Publication Date



Technical Report: UTEP-CS-12-31

To appear in Journal of Uncertain Systems, 2013, Vol. 7.


In practice, we are often interested in order relations (e.g., when we describe preferences) or equivalence relations (e.g., when we describe clustering). Often, we do not have a complete information about the corresponding relation; as a result, we have several relations consistent with our knowledge. In such situations, it is desirable to know which elements a and b are possibly connected by the relation and which are necessarily connected by this relation. In this paper, we provide a full description of all such possible and necessary orders and equivalence relations. For example, possible orders are exactly reflexive relations, while necessary orders are exactly order relations.

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