(eng): Extending the notion of belief functions to fuzzy sets leads to the generalization of several key concepts of the classical Dempster- Shafer theory. In this paper we concentrate on characterizing normalized belief functions and their fusion by means of a generalized Dempster rule of combination. Further, we introduce soft-normalization that arises by either rising up the usual level of contradiction above 0, or by decreasing the classical level of normalization below 1.