Using MIN function to return equal minimum values

Hi,

I would greatly appreciate if someone could help me--I have been searching on here for hours but nothing seems to apply exactly to my problem. Let me give you some context:

I have an Excel worksheet with survey results on love attitudes. I have already created basic SUM formulas to calculate each person's score for each of the 6 kinds of love. But now I need a formula that picks out the MINIMUM score(s) and spits out which type of love (column) they belong to. I want it to include all "ties," so if someone scored equally low in more than 1 type of love, I want it to be brought to my attention as well.

To visualize this, please see attached Excel file.

The function I have in AF2 to make the type of love with the MIN score appear is this:
=INDEX($Z$1:$AE$1,MATCH(MIN(Z2:AE2),Z2:AE2,0))

Thanks bunches for any help you can provide!!