Rationalization of choice when preferences are vague

In this paper, we discuss the decision situation where the (vague) preferences are represented by fuzzy relations. There are two ways to interpret this situation: (i) an individual decision maker chooses perfect rankings from a set and uses that combination of rankings as her/his preference ranking. (ii) or a group of decision makers are reporting perfect rankings but their group decision is a combination of individual rankings. Rationality of decisions is measured by the degree they match (explain) observed choice behaviour. We work with this well-established notion of rationality and extend it to situations where the observed choice behaviour is partial and incomplete. We derive a condition which, if satisfied, rationalizes the observed choice behaviour when the underlying preferences are vague.