On power ordered sets
by
Dietmar Scbweigert
University of Kaiserslautern, Germany

Power ordered sets are a generalization of Boolean algebras and are defined by injective monotone maps.

In spite of the complicated definition this concept has many applications in mulitcriteria optimization, decision theory, game theory and the theory of voting. We like only to mention the application of the problems; spanning trees, shortest paths, traveling salesman tours and on optimal knapsacks. Furthermore we can extend this concept for every relation and we have examples of graphs and groups. Therefore this theory stands betweeen the sets and relations between power sets and power relations and therefore proposition logic and predicate logic.

Date received: July 26, 2001