On Normalization of Relations in Relational Databases

A key is simple if it consists of a single attribute. It is shown that if a relation schema is in third normal form and every key is simple, then it is in projection-join normal form (sometimes called fifth normal form), the ultimate normal form with respect to projections and joins. Furthermore, it is shown that if a relation schema is in Boyce-Codd normal form and some key is simple, then it is in fourth normal form (but not necessarily projection-join normal form). These results give the database designer simple sufficient conditions, defined in terms of functional dependencies alone, that guarantee that the schema being designed is automatically in higher normal forms.

The analysis of a relational database to reduce its component schemes into fourth normal form is not trivial. Decompositions into Boyce–Codd normal form is not difficult, but the concepts and analysis needed to further decompose into fourth normal form are usually difficult to comprehend and use. A diagrammatic representation of dependencies is described which provides an informal aid to the construction of relational schemes in fourth normal form.

Although relational languages do not require higher normal forms, they are nevertheless useful as tools for analysis of data and for the imposition of constraints which protect data from some update anomalies. As the first to the third normal forms have been covered before, we shall devote this chapter to the other normal forms, in particular the fourth normal form. We shall also attempt to answer questions such as “is there an ultimate normal form?” and make some comments on the practical usefulness of some of the more exotic theoretical work on normalisation.

In the conceptual design of relational databases one of the main goals is to create a conceptual scheme, which minimize redundancies and eliminate deletion and addition anomalies, i.e. to create relation schemes in some good normal form. The study of relational databases has produced a host of normal forms: 2NF, 3NF, BCNF, Elementary-Key Normal Form, 4NF, Weak 4NF, PJ/NF, DK/NF, LTKNF, (3,3)NF, etc. There are two features which characterize these normal forms. First, they consider each relation separately. We believe that a normal form (which reflects the goodness of the conceptual design) should be related to the whole conceptual scheme. Second, the usefullness of all normal forms in relational database design have been based on the assumption that a data definition language (DDL) of a database management system (DBMS) is able to enforce key dependencies. However, different DDLs have different capabilities in defining constraints. In this paper we will discuss the design of conceptual relational schemes in general. We will also define a good normal form (GNF) which requires a minimally rich DDL; this normal form is based only on a primitive concept of constraints. We will not, however, discuss the normalization process itself – how one might, if possible, convert a relation scheme that is not in some normal form into a collection of relation schemes each of which is in that normal form.

The traditional relational database model may be extended into a fuzzy database model based on the mathematical framework of fuzzy set theory to process imprecise or uncertain information. While designing such a fuzzy relational database model that does not suffer from data redundancy and anomalies, the present authors have defined several fuzzy normal forms in ref [1]. However, as one decomposes an unnormalized relation into a desired normal form, it should also satisfy the essential properties of dependency preservation and lossless join of relation schemes which take a significant role in the design theory of a relational database. We have concentrated on these two important issues in this paper and have designed algorithms that confirm dependency preservation and lossless join decomposition of an unnormalized relation into the fuzzy third normal form or fuzzy Boyce Codd normal form. The algorithms have been tested and validated with examples.

Normal forms and syntactic completeness proofs for functional independencies

Database normalization is a process which eliminates redundancy, organizes data efficiently and improves data consistency. Functional, multivalued, and join dependencies (FDs, MVDs, and JDs) play fundamental roles in relational databases where they provide semantics for the data and at the same time are the foundations for database design. In this study we investigate the issue of defining functional, multivalued and join dependencies and their normal forms in XML database model. We show that, like relational databases, XML documents may contain redundant information, and this redundancy may cause update anomalies. Furthermore, such problems are caused by certain dependencies among paths in the document. Our goal is to find a way for converting an arbitrary XML Schema to a well-designed one that avoids these problems. We extend the notion of tuple for relational databases to the XML model. We show that an XML tree can be represented as a set of tree tuples. We introduce the definitions of FD, MVD, and JD and new Normal Forms of XML Schema that based on these dependencies (X-1NF, X-2NF, X-3NF, X-BCNF, X-4NF, and X-5NF). We show that our proposed normal forms are necessary and sufficient to ensure all conforming XML documents have no redundancies.

