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New operations for informative combination of two partial order relations with illustrations on pollution data

Michaël Rademaker (UGent) , Bernard De Baets (UGent) and Hans De Meyer (UGent)
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Abstract
We discuss various ways in which to construct and process partial order relations or partially ordered sets (posets) in the context of ranking objects on the basis of multiple criteria. Oftentimes, it is undesirable or even impossible to devise a weighting scheme to compute a final score on the basis of the criteria. An alternative is then to restrict oneself to the information contained in the partial ordering of all objects implied by the criteria. We will consider some ways in which one can exploit partial order relations to determine a ranking of a collection of objects. More exactly, we will examine how to combine information coming from two sources, both for the case in which the sources are considered to be equally important, as well as for the case in which one source of information should take priority. We illustrate the concepts on pollution data coming from 59 regions in Baden-Wurttemberg.
Keywords
Hasse diagrams, linear extensions, partially ordered set, Information systems in chemistry, environmental informatics, transitive combination of partial order relations, decision support, RANDOM LINEAR EXTENSIONS, T-TRANSITIVE CLOSURES, RANKING PROBABILITIES, RANDOM GENERATION, CHEMICALS, DIAGRAMS, POSET, TESTS, SETS

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Citation

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Chicago
Rademaker, Michaël, Bernard De Baets, and Hans De Meyer. 2008. “New Operations for Informative Combination of Two Partial Order Relations with Illustrations on Pollution Data.” Combinatorial Chemistry & High Throughput Screening 11 (9): 745–755.
APA
Rademaker, M., De Baets, B., & De Meyer, H. (2008). New operations for informative combination of two partial order relations with illustrations on pollution data. COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING, 11(9), 745–755.
Vancouver
1.
Rademaker M, De Baets B, De Meyer H. New operations for informative combination of two partial order relations with illustrations on pollution data. COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING. 2008;11(9):745–55.
MLA
Rademaker, Michaël, Bernard De Baets, and Hans De Meyer. “New Operations for Informative Combination of Two Partial Order Relations with Illustrations on Pollution Data.” COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING 11.9 (2008): 745–755. Print.
@article{519545,
  abstract     = {We discuss various ways in which to construct and process partial order relations or partially ordered sets (posets) in the context of ranking objects on the basis of multiple criteria. Oftentimes, it is undesirable or even impossible to devise a weighting scheme to compute a final score on the basis of the criteria. An alternative is then to restrict oneself to the information contained in the partial ordering of all objects implied by the criteria. We will consider some ways in which one can exploit partial order relations to determine a ranking of a collection of objects. More exactly, we will examine how to combine information coming from two sources, both for the case in which the sources are considered to be equally important, as well as for the case in which one source of information should take priority. We illustrate the concepts on pollution data coming from 59 regions in Baden-Wurttemberg.},
  author       = {Rademaker, Micha{\"e}l and De Baets, Bernard and De Meyer, Hans},
  issn         = {1386-2073},
  journal      = {COMBINATORIAL CHEMISTRY \& HIGH THROUGHPUT SCREENING},
  language     = {eng},
  number       = {9},
  pages        = {745--755},
  title        = {New operations for informative combination of two partial order relations with illustrations on pollution data},
  volume       = {11},
  year         = {2008},
}

Web of Science
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