A Private Set Operation (PSO) protocol involves at least two parties with their private input sets. The goal of the protocol is to learn the output of a set operation, e.g., set intersection, on the parties’ input sets, without revealing any information about the items that are not in the output set. Commonly, the outcome of the set operation is revealed to parties and no one else. However, in many application areas of PSO, the result of the set operation should be learned by an external participant who does not have an input set. We call this participant the decider. In this paper, we present new variants of multi-party PSO, for the external decider setting. All parties except the decider have a private set. Parties other than the decider neither learn this result, nor anything else from this protocol. Moreover, we studied generic solutions to the problem of PSO in the presence of an external decider.