Types of Functional dependencies in DBMS

In relational database management, functional dependency is a concept that specifies the relationship between two sets of attributes where one attribute determines the value of another attribute. It is denoted as X → Y, where the attribute set on the left side of the arrow, X is called Determinant, and Y is called the Dependent. 

What is Functional Dependency?

A functional dependency occurs when one attribute uniquely determines another attribute within a relation. It is a constraint that describes how attributes in a table relate to each other. If attribute A functionally determines attribute B we write this as the A→B.

Functional dependencies are used to mathematically express relations among database entities and are very important to understanding advanced concepts in Relational Database Systems.

Example:

From the above table we can conclude some valid functional dependencies:

• roll_no → { name, dept_name, dept_building }→  Here, roll_no can determine values of fields name, dept_name and dept_building, hence a valid Functional dependency
• roll_no → dept_name , Since, roll_no can determine whole set of {name, dept_name, dept_building}, it can determine its subset dept_name also.
• dept_name → dept_building ,  Dept_name can identify the dept_building accurately, since departments with different dept_name will also have a different dept_building
• More valid functional dependencies: roll_no → name, {roll_no, name} ⇢ {dept_name, dept_building}, etc.

Here are some invalid functional dependencies:

• name → dept_name   Students with the same name can have different dept_name, hence this is not a valid functional dependency.
• dept_building → dept_name    There can be multiple departments in the same building. Example, in the above table departments ME and EC are in the same building B2, hence dept_building → dept_name is an invalid functional dependency.
• More invalid functional dependencies: name → roll_no, {name, dept_name} → roll_no, dept_building → roll_no, etc.

Read more about What is Functional Dependency in DBMS ?

Types of Functional Dependencies in DBMS

1. Trivial functional dependency
2. Non-Trivial functional dependency
3. Multivalued functional dependency
4. Transitive functional dependency

1. Trivial Functional Dependency

In Trivial Functional Dependency, a dependent is always a subset of the determinant. i.e. If X → Y and Y is the subset of X, then it is called trivial functional dependency.

Symbolically: A→B is trivial functional dependency if B is a subset of A.

The following dependencies are also trivial: A→A & B→B

Example 1 :

• ABC -> AB
• ABC -> A
• ABC -> ABC

Example 2:

Here, {roll_no, name} → name is a trivial functional dependency, since the dependent name is a subset of determinant set {roll_no, name}. Similarly, roll_no → roll_no is also an example of trivial functional dependency. 

2. Non-trivial Functional Dependency

In Non-trivial functional dependency, the dependent is strictly not a subset of the determinant. i.e. If X → Y and Y is not a subset of X, then it is called Non-trivial functional dependency.

Example 1 :

• Id -> Name
• Name -> DOB

Example 2:

Here, roll_no → name is a non-trivial functional dependency, since the dependent name is not a subset of determinant roll_no. Similarly, {roll_no, name} → age is also a non-trivial functional dependency, since age is not a subset of {roll_no, name} 

3. Semi Non Trivial Functional Dependencies 

A semi non-trivial functional dependency occurs when part of the dependent attribute (right-hand side) is included in the determinant (left-hand side), but not all of it. This is a middle ground between trivial and non-trivial functional dependencies. X -> Y is called semi non-trivial when X intersect Y is not NULL. 

Example:

Consider the following table:

Functional Dependency:

{StudentID,CourseID}→CourseID

This is semi non-trivial because:

• Part of the dependent attribute (Course_ID) is already included in the determinant ({Student_ID, Course_ID}).
• However, the dependency is not completely trivial because {StudentID}→CourseID is not implied directly.

4. Multivalued Functional Dependency

In Multivalued functional dependency, entities of the dependent set are not dependent on each other. i.e. If a → {b, c} and there exists no functional dependency between b and c, then it is called a multivalued functional dependency.

Example:

In this table:

• X: bike_model
• Y: color
• Z: manuf_year

For each bike model (bike_model):

1. There is a group of colors (color) and a group of manufacturing years (manuf_year).
2. The colors do not depend on the manufacturing year, and the manufacturing year does not depend on the colors. They are independent.
3. The sets of color and manuf_year are linked only to bike_model.

That’s what makes it a multivalued dependency.

In this case these two columns are said to be multivalued dependent on bike_model. These dependencies can be represented like this:

Read more about Multivalued Dependency in DBMS.

5. Transitive Functional Dependency

In transitive functional dependency, dependent is indirectly dependent on determinant. i.e. If a → b & b → c, then according to axiom of transitivity, a → c. This is a transitive functional dependency.

Example:

Here, enrol_no → dept and dept → building_no. Hence, according to the axiom of transitivity, enrol_no → building_no is a valid functional dependency. This is an indirect functional dependency, hence called Transitive functional dependency.

6. Fully Functional Dependency

In full functional dependency an attribute or a set of attributes uniquely determines another attribute or set of attributes. If a relation R has attributes X, Y, Z with the dependencies X->Y and X->Z which states that those dependencies are fully functional.

Read more about Fully Functional Dependency.

7. Partial Functional Dependency

In partial functional dependency a non key attribute depends on a part of the composite key, rather than the whole key. If a relation R has attributes X, Y, Z where X and Y are the composite key and Z is non key attribute. Then X->Z is a partial functional dependency in RBDMS.

Read more about Partial Dependency.

Conclusion

Functional dependency is very important concept in database management system for ensuring the data consistency and accuracy. In this article we have discuss what is the concept behind functional dependencies and why they are important. The valid and invalid functional dependencies and the types of most important functional dependencies in RDBMS. We have also discussed about the advantages of FDs. 

For more details you can refer Database Normalization and Difference between Fully and Partial Functional Dependency articles.