"Uncertainty in Partially Ordered Sets as a Natural Generalization of I" by David Mireles and Olga Kosheleva

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Departmental Technical Reports (CS)

Uncertainty in Partially Ordered Sets as a Natural Generalization of Intervals: Negative Information Is Sufficient, Positive Is Not

David Mireles, The University of Texas at El Paso
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

10-2010

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Technical Report: UTEP-CS-10-44

Published in Journal of Uncertain Systems, 2011, Vol. 5, No. 2, pp. 96-101.

Abstract

In many real-life applications, we have an ordered set: a set of all space-time events, a set of all alternatives, a set of all degrees of confidence. In practice, we usually only have a partial information about an element x of this set. This partial information includes positive knowledge: that a <= x or x <= a for some known a, and negative knowledge: that it is not true that a <= x or x <= a for some known a. In the case of a total order, the set of all elements satisfying this partial information is an interval. We show that in the general case of a partial order, the corresponding analogue of an interval is a convex set. We also show that in general, to describe partial knowledge, it is sufficient to have only negative information about x but it is not sufficient to have only positive information.

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