Create a saved search to show me all the items on my webstore that do not have a preferred category

We want to have a saved search that shows us all the items we have listed on our website that do not have a preferred category selected. It is a simple check box next to the site category we prefer it to be in. Yet we can not show a saved search that displays the items that do not have this check box checked. Or even a search to show which category is selected as the preferred category for our items.

Can any one tell me if there is a way to perform this search or something along these lines so I can at least see the items that do not have the checkbox checked.