Dependency preservation and lossless join decomposition in fuzzy normalization

Information imprecision and uncertainty exist in many real-world applications, and for this reason fuzzy data modeling has been extensively investigated in various database models. In particular, Zadeh’s fuzzy set theory has been identified as a successful technique for modeling imprecise and uncertain information in various database models. This has resulted in numerous contributions, mainly with respect to the popular fuzzy conceptual data models (fuzzy ER/EER model, fuzzy UML data model, and etc.) and fuzzy logical database models (fuzzy relational database model, fuzzy object-oriented database model, and etc.). Also, it is shown that fuzzy set theory is very useful in Web-based business intelligence. Therefore, topics related to the modeling of fuzzy data are considered very interesting in XML since it is the current standard data representation and exchange format over the Web. In particular, to manage fuzzy XML data, it is necessary to integrate fuzzy XML and various fuzzy databases, and various fuzzy database models (fuzzy relational database model and fuzzy object-oriented database model) need to be used for mapping to and from the fuzzy XML models. Therefore, in this chapter, we mainly introduce several fuzzy database models, including fuzzy UML data model, fuzzy relational database model, and fuzzy object-oriented database model. Before that, we briefly introduce some notions of fuzzy set theory.

Proximity relations in the fuzzy relational database model

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.

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

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.

1 - The Relational Database Model

Fuzzy normal forms can be generated with an application of "Normal Form Generation Algorithm" on fuzzy truth tables. This takes place at the third level of knowledge representation, i.e., propositional level. It is shown that at least three distinct sets of normal forms can be generated depending on the axioms one is willing to impose on the propositional fuzzy set and logic theories. All are conjunctive-disjunctive and complement based De Morgan logics with the following three classes of axioms that identify each general class of fuzzy normal forms in order of least to most restrictive set of axioms in the following sense: 1) boundary and monotonicity; 2) boundary, monotonicity, associativity and commutativity; and 3) boundary, monotonicity, associativity, commutativity and idempotency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This study deals with multivalued dependency properties in fuzzy relational data models called fuzzy multivalued dependency. After giving a definition of this property, it is shown that it has common inference rules to those of relational databases. It also found that an ABU algorithm in relational data models can be applied to test lossless join decomposition in fuzzy relational data models for a given set of fuzzy multivalued dependencies.

Extending the fuzzy database with fuzzy numbers

Binary equality implication constraints, normal forms and data redundancy

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 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.

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.

The relational approach has been applied very literally to temporal databases. For example, the SALARY and DEPT of an employee do not necessarily change at the same time, resulting in a split of information into two tables: NAME SALARY START END and NAME DEPT START END, where START and END are instants of time, treated as special attributes. A unit of information, such as salary of an employee, is further split into several tuples. Normal forms, dependencies and other nice concepts of relational databases remain inapplicable to the temporal case. We propose that a tuple, the fundamental molecular unit of information, be viewed as a function from a union of finitely many intervals of time into domains of attributes. This eliminates the problems stated above. It gives rise to elegant relational algebra, tuple calculus and other query languages and brings temporal databases within the classical framework. It is hoped that this model will draw the attention of researchers to temporal databases.