Sort nested arrays to find as many matches as possible

I have a, structure in the form like TYPES / NAME, where TYPES are nested string arrays like 'type a: 'Lorem','Ips','sum','Lor','em'' and 'type b: 'sum', 'Lor', 'Other' and so on. Now I want to sort the whole structure into groups to find the best matches. For example, you have many cooking recipes with many ingredients (nested array in structure) and you want to find out what you can buy to cook as many meals as possible with as few ingredients as possible. Anyway, I want to get the group names sorted based on which groups match best.

Is there a toolbox for big data analytics like this or something similar. Or is there a simple solution to do the analysis right in the structure?