Below is a part of the description about RelationshipType from AS 2005 BOL.

ms-help://MS.SQLCC.v9/MS.SQLSVR.v9.en/uas9/html/fce511af-66d7-42fc-bb3a-6c516f16b10e.htm

....If you define a relationship as flexible, aggregations are not dropped
and recomputed after an incremental update. If you define a relationship as
rigid, Analysis Services retains aggregations when the dimension is
incrementally updated. If a relationship that is defined as rigid actually
changes, Analysis Services generates an error during incremental processing.
Specifying the appropriate relationships and relationship properties
increases query and processing performance.
Does someone have more detailed information on this?

Thanks in advance,

Ohjoo Kwon