How to describe partially ordered preferences, mathematical foundations

In reality, a person is often unsure about which of the alternatives is the best. In mathematical terms, the person’s preferences form only a partial order. There exist several heuristic formalisms for describing such partial orders, but due to their heuristic character, we cannot guarantee that these formalisms are general enough to describe the preferences of all reasonable decision makers, and at the same time, narrow enough not to include partial ordering relations that do not satisfy natural reasonable conditions.