Can I define an attribute in TIME dimension?

Can I define an attribute in TIME dimension?

No, you cannot. Time filter is designed in such a way that you cannot add any new attribute to it. But you can create an attribute and use it while publishing the KPI to get the output as required. For example, if Days (Monday, Tuesday, etc.) have to be shown in the TIME filter. Create an attribute called 'Day Name' pointing to the DAY_NAME column in the DIM_DATE table. Use this attribute while publishing the KPI.