A long long time ago, in a building far far away, two
Jedis developers called Sreepada Santhegudda and Sergei Gundorov showed me a solution they came up with for a single-select Analysis Services filter web part.
While SharePoint ships with a set of filters that allow users to build interesting dashboards, and while one of them allows you to select dimension members for filtering, the solution is by no means a one-size-fits-all solution. Apart from the issue of having a somewhat convoluted way of doing single select (you essentially need to un-select all elements one way or another and then select the item you want - and then, when you want to switch from one member to another, you need to remember to un-select the previously selected one).
They have sent me the solution eons ago and one way or another, I kept procrastinating and never posted it - Mike Reese prodded me enough that I felt totally ashamed of myself and so I finally got off my fat behind and posted it. Anyway - here's the solution, including source code, for your usage. They also have a document that explain usage and installation.
Here's a screen-shot that shows the simplified selection mechanism:
I have created an MSDN Code Sample library and have uploaded it to there. Enjoy!!!