A generalization of probability theory on MV-algebras to IF-events

Since probability theory on IF-events constructed with respect to the Łukasiewicz connectives can be embedded into a convenient MV-algebra, all results of the MV-algebra are applicable to IF-events. In this paper we introduce more general connectives. Results from probability theory on MV-algebras cannot be used for this choice of connectives. However, some important results, such as the Central Limit Theorem, can still be obtained by somewhat different methods, which are presented in this paper. The fact that the proposed generalization is not trivial is illustrated by two one-parameter systems.