The class of nearest belief functions to a given probability measure

The paper is devoted to the solution of two problems. The first one consists of finding a probability measure which deviates at root-mean-square from a given belief function. The other problem is the inverse one, that is for a given probability measure it is necessary to find a class of belief functions which deviate at root-mean-square from a given probability measure. We find a description of the class of nearest belief functions in the form of system inequalities and indicate a subset of extreme points of this class.