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

Journal Article · Thu Aug 01 00:00:00 EDT 2013 · Soft Computing, 17(8):1379-1391

DOI:https://doi.org/10.1007/s00500-013-1010-1· OSTI ID:1091496

Zapata, Francisco; Kreinovich, Vladik; Joslyn, Cliff A.; Hogan, Emilie A.

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.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1091496
• Report Number(s): PNNL-SA-87281
• Journal Information: Soft Computing, 17(8):1379-1391, Journal Name: Soft Computing, 17(8):1379-1391
• Country of Publication: United States
• Language: English