@complete{@arr_a} = ...;
[download]

It's not clear what exactly you want to assign, though. Does the following work for you?

#!/usr/bin/perl
use warnings;
use strict;

use Data::Dumper;
use XML::LibXML;

my $xml = 'XML::LibXML'->load_xml( string => <<'__XML__');
<root>
  <node a="a b" b="A B" c="AA BB"/>
  <node a="1" b="2" c="3"/>
  <node a="X Y Z" b="x y z" c="xx yy zz"/>
</root>
__XML__

my %complete;
for my $node ($xml->documentElement->findnodes('*')) {
    my ($a, $b, $c) = map $node->getAttribute($_), 'a', 'b', 'c';

    if (3 == grep defined, $a, $b, $c) {
        my @arr_a = split (/ /, $a);
        my @arr_b = split (/ /, $b);
        my @arr_c = split (/ /, $c);
        @complete{@arr_a} = map [ shift @arr_b, shift @arr_c ], @arr_a
+;
    } else {
        print "Warning! \n";
    }
}
print Dumper \%complete;
[download]

Update: Note that I populate the hash only if all the attributes are defined. In your case, the @arr_X arrays were global, so the hash was repopulated again with the old values. (I use strict and warnings, why don't you?)

The map expression might look a bit complex for an untrained eye. It just picks one element from b and c for each element of a.

Thank you a lot ! Your solution helped me to solve this Problem. Now I understand, why it never worked for me. Also thank your for showing me the right way to work further. Best regards!

      
    %complete =(
            @arr_a=>[@arr_b, @arr_c],    
          );
[download]

$complete{$a} = [@arr_b, @arr_c];
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