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I have an expressioN as follows:
Honestly I've never really fully understood the point of the only function except in some rare cases so I could be wrong here, but I don't understand why you are using only here. It looks like using STOPDATE={">=(=ONLY(DATE_START))"} would be the same as STOPDATE={">=DATE_START"} which I don't think would work anyway for several reasons. Your question is a little vague and I'm not sure I really follow but I think your first problem is that set analysis is calculated once per chart, not once per row. Looking at your post I can't really be sure that you need the set analysis to calculate into a different result for each row but I'm assuming you do unless you actually only want one start date for the entire chart.
Assuming that is your problem you probably need to be something tricky with the aggr function. Something like....
=count(distinct
aggr(
if([STOPDATE]>=[DATE_START] And [STARTDATE]<=[DATE_STOP]
[ID]
)
,[ID],[DATE_START],[DATE_STOP],[STARTDATE], [STOPDATE]
)
)
I didn't realize you had four different dates when I wrote the code above so to be honest I'm not sure if it is going to work or not off the top of my head... but it's probably worth a shot. Again I don't know if I fully understand the question but hopefully something I said was helpful.
I use only- function for choose selected value from both date_stop and date_start