A note on the convex structure of uncertainty measures on MV-algebras

Abstract

In this paper we address the issue of providing a geometrical characterization for the decision problem of asking whether a partial assignment β:fi → αi mapping fuzzy events f i into real numbers αi (i = 1, ...,n) extends to a generalized belief function on fuzzy sets, according to a suitable definition. We will characterize this problem in a way that allows to treat it as the membership problem of a point to a specific convex set. © 2013 Springer-Verlag.