Bifuzzy probabilistic sets

Abstract The paper introduces the notion of bifuzzy (in another terminology - intuitionistic) probabilistic sets, i.e. those determined by the so-called defining functions describing the belonging or the non-belonging of an element to a set of some objects, with respect paid to the randomness of choosing them. In the paper the authors present the properties of these sets, give a number of definitions and theorems, and ascertain that the family of bifuzzy probabilistic sets forms a complete pseudo-Boolean algebra. Besides, they define various moments and indicate their important properties.