A descriptive definiton of the probability on intuitionistic fuzzy sets

In [2] a general probability theory has been constructed for intuitionistic fuzzy events ([1]) defined on any probability space (Ω,S, P ). To any element A belonging to the family F of all intuitionistic fuzzy events a compact interval P(A) on the real line is assigned. In the paper we consider a mapping P : F → J , where J is the family of all compact intervals. Some properties of P are postulated axiomatically. Then a representation theorem is proved stating that to any mapping P satisfying the properties there exists a probability measure P : S → [0, 1] such that P(A) can be expressed by the help of P similarly as it has been done in [2].