in fuzzy relational databases

In the context of the Semantic Web, fuzzy extensions to OWL (the W3C standard ontology language) and Description Logics (DLs, the logical foundation of OWL) have been extensively investigated, and there are many real fuzzy DL ontology knowledge bases. Therefore, how to store fuzzy DL ontology knowledge bases has become an important issue. In this paper, we propose an approach and implement a tool for storing fuzzy DL ontology knowledge bases in fuzzy relational databases. Our chosen formalism is a fuzzy extension of the very expressive DL SHOIN(D), which is the main logical foundation of the standard ontology language OWL, so that our storage approach can store not only fuzzy DL-knowledge bases but also fuzzy ontology knowledge bases. Firstly, we give a formal definition of fuzzy DL-knowledge bases. In the definition, we consider the constructors of both fuzzy SHOIN(D) DL and fuzzy OWL ontology and add some common fuzzy datatypes (e.g., trapezoidal values, interval values, approximate values, and labels) into the knowledge bases. On this basis, we propose an approach which can store fuzzy DL-knowledge bases in fuzzy relational databases, and provide an example to well explain the approach. The correctness and quality of the storage approach are proved and analyzed. Furthermore, following the proposed approach, we implemented a prototype tool, which can automatically store fuzzy DL-knowledge bases. Finally, we make a discussion about the query problem and make a comparison with the existing works.

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.

Multivalued Dependencies in Fuzzy Multivalued Relational Databases Using Fuzzy Functions

In this paper we discuss an important integrity constraint called multivalued dependency (mvd), which occurs as a result of the first normal form, in the framework of a newly proposed model called fuzzy multivalued relational data model. The fuzzy multivalued relational data model proposed in this paper accommodates a wider class of ambiguities by representing the domain of attributes as a “set of fuzzy subsets”. We show that our model is able to represent multiple types of impreciseness occurring in the real world. To compute the equality of two fuzzy sets/values (which occur as tuple-values), we use the concept of fuzzy functions. So the main objective of this paper is to extend the mvds in context of fuzzy multivalued relational model so that a wider class of impreciseness can be captured. Since the mvds may not exist in isolation, a complete axiomatization for a set of fuzzy functional dependencies (ffds) and mvds in fuzzy multivalued relational schema is provided and the role of fmvds in obtaining the lossless join decomposition is discussed. We also provide a set of sound Inference Rules for the fmvds and derive the conditions for these Inference Rules to be complete. We also derive the conditions for obtaining the lossless join decomposition of a fuzzy multivalued relational schema in the presence of the fmvds. Finally we extend the ABU's Algorithm to find the lossless join decomposition in context of fuzzy multivalued relational databases. We apply all of the concepts of fmvds developed by us to a real world application of “Technical Institute” and demonstrate that how the concepts fit well to capture the multiple types of impreciseness.

A Framework for Fuzzy Ontology Storing onto Relational Database within an a Priori Data Integration System

in data integration systems; but it can be strongly fixed when using ontology in an a priori approach where local ontology concepts are linked with shared ontology prior to populating data in corresponding sources. In this paper, we describe a defying context where local source is described by a fuzzy OWL ontology within an integration system using an a priori approach to achieve automatic integration for new data sources. We propose a conceptual framework starting by shared ontology and producing a target fuzzy Relational Database for every ontology-based local source participating in the integration system. Assuming shared ontology is a consensus in a given domain, this framework provides various contributions. It aims to solve ahead the problem of heterogeneous data sources because the local ontology that references the shared ontology is used to generate the conceptual data model for the target fuzzy Relational Database. To do this, it extends the a priori approach to deal with uncertainty which is a very common requirement in real world applications. Its storage process may be run on most of popular RDBMS. It is using a fuzzy OWL which represents most of fuzzy ontology constructs.