Context. The complexity of understanding the concept of multivalued dependencies (when setting out their theoretical foundations, an axiomatic approach is used) in relational (table) databases leads to problems of their modeling, which in turn can cause a violation of data integrity. A partial solution to these issues is facilitated by the search for equivalent axiomatic systems of multivalued dependencies that are minimal in terms of the number and power of their components. This, in turn, requires establishing the equivalence of these axiomatic systems and proving the independence of their elements. The object of the study is the axiomatisations of multivalued dependencies.The purpose of the work is to establish the equivalence of two axiomatic systems of multivalued dependencies, one of which is minimal in terms of the number and power of components, and to prove the independence of specified axiomatics. Method. Set-theoretic and logical-algebraic methods are used in the construction of proofs. The equivalence of two axiomatic systems of multivalued dependencies is established classically: the relation of syntactic inference is considered and sequences of multivalued dependencies are constructed that are proofs of the rules of each axiomatics from the components of the other. To build proof of independence of the axiomatic system, models of relational schemes are proposed, such that for an axiom or rule whose independence is being proved, it is impossible to construct proof from set of other axioms or rules.Results. Equivalence of the axiomatisation of multivalued dependencies proposed by a group of scientists Beeri, Fagin and Howard and the Biskup’s axiomatisation of multivalued dependencies has been established. The independence of the Biskup’s axiomatic system is proved in the sense that without loss of completeness it is impossible to remove neither the only axiom nor none of the inference rules.Conclusions. The independence of the Biskup’s axiomatisation of multivalued dependencies, which has no more in number and power of components than other axiomatic systems of multivalued dependencies, is proved. Using such axiomatic system has advantages in the development of CASE-tools (Computer-Aided Software Engineering Tools), which include the implementation of reducing the relational database schema to the fourth normal form, and also, when manually designing a logical model of a relational database.

Vague relational database models generalize the classical relational database model by allowing uncertain and imprecise information by means of vague set theory. In this paper, we have introduced vague extensions of the normal forms for a similarity based vague relational database model. Firstly, we have designed an algorithm to find the vague closure of an attribute set which can be utilized to find vague key. Next, with the concepts of α-vfd and partial α-vfd as introduced in [1], we have defined different vague normal forms in a vague relational database. We have also presented examples based on real life application to demonstrate how normalization based on α-vfds of vague relation may be done.KeywordsVague setsimilarity measure of vague sets α-vfd partial α-vfd vague keyvague closure of attribute setvague normal forms

Binary equality implication constraints, normal forms and data redundancy

6 - Normalization

This paper is about designing a complete interactive tool, named JMathNorm, for relational database (RDB) normalization using Mathematica. It is an extension of the prototype developed by the same authors [1] with the inclusion of Second Normal Form (2NF), and Boyce-Codd Normal Form (BCNF) in addition to the existing Third normal Form (3NF) module. The tool developed in this study is complete and can be used for real-time database design as well as an aid in teaching fundamental concepts of DB normalization to students with limited mathematical background. JMathNorm also supports interactive use of modules for experimenting the fundamental set operations such as closure, and full closure together with modules to obtain the minimal cover of the functional dependency set and testing an attribute for a candidate key. JMathNorm's GUI interface is written in Java and utilizes Mathematica's JLink facility to drive the Mathematica kernel.

We propose a normal form for nested relations, called NF-NR, which removes undesirable anomalies from a nested relational database schema. Both functional dependencies and multivalued dependencies are considered. NF-NR reduces to 3NF/4NF if the nested relation considered is actually a flat relation. Especially, NF-NR removes global redundancies among a set of nested relations. Two approaches to NF-NR database design, namely the restructuring rules approach and the ER approach, are discussed. We relate NF-NR to ER-NF, a normal form of ER defined earlier, by defining a simple mapping from an ERD in ER-NF to a set of nested relations in NF-NR. This approach effectively removes ambiguitics and redundancies on a semantic level and hence gives a set of nested relations with clean semantics and yet in good normal form. A set of desirable properties for any normal form for nested relations are described and an evaluation of several existing normal forms is given based on this set of properties. The evaluation shows that NF-NR improves over previously proposed normal forms in various aspects and is a more practical normal form for nested relations.

Tracking application is widely used to help outdoor activities. One of them is used to help tourists who do tourist destinations in group activities. Tourist tracking application requires data on the position of tourists on earth. This coordinate data can be obtained using latitude and longitude data from GPS (Global Positioning System). Coordinate latitude and longitude position of tourists from time to time are stored in a database. Database Selection for media storage will determines the level of speed and ease in accessing data. There are some differences in designing the structure of the MySql and Firebase databases. Relational Database begins with identification of entities involved in the system. One entity with another entity is related and has a cardinality level of the relationship. Relational database implementation in the form of tables in normal forms that are interconnected. Data will be stored in columns and rows. Normalization of tables causes high query computation when calling data that involves many tables. Firebase, which is one of the NoSql databases, in building data structures is stored in JSON objects. JSON tree structures usually consider the display of information that will be presented to users. So that the generated JSON tree has high efficiency and speed in processing data. In this study a comparison between the design of the relational database structure, namely MySql and NoSql Firebase database structure was developed. Firebase is more power full for the development of applications which update data in realtime and and handle a lot of coordinate data such as tourist tracking applications. Applications that do not have complex data relations such as tourist tracking applications are more suitable to use firebase than using MySQL.

An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic