How to use MySQL’s MATCH AGAINST in WP_Query?

As far as I know, you can’t use MATCH()... AGAINST in WP_Query. The possible values for comparison are the following:

=
!=
>
>=
<
<= 
LIKE
NOT LIKE
IN
NOT IN
BETWEEN
NOT BETWEEN
NOT EXISTS
REGEXP
NOT REGEXP
RLIKE

Which the default is =. However, you can use MATCH() AGAINST in a generic query to use by $wpdb. For example:

$wpdb->prepare(" AND MATCH($wpdb->posts.post_title, $wpdb->posts.post_content) AGAINST(%s)", $search );

There are also some __not_in parameters you can use in your query, such as:

$query = new WP_Query( array( 'tag__not_in' => array( 1, 2, 3 ) ) );

Which will search the posts that don’t have the tag IDs of 1, 2 and 3.

This Codex Page and Core ticket might be able to help you.