Fifth normal form (5NF)

Fifth Normal Form (5NF), also known as Project-Join Normal Form (PJNF), is a level of database normalization that addresses complex multi-valued dependencies in a relational database. It is an extension of the Boyce-Codd Normal Form (BCNF).

In 5NF, a relation is considered to be in the highest level of normalization. It satisfies two main criteria:

  1. It is in BCNF: A relation is in BCNF if for every non-trivial functional dependency (X -> Y), X is a superkey. BCNF ensures that there are no non-trivial functional dependencies between candidate keys and non-key attributes.
  2. It is free from join dependencies: A join dependency occurs when a relation can be expressed as a join of two or more smaller relations. In 5NF, a relation must be free from any non-trivial join dependencies. This means that all attributes in the relation must be functionally dependent on the entire primary key.

To achieve 5NF, a relation may need to be decomposed into multiple smaller relations. This decomposition is done based on the multi-valued dependencies present in the relation. Multi-valued dependencies arise when an attribute is dependent on a subset of the key, rather than the entire key. By decomposing the relation and eliminating the multi-valued dependencies, we ensure that each relation satisfies the BCNF and join dependency criteria.

It’s worth noting that achieving 5NF comes with a trade-off. While it eliminates complex multi-valued dependencies, it can lead to an increased number of relations and potentially more complex queries to retrieve the required data. Therefore, the decision to normalize a database to 5NF should be based on the specific requirements and characteristics of the application.

Example of Fifth normal form (5NF):

Sure! Let’s consider a hypothetical example to illustrate the Fifth Normal Form (5NF) in a database.

Let’s say we have a database for a library, and we want to represent the books, authors, and the genres they belong to. We can start by creating the following relations:

  1. Relation: Books Attributes: [BookID, Title, ISBN]
  2. Relation: Authors Attributes: [AuthorID, AuthorName]
  3. Relation: Genres Attributes: [GenreID, GenreName]

To achieve 5NF, we need to ensure that there are no multi-valued dependencies and that the relations satisfy BCNF. In this case, let’s assume that a book can have multiple authors, and an author can write multiple books. Additionally, a book can belong to multiple genres, and a genre can have multiple books.

To eliminate the multi-valued dependencies, we need to decompose the relations further. We introduce additional relations to represent the relationships between books, authors, and genres:

  1. Relation: BookAuthors Attributes: [BookID, AuthorID]

    This relation represents the many-to-many relationship between books and authors. Each record in this relation indicates that a specific book (identified by BookID) was written by a specific author (identified by AuthorID).

  2. Relation: BookGenres Attributes: [BookID, GenreID]

    This relation represents the many-to-many relationship between books and genres. Each record in this relation indicates that a specific book (identified by BookID) belongs to a specific genre (identified by GenreID).

Now, we have decomposed the original relations and eliminated the multi-valued dependencies. Each relation satisfies BCNF, and there are no join dependencies between them.

It’s important to note that in a real-world scenario, the database design and decomposition to 5NF may involve additional attributes and relations depending on the specific requirements and complexities of the domain being modeled.