Vague Normalization in a Relational Database Model

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.

In order to model the imprecise and uncertain information, different classical relational data model have been studied in literature using vague set theory. However, neutrosophic set, as a generalized vague set, has more powerful ability to process fuzzy information than vague set. In this paper, we have proposed a neutrosophic relational database model and have defined a new kind of neutrosophic functional dependency (called  -nfd) based on the -equality of tuples and the similarity measure of neutrosophic sets. Next, we present a set of sound neutrosophic inference rules which are similar to Armstrong’s axioms for the classical case. Finally, partial  -nfdand neutrosophic key have been studied with the new notion of  -nfdand also tested.

The subject of the study is the methods of intellectual analysis, namely the construction of a decision tree, associative analysis, the identification of patterns between related events based on data presented by a relational model. The purpose of the study is to analyze the features of information units and data structures, using the example of relational systems that affect the technology of knowledge extraction. Tasks: the article solves the following tasks: to consider the relational data model as the most popular and effective data structure used in intelligent information systems for data processing and storage; to analyze the operations of relational algebra, the operational component of the relational data model regarding the application of aggregate functions; to develop a general formal statement of the problem of knowledge extraction from a relational database; to consider the concept of functional associative rules; the ID3 decision tree generation algorithm focused on data processing in relational systems is analyzed. The following methods are implemented: modern view and trends in the field of data mining; features of building information systems based on relational databases, relational algebra, theory of normalization of relations; analysis of literature on the topic of research; comparative analysis. Results achieved: the relational data model is considered as the most effective data structure used in intelligent information systems for data processing and storage. A group of aggregate functions of relational databases is identified and analyzed with respect to key attributes of the relation, which makes it possible to build logical dependencies between information units of the subject area being analyzed. The task of extracting knowledge from the database is formally formulated. The concept of functional associative rules is introduced. The ID3 decision tree generation algorithm focused on data processing in relational systems is carefully analyzed. The semantic network (SN), built on the basis of the proposed approach, allows to increase the efficiency of decision support systems. Conclusions: the universal approach proposed in the article to build a relational data model of an information system for searching for associative patterns in data allows to solve a whole class of typical tasks in which objects are connected by a "many-to-many" relationship or M →N. The relational database model is proposed as a universal information structure for solving associative analysis tasks and presenting knowledge in the form of a semantic network. The examples given in the article confirm the effectiveness of the developed and considered approaches to solving the problem of data mining in the environment of relational systems. Solving the problem of identifying knowledge in data will allow to improve the quality of management decisions made.

Relational Database Design and Implementation

The Access Path Specification Language (APSL) is a high-level essentially nonprocedural language for specifying restructuring transformations of network databases. It does so in terms of application-oriented concepts such as access strategies and selection criteria. APSL's approach to restructuring emphasizes description of the source structures from which target data is to be retrieved, rather than the operations needed to convert source constructs to target constructs. The latter approach is used by most current systems to restructure hierarchical data.APSL is based on the Relational Interface Model (RIM) of data, which permits a suitably restricted network database to be viewed simultaneously as a relational database in first normal form. Any restructuring of a RIM database which can be performed by the relational algebra operations Join, Select, Project, and Union can be described in APSL.APSL has been implemented as the restructuring specifications language in the Michigan Data Translator.

1 - The Relational Database Model

Some results about normal forms for functional dependency in the relational datamodel

Many types of maritime incident databases have been established that allow people to learn from past incidents and develop corresponding mitigation measures. However, our investigation of multiple international and national databases shows that most existing databases only record basic information regarding incidents in a single table. Lots of useful information is not included in the database (i.e., limited extension of the database). Meanwhile, some basic information is recorded tautologically (i.e., data redundancy). In this paper, two widely used databases are taken as examples, the Global Integrated Shipping Information System and the Lloyd's List Intelligence, to explain these common problems of existing databases. To overcome these limitations and improve the efficiency of data maintenance, this paper develops a relational maritime safety management database. The entity-relationship model is first used to depict the inter-related semantic information surrounding maritime incidents, and a relational database model is subsequently formed. Microsoft Access is employed to implement the proposed database, and a database application is also designed to demonstrate the utility of the database. Our preliminary study shows that the proposed database is implementable and has potential usage for both industry and academic research.

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.

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.

A new normal form, namely, object-normal form (ONF), is introduced. It is shown that the existing definitions of the fifth normal form (5NF) are unsatisfactory. The correct definition is given for the first time. The importance of the 5NF is demonstrated. For improving data representation in a database with a 5NF schema, the notion of negating relation is introduced. It serves as a basis for the new normal form, namely, the sixth normal form. Combining requirements of the ONF and other normal forms, new normal forms are defined: the fourth object-normal form, the fifth object-normal form, and the sixth object-normal form. It is shown that the standard order of steps of the normalization procedure should be changed: first, the specific requirements of the fourth normal form should be satisfied, and only then the requirements of the second normal form, and so forth.

Hands-on training in relational database concepts

The storage of data is a key issue of information systems, which is an important foundation for data query and data mining. Relational database model has been proven to be a very useful data-storage technique. As information is stored as data in relational databases, the induction of concepts from data is a pivotal topic in the data mining field. Formal Concept Analysis (FCA) turns out to be a perfect instrument for a meaningful and conceptual exploration of the stored data. In FCA, conceptual scaling provides a complete framework for transforming any many-valued context (i.e., relation/table) into a context (called a derived context), in which each many valued attribute is given a scale. The attributes in a scale basically describe meaningful features of the values of the initial attribute. From the logical point of view, complement operation plays a very important role in relational databases and data query systems. In this paper, we provide the connections between the concepts of binary relations and those of complementary binary relations, and propose an approach toward normalizing (complementary) scales, i.e., each (complementary)scale can be represented by a set of statements. One advantage of normalizing scales is to avoid generating huge derived relations, and hence this approach reduces storage cost. By the normalization, the concept lattice of the complement of a derived relation is reduced to a combination of the concept lattice of the derived relation and a set of statements.

Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

The article outlines the methods for creating SQL queries in relational databases. The use of the structured query language SQL in relational databases is substantiated. It provides information about the SQL standard and the three-tier database organization system. The author describes the choice of a data model based on the conceptual level using to that end an example of the Kokand Pedagogical Institute as the relational database model. A relational conceptual diagram of the information model of a pedagogical institute is compiled. Such a conceptual diagram is depicted using a cluster. Objects of the subject area are depicted in the form of tables, which differ from each other in geometric shapes or colors. The relationships between tables in Microsoft Access are presented. The basic rules for creating and filling tables in SQL using the instructions CREATE TABLE and INSERT INTO are considered. The syntax of the SELECT statement is given. All offers of the SELECT statement and their order are listed. Examples are given for compiling simple queries and subqueries in SQL using the SELECT statement for the database of the Kokand Pedagogical Institute. Information about the order of execution of internal and external requests is given. The article considers the ORDER BY offer of a SELECT statement for sorting query results.