You imply, but don't say explicitly, that all your arrays are the same size. Is this correct? Assuming it is, you have something like:
@numbers = (1,2,3,4,5,6,7);
@words = ('one', 'two', 'three', 'four', 'five', 'six', 'seven');
@odd_even = ('odd', 'even', 'odd', 'even', 'odd', 'even', 'odd');
@prime = ('not', 'prime', 'prime', 'not', 'prime', 'not', 'prime');
And you want to be able to sort all of them together, based on one of them  bringing the even numbers to the front, say?
Have you considered an array of arrays?
@numbers_with_attributes = ( [1, 'one', 'odd', 'not'],
[2, 'two', 'even', 'prime'],
[3, 'three', 'odd', 'prime'],
[4, 'four', 'even', 'not'],
[5, 'five', 'odd', 'prime'],
[6, 'six', 'even', 'not'],
[7, 'seven', 'odd', 'prime'],
);
@alpha_sort = sort { $a[1] cmp $b[1] } @numbers_with_attributes;
