Groupe d’études et de recherche en analyse des décisions


Semilattices Distributive Over a Max Operation


A semilattice S is an associative, commutative and idempotent binary operation on a set. The product xy then corresponds to the least upper bound in the order . The maximum operation in a total order (chain) C is a particular kind of semilattice. Let S and C be defined on the same underlying set. We provide necessary and sufficient conditions for the distributive law to hold. These conditions are in terms of the semilattice and chain order structures, they are essentially graph-theoretical in nature, and they involve a concept of convexity.

, 13 pages