Members, Tuples, and Sets

Members represent the concrete data of this meta-definition (e.g. Switzerland as a country). Each level of a given hierarchy will 'produce' a member with a parent-child relationship.

The object representing the upper level of Switzerland (continent) is also a member in MDX:

[Geography].[Geo].[Europe]: is a continent (with all European countries as children)

[Geography].[Geo].[Europe].[Switzerland]: is a country whose parent member is Europe )

[Geography].[Geo].[Europe].[Switzerland].[Geneva]: is a city (whose parent member is Switzerland)

Representing the full hierarchy on rows as a tree, would appear as follows:

    Select
        [Measures].[Amount] on 0,
        [Geography].[Geo].members on 1
    From
        [Sales]

A tuple is the intersection of one (and only one) member taken from each of the dimensions in the cube. A tuple identifies a single cell in the multi-dimensional matrix.

The easiest way to understand a tuple is to look at an Excel sheet. In the Excel sheet a cell is identified by A1, A2, A3, B1, B2, B3, etc. Here A represents a coordinate from the columns and 1 represents a coordinate from the rows. We put these together and we can uniquely identify a cell in the sheet. Here A1, B1 are examples of tuples. In a OLAP cube there are many dimensions and a tuple is defined as a list of a single hierarchy member taken from all the dimensions (e.g. [New York], [2009]). The net effect is the same. The tuple always points to a single cell in the OLAP cube.

When defining our business case, we defined several dimensions and one measure. Those dimensions can be seen as discrete coordinates (discrete as they have a limited amount of possibilities) of a cube. Just as 'x,y,z' represent the coordinates of points in space, members of our dimensions represent the coordinates in our cube. The measure being the value of this cube.

For example, 'Patty Bing sold one corporate license 2009 Q4 in Los Angeles' is represented by the tuple:

([People].[Patty Bing], [Prod].[License].[Corporate], [Time].[Calendar].[Q4 2009], [Geography].[Geo].[Los Angeles], [Measures].[Amount])

A tuple dimensionality is defined as the ordered list of the member's hierarchies. For example, the previous tuple dimensionality is:

( [People].[People], [Product].[Prod], [Time].[Calendar], [Geography].[Geo], [Measures] )

Within a hierarchy, intermediate members (a.k.a. parent members) do not represent actual coordinates of measures in our cube. Therefore, the MDX aggregation and calculation engine is going to compute those measures by aggregating the measures' values of their children (and grandchildren).

This means that ( [Patty Bing], [2009] ) is going to return the 'amount of licenses' sold by Patty during the whole year 2009 (aggregating the amount for each quarter of 2009).

Sets are an ordered collection of 0 or more tuples (note that a member is considered to be a tuple containing a single element) with the same dimensionality. Unlike a mathematical set, an MDX set may contain duplicates. So, the same member/tuple can be in a list twice. Sets are defined using curled brackets:

{ [Geography].[Geo].[Europe].[Switzerland], [Geography].[Geo].[Europe].[France] }

Members of a set must be from the same hierarchy. For example, the following set is invalid:

{ [Geography].[Geo].[Europe].[Switzerland], [Product].[License].[Corporate] }

The following set is invalid because of different tuple dimensionalities:

{ ( [Time].[Calendar].[2010], [Geography].[Geo].[Europe].[Switzerland] ),
  ( [Time].[Calendar].[2010], [Product].[License].[Corporate] ) }

Next chapter: Member Name.