Determinants define functional dependencies between query items. Use determinants to avoid double-counting in denormalized data
Multi grain means having multiple granularities at FM i.e. we use determinants for this.
Example:
When we want to join 2 tables with different granularity we use determinants.
Determinants are required to avoid double counting of fact data when dimensions connect to fact tables at levels of granularity that have repeating keys. A simple example that illustrates this scenario is that of a time dimension that has months and days. The month will repeat for each day in the month. For example, May 1, May 2, May 3, et cetera. You wouldn’t want to aggregate the values of the month for each day in the month.
The second scenario is one where a query subject behaves as a dimension and has multiple levels of granularity and will be joined to fact data on different sets of keys. For example, the time dimension has multiple levels. It is joined to inventory on the month key because inventory is tracked by month. It is also joined to the sales fact on the day key because sales are tracked by day.
Another less common scenario includes the use of BLOB data types in a query subject. Query and BLOB data type values in a query subject require additional key and indexed information. If this information is not present in the data source, you can add it via determinants.
http://cognosteacher.blogspot.com/2012/01/determinants-explained-with-example.html
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