Effect algebraic extensions of generalized effect algebras and two-valued states

摘要

D-posets and effect algebras are very natural structures to be carriers of probabilities for events with fuzziness, uncertainty or unsharpness. In spite of that there are effect algebras admitting no states and probabilities. We give necessary and sufficient conditions for existence of two-valued states on Archimedean atomic effect algebras. Consequently a construction of states, probabilities from bounded orthogonally additive measures existing on some ideal sub-generalized effect algebras is shown.