You can use calculated members to aggregate a custom group of dimension members. For example, you can create a calculated dimension member that sums a group of California cities.
CREATE MEMBER [Sales].[Customers].[All
Customers].[USA].[CA].[City Group] AS
'Aggregate([Altadena],\[Arcadia],\[Bellflower])'
After you execute this statement, you can use [City Group] as a shortcut to the sum of the three California cities. How would you rewrite the above statement so that [City Group] is a shortcut to the same set of three California cities? This time you don't want the sum; you want the results to list all three cities every time you use the name [City Group].
The answer is
CREATE SET [Sales].[City Group] AS
'{[Altadena],\[Arcadia],\[Bellflower]}'
A set is a shorthand notation for a group of members. You can specify this group of members as any MDX set expression. Beyond the obvious benefit of less typing, sets can also help performance. If you have a single query or a set of queries that use the same set of members repeatedly, you might want to create a set. OLAP Services can resolve the set expression once and cache it for multiple uses.
MDX stores sets differently from the way it stores calculated members. A calculated member appears in a dimension hierarchy, whereas a set is stored at the cube level. Notice in the above example that the cube name [Sales] is the prefix for [City Group]. If you store calculated members this way, then the result set can include members from different dimensions.