The Identification Types of the Components of a Cluster - Assignment Example

? Creating an Extended Entity Relationship Model (EERM) Creating an Extended Entity Relationship Model (EERM) We use a classical four-layered approach to inductive specification of database structures. The first layer is the data environment, called the basic data type scheme, which is defined by the system or is the assumed set of available basic data. The second layer is the schema of a given database. The third layer is the database itself representing a state of the application's data often called micro-data. The fourth layer consists of the macro-data that are generated from the micro-data by application of view queries to the micro-data (DIETRICH, 2011). The second layer is diversely treated by database modeling languages. Nevertheless, there are common features, especially type constructors. A common approach in most models is the generic definition of operations according to the structure of the type. The inductive specification of structuring is based on base types and type constructors. A type constructor is a function from types to a new type. The constructor can be supplemented with a selector for retrieval (like Select) with a retrieval expression and update functions (like Insert, Delete, and Update) for value mapping from the new type to the component types or to the new type, with correctness criteria and rules for validation, with default rules; current date for data assignment, with one or several user representations, and with a physical representation or properties of the physical representation. A base type is an algebraic structure B = (Dom(B); Op(B); Pred(B)) with a name, aSet of values in a domain, a set of operations and a set of predicates. A class BC on the base type is a collection of elements from Dom (B). Usually, BC is required to be a set (DIETRICH, 2011). It can be also a list (denoted by < : >) multi-set ({|.|}), tree etc. Classes may be changed by applying operations. Elements of a class may be classified by the predicates. The value set can be discrete or continuous, finite or infinite. We typically assume discrete value sets. Typical predicates are comparison predicates such as ; ·; 6=; ?; =. Typical functions are arithmetic functions such as, - and x. The set of integers is given by the Integer Set. The base type is extended to a data type by explicit definition of properties of the under-lying value sets. Precision and accuracy; data can be precise to a certain extent. Precision is the degree of refinement in the calculations. Accuracy is a measure of how repeatable the assignment of values for properties is. Granularity: Scales can be fine or coarse. The accuracy of data depends on the granularity of the domain which has been chosen for the representation of properties. Ordering: The ordering of values of a given domain can be based on ordering schemes such as lexicographic, geographic or chronological ordering or on exact ordering such as orderings on natural numbers. The ordering can also be based on ontologies or categories. Scales have a range with lowest values and highest values. These values can be finite or infinite, if they are finite then overflow or underflow errors might be the result of a computation. Classification: The data can be used for representation of classifications; the classification can be linear, hierarchical, etc. The classification can be mono-hierarchical or poly-hierarchical, mono-dimensional, poly-dimensional, analytical, synthetically or even monothetic. The classification can be based on ontologies and can be maintained with thesauri. Presentation: The data type can be mapped to different representation types dependent on several parameters. For instance, in Web applications, the format chosen for presentation types of pictures depends on the capacity of the channel, on the compression etc. The presentation might be linear or hierarchical, and it can be layered. Implementation: The implementation the attribute type depends on the properties of the DBMS. The implementation type also influences the complexity of computations. During the design of databases, default values can be assigned in order to store properties regarding the existence of data such as `exists but not at the moment', `exist but not known', `exists, but under change', `at the moment forbidden/system defined/wrong', `not reachable', `until now not reachable', `not entered yet', `not transferable/transferred', `not applicable to the object'. Usually, only one default value is allowed. An example of a default value is the null value. Casting functions: We assume that type systems are (strongly) typed. In this case, we are not able to compare values from different domains and new values from a set of values taken from different domains. Casting functions can be used to map the values of a given domain to values of another domain. It should be noted that the data type restricts the operations that can be applied (DIETRICH, 2011). Databases often store units of measure which use a scale of some sort. Scales can be classified according to a set of properties such as the following; a natural origin point of sale represented usually by a meaningful `zero,' which is not just a numeric zero; applicability of meaningful operations that can be