In Database Management Systems (DBMS), multivalued dependency (MVD) deals with complex attribute relationships in which an attribute may have many independent values while yet depending on another attribute or group of attributes. It improves database structure and consistency and is essential for data integrity and database normalization.
MVD or multivalued dependency means that for a single value of attribute ‘a’ multiple values of attribute ‘b’ exist. We write it as,
a --> --> b
It is read as a is multi-valued dependent on b. Suppose a person named Geeks is working on 2 projects Microsoft and Oracle and has 2 hobbies namely Reading and Music. This can be expressed in a tabular format in the following way.

Example
Project and Hobby are multivalued attributes as they have more than one value for a single person i.e., Geeks.
What is Multivalued Dependency?
When one attribute in a database depends on another attribute and has many independent values, it is said to have multivalued dependency (MVD). It supports maintaining data accuracy and managing intricate data interactions.
Multi Valued Dependency (MVD)
We can say that multivalued dependency exists if the following conditions are met.
Conditions for MVD
Any attribute say a multiple define another attribute b; if any legal relation r(R), for all pairs of tuples t1 and t2 in r, such that,
t1[a] = t2[a]
Then there exists t3 and t4 in r such that.
t1[a] = t2[a] = t3[a] = t4[a]
t1[b] = t3[b]; t2[b] = t4[b]
t1 = t4; t2 = t3
Then multivalued (MVD) dependency exists. To check the MVD in given table, we apply the conditions stated above and we check it with the values in the given table.

Example
Condition-1 for MVD
t1[a] = t2[a] = t3[a] = t4[a]
Finding from table,
t1[a] = t2[a] = t3[a] = t4[a] = Geeks
So, condition 1 is Satisfied.
Condition-2 for MVD
t1[b] = t3[b]
And
t2[b] = t4[b]
Finding from table,
t1[b] = t3[b] = MS
And
t2[b] = t4[b] = Oracle
So, condition 2 is Satisfied.
Condition-3 for MVD
∃c ∈ R-(a ∪ b) where R is the set of attributes in the relational table.
t1 = t4
And
t2=t3
Finding from table,
t1 = t4 = Reading
And
t2 = t3 = Music
So, condition 3 is Satisfied. All conditions are satisfied, therefore,
a --> --> b
According to table we have got,
name --> --> project
And for,
a --> --> C
We get,
name --> --> hobby
Hence, we know that MVD exists in the above table and it can be stated by,
name --> --> project
name --> --> hobby
Conclusion
- Multivalued Dependency (MVD) is a form of data dependency where two or more attributes, other than the key attribute, are functionally dependent on each other, but not on the key itself.
- Data errors and redundancies may result from Multivalued Dependency.
- We can normalize the database to 4NF in order to get rid of Mutlivalued Dependency.
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