Ontology Based Fuzzy Query Execution

Database engineering has been progressed up to the Relational database stage. Fuzzy information administration in databases is a complex process in view of adaptable information nature and heterogeneous database frameworks. Relational Database Management System (RDBMS) can just handle fresh information but cannot handle precise data information. Structured Query Language (SQL) is a very powerful tool but can handle data which is crisp and precise in nature. It is not able to fulfill the requirements for information which is indeterminate, uncertain, inapplicable and imprecise and vague in nature. The goal of this work is to use Fuzzy technique in RDBMS. But, Fuzzy Relational Database Management System (FRDB) requires complex data structures, in most cases, are dependent on the platform in which they are implemented. A solution that involves representing an FRDB using an Ontology as an interface has been defined to overcome this problem. A new Fuzzy Query Ontology is proposed in this dissertation with implementation. The implementation layer, which is responsible for parsing and translating user requests into the corresponding DB implementations in transparent, is required to establish communication between the Ontology and the relational databases management system (RDBMS). This ontology defines a framework for storing fuzzy data by defining those using classes, slots, and instances. An Ontology is an explicit and formal specification of a conceptualization. Ontologies provides a shared understanding of a domain which allows interoperability between semantics.

Sugeno-Type Fuzzy Inference Model for Stock Price Prediction

operations of the prediction of stock price are complex and risky due to fluctuation in the stock market because of the vagueness, incompleteness, and uncertainty of the information used. However, it is therefore as a matter of necessity to seek to foresee stock prices because traders need to know when to invest in order to get the maximum return of the investment. This paper proposes a Sugeno-type fuzzy inference system for stock price prediction using technical indicators as its input values. Knowledge Base, Fuzzification, Inference Engine and Defuzzification are the essential components of our model. We explore Sugeno-type fuzzy inference engine to optimize the estimated result. We evaluate the degree of participation of each input parameter with Trapezoidal membership function. Center of Gravity technique is employed for defuzzification. We employ object oriented design tool to model our database. MATLAB and fuzzy relational database are used in the implementation of our study. The development of this system is based on the selection of stock data history which are studied and used for training the system. This system provides vital support to stock traders, researchers and other financial experts in making decisions as regards stock trading.

English

Fuzziness in databases is used to denote uncertain or incomplete data. Relational Databases stress on the nature of the data to be certain. This certainty based data is used as the basis of the normalization approach designed for traditional relational databases. But real world data may not always be certain, thereby making it necessary to design an approach for normalization that deals with fuzzy data. This paper focuses on the approach for designing the fifth normal form (5NF) based on join dependencies for fuzzy data. The basis of join dependency for fuzzy relational databases is derived from the basic relational database concepts. As join dependency implies an multivalued dependency by symmetry the proof of join dependency based normalization is stated from the perspective of multivalued dependency based normalization on fuzzy relational databases.

Rough Fuzzy Relation on Two Universal Sets

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.

Lossless Join Decomposition for Extended Possibility-Based Fuzzy Relational Databases

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.

Modeling fuzzy information in fuzzy extended entity-relationship model and fuzzy relational databases

Computer applications in non-traditional area have put requirement on conceptual data modeling. Some conceptual data models, being the tool of design databases, have been proposed. Information in real world application is often vague or ambiguous. Currently few researches have been done in modeling fuzziness in conceptual data model and design of fuzzy databases. In this paper, based on fuzzy set theory, different levels of fuzziness are introduced into the EER (enhanced/extended entity-relationship) model and the corresponding representations are given. The EER model is then extended to fuzzy EER model. The formal mapping of the fuzzy EER model into the fuzzy relational database schema is proposed in the paper.

Fuzzy Object Oriented Database versus FRDB for Uncertainty Management

It is impossible to capture all of the semantics of real world information and to model it in a perfect way. Uncertain information being lacking information, individual interpretation of knowledge is taken into account. Most widely used relational model faced much difficulty to handle complex data requirements. The size of databases and their changing composition such as graphics, video and sound, as well as numbers and text invited a reorganization of existing information systems. Object oriented database draw their strength from graphical user interfaces, advanced data management capabilities and powerful modeling techniques. So in order to deal with inexactness fuzzy techniques have been extensively integrated with more advanced object oriented database system which is capable to represent and manipulate the complex objects as well as complicated and uncertain relationship exiting among them. In this paper uncertainty using Fuzzy Object Oriented Database and Fuzzy Relational Data Base is illustrated.