Possibilistic Variables and Akian Semirings

The relationship between possibility measures and Akian’s semiring-valued idempotent probabilities is studied. The semiring operations in [0, 1] for which both theories overlap are shown to be the maximum and an arbitrary 1-Lipschitz triangular norm. Sufficient conditions are then given for the notion of convergence in law to be independent of the choice of a specific triangular norm.