The case when the source of information provides precise belief function/mass,within the generalized power space,has been studied by many people.However,in many decision situations,the precise belief structure is not always available.In this case,an interval-valued belief degree rather than a precise one may be provided.So,the probabilistic transformation of imprecise belief function/mass in the generalized power space including Dezert-Smarandache (DSm) model from scalar transformation to sub-unitary interval transformation and,more generally,to any set of sub-unitary interval transformation is provided.Different from the existing probabilistic transformation algorithms that redistribute an ignorance mass to the singletons involved in that ignorance proportionally with respect to the precise belief function or probability function of singleton,the new algorithm provides an optimization idea to transform any type of imprecise belief assignment which may be represented by the union of several sub-unitary (half-) open intervals,(half-) closed intervals and/or sets of points belonging to [0,1].Numerical examples are provided to illustrate the detailed implementation process of the new probabilistic transformation approach as well as its validity and wide applicability.