performed on the units; existence of natural orderings of the units; existence of a natural metric function on the units. Metric functions obey triangular property are symmetric and map identical objects to the scales origin. For instance, adding weights is meaningful whereas adding shoe sizes looks odd. The plus operation can be different if a natural ordering exists. Metric values are often relative values that are perceived in different ways, e.g. the intensity of light we, thus, extend basic data types to extended data types by description of precision and accuracy, granularity, order, classification, presentation, implementation, special values, null, default values, casting functions, and scale. This extended specification approach avoids the pitfalls of aggregation. Aggregation functions can be applied to absolute and ratio values without restriction. Additive aggregation and min/max functions can be applied to interval values. The average function can only be applied to equidistant interval values. The application of aggregation functions such as summarization and average to derived values is based on conversions to absolute or ratio values. Comparison functions such as min/max functions can be applied to derived values only by attribution to ratio or absolute values. The average function can only be applied to equidistant interval values. Aggregation functions are usually not applicable to nominal values, ordinal values, and rank values. For reasons of simplicity; we restrict the model to tuples and to set constructors. However, list and bag constructors can be used whenever type constructors are allowed. In some cases, (entity) types may be combined into a union of types or so called cluster types. Since we need to preserve identification, we restrict the union operation to disjoint unions. Clusters based on entity types can be defined by the disjoint union of types. Furthermore, we require that the identification types of the components of a cluster are domain-compatible. First-order relationship types that have only one entity type are called unary, those with two entity types are called binary and those with several labeled occurrences of the same entity type are called recursive. Labels can be omitted if the types can be distinguished. We may generalize the notion of first-order relationship types to relationship types of arbitrary order. We may also use constructors Cartesian product, union; disjoint union, power set, bags (multisets), and list for definition of complex components. The disjointness for clusters can be weakened for relationship types. We distinguish between specialization types and generalization types. Specialization is used whenever objects obtain more properties, may play a variety of roles, and use more functions. Generalization introduces the role-of relationship or the affiliation between a subtype entity and its type. Therefore, the constructs are different, for the generalization, the generic type must be the union of its subtypes. Thus, the subtypes can be virtually clustered by the generic type (DIETRICH, 2011). This is the case for specialization. Specialization of a role of the subtype can be changed. Generalization is usually defined through a cluster type. Cluster type can be translated to a relational type or to a relational view. Functions are inherited upwards, that is, from one type of abstraction. Abstractions typically do not have their own functions. Variations and versions can be modeled on the basis of hierarchy abstraction. Hierarchies may be combined, and the root types of the hierarchies are generalized to a common root type. The variation of the root type is formed by a number of dimensions applicable to the type. For instance, addresses have specialization dimension, a language dimension, applicability dimension and a classification dimension. Schemata may have a number of dimensions. We observe that types in a database schema are of very different usage. This usage can be made explicit. Extraction of this utilization pattern shows that each schema has a number of internal dimensions. Specialization dimension based on roles objects play or, on categories into which objects are separated; association dimension through bridging related types and in adding meta-characterization on data quality; usage, meta-characterization or log dimension characterizing log information such as the history of database evolution. The association to business steps and rules, and the actual usage; data quality, lifespan and history dimension, we may abstract from the last two dimensions during database schema development and add these dimensions as the last step of conceptual modeling. In this case, the schema, this is considered, until this step is concerned with the main facets of the application. Tables $sql = "CREATE TABLE Customers ( PID INT NOT NULL AUTO_INCREMENT, PRIMARY KEY(PID), FirstName CHAR(15), LastName CHAR(15), Phone number INT )"; $sql = "CREATE TABLE Agent ( PID INT NOT NULL AUTO_INCREMENT, PRIMARY KEY(PID), FirstName CHAR(15), LastName CHAR(15), )"; $sql = "CREATE TABLE Order ( PID INT NOT NULL AUTO_INCREMENT, PRIMARY KEY(PID), Order Name CHAR(15), )"; References DIETRICH, S. (2011). Fundamentals of object databases object-oriented and object-relational design. [S.l.], Morgan & Claypool. Read More