GENERALIZATIONS OF SEMIORDERS - A REVIEW NOTE

Semiorders may form the simplest class of partially ordered sets that accommodate thresholds of discriminability in binary comparisons. Many other classes of ordered sets that generalize the uniform-threshold f eature of semiorders have been studied in recent years. This note desc ribes a variety of generalizations and their interrelationships, inclu ding equivalences and proper inclusions between classes. Nine nonequiv alent classes are designated as interval orders, bisemiorders, split s emiorders, unit tolerance orders, unit bitolerance orders, tolerance o rders, bitolerance orders, semitransitive orders, and subsemiorders. E ach is defined by an interval representation or by a few minimal forbi dden configurations. All proper inclusions between classes are identif ied along with equivalences to other classes. (C) 1997 Academic Press.