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Title: Orders on Intervals Over Partially Ordered Sets: Extending Allen's Algebra and Interval Graph Results

To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen’s algebra describes all possible relations between intervals on the real line, and ordering relations between such intervals are well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of the relation between intervals, and extend the results about interval graphs to intervals over posets.
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Journal Article
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Journal Name: Soft Computing, 17(8):1379-1391
Research Org:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
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Country of Publication:
United States