Multi-valued Dependency
A Multi-Valued Dependency(MVD) over schema R is a statement of the form X →→ Y where X, Y Í schema(R).
An MVD X →→ Y is satisfied in a relation r over R, denoted by r |= X →→ Y, for all t1, t2 Î r, if t1[X] = t2[X], there exists t3, t4 such that:
1) t1[X] = t2[X]= t3[X] = t4[X],
2) t3[Y] = t1[Y], t3[Z] = t2[Z] and
3) t4[Y] = t2[Y], t4[Z] = t1[Z],
where Z = schema(R) - XY
Set M of multivalued dependencies in our banking example
Customer-credit-card-schema: customer-ID →→ credit_card_number
Each customer has a number of credit cards issued by the bank, which are identified by the numbers printed on the credit cards.
Customer-credit-card-schema: customer-ID →→ account-number
Each customer has a number of saving accounts in the bank, which are identified by the saving account numbers. The owner of a credit card can use it to access the current balance of all the saving accounts that he or she has in the bank. Any saving account that an owner can access using one credit card can also be accessed using another credit card of the same owner.
customer_ID credit_card_number account_number Amy 0000-1111-1111-1111 0-1-2222-3333-4444 Amy 0000-1111-1111-1111 0-1-2222-3333-5555 C8392380567 0000-1111-1111-2222 0-1-2222-3333-5555 C8392380567 0000-1111-1111-2222 0-1-2222-3333-4444 C8954385123 0000-2222-2222-2222 0-1-2222-2222-2222 C2389490434 0000-3333-3333-3333 0-1-3333-3333-3333 C9384899234 0000-4444-4444-4444 0-1-4444-4444-4444 C0930238083 0000-5555-5555-5555 0-1-5555-5555-5555 C3487327487 0000-6666-6666-6666 0-1-6666-6666-6666 C3249893849 0000-7777-7777-7777 0-1-7777-7777-7777 C3948938442 0000-8888-8888-8888 0-1-8888-8888-8888 C2394893848 0000-9999-9999-0000 0-1-9999-9999-0000 C2394893848 0000-9999-9999-0000 0-1-9999-9999-1111 C2394893848 0000-9999-9999-1111 0-1-9999-9999-0000 C2394893848 0000-9999-9999-1111 0-1-9999-9999-1111