Predict set elements based on other elements
Maybe you could use some algorithm that solves "Market Basket Analysis". The problem is explained here: 


  Market Basket Analysis is a modelling technique based upon the theory
  that if you buy a certain group of items, you are more (or less)
  likely to buy another group of items. For example, if you are in an
  English pub and you buy a pint of beer and don't buy a bar meal, you
  are more likely to buy crisps (US. chips) at the same time than
  somebody who didn't buy beer.


http://albionresearch.com/data_mining/market_basket.php

One example of such an algorithm is: https://en.wikipedia.org/wiki/Association_rule_learning