Rule Generation by Means of Lattice Theory

R. Brüggemann S. Pudenz, H-G. Bartel

A rather small data matrix of seven chemicals and 17 different ecotoxicological end points is examined by lattice theory. Especially the Formal Concept Analysis, developed since 1980 by the school of Wille is applied. The heart of this mathematical method is the concept, consisting of a pair of sets, which are related to each other (Galois Connection). The one set is a subset of objects, the other a subset of properties. The concepts are partially ordered due a subset relation among those sets. From the subset relation implications are derived. Here -after giving some reading examples- implications are discussed. For example the following question can be answered: Is there a chemical that has a high ecotoxicological effect for example on both Tanytarsus diss. (insect) and Rana catesbeiana (amphibium)? Our chemical set has no one, which has these properties in common. Other examples are discussed.

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