Fuzzy Events Realized by Finite Probabilistic Automata

In this paper the concept of prob'abilistic events is introduced and their closure properties under the operations on the set of all fuzzy events are studied. I t is shown that the mean of probabilistie events is a probabilistie event and the set of all probabilistie events is closed under the transposition and the operation of the convex-combination. A sufficient conditioll for the union and the intersection of two probabilistie events to be probabilisti c events in the sense of fuzzy sets is given. In the last two sections we showed some families of probabilistic events closed or approximately closed under the operation of the union and the intersection and the complementation.