4NF relation


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Fourth Normal Form (4NF)

When attributes in a relation have multi-valued dependency, further Normalization to 4NF and 5NF are required. Let us first find out what multi-valued dependency is.

multi-valued dependency is a typical kind of dependency in which each and every attribute within a relation depends upon the other, yet none of them is a unique primary key.

Consider a vendor supplying many items to many projects in an organization. The following are the assumptions:

  1. A vendor is capable of supplying many items.
  2. A project uses many items.
  3. A vendor supplies to many projects.
  4. An item may be supplied by many vendors.

A multi valued dependency exists here because all the attributes depend upon the other and yet none of them is a primary key having unique value.

Vendor Code Item Code Project No.
V1 I1 P1
V1 I2 P1
V1 I1 P3
V1 I2 P3
V2 I2 P1
V2 I3 P1
V3 I1 P2
V3 I1 P3

The given relation has a number of problems. For example:

  1. If vendor V1 has to supply to project P2, but the item is not yet decided, then a row with a blank for item code has to be introduced.
  2. The information about item I1 is stored twice for vendor V3.

Observe that the relation given is in 3NF and also in BCNF. It still has the problem mentioned above. The problem is reduced by expressing this relation as two relations in the Fourth Normal Form (4NF). A relation is in 4NF if it has no more than one independent multi valued dependency or one independent multi valued dependency with a functional dependency.

The table can be expressed as the two 4NF relations given as following. The fact that vendors are capable of supplying certain items and that they are assigned to supply for some projects in independently specified in the 4NF relation.


Vendor Code Item Code
V1 I1
V1 I2
V2 I2
V2 I3
V3 I1


Vendor Code Project No.
V1 P1
V1 P3
V2 P1
V3 P2

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