Geometric conditional belief functions
نویسنده
چکیده
In this paper we study the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the simplex of all belief functions. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We show here that defining geometric conditional b.f.s by minimizing Lp distances between b and the conditioning simplex in the mass space produces simple, elegant results with straightforward interpretations in terms of degrees of belief. In opposition, the same conditional b.f.s in the belief space often deliver pseudo belief functions with less natural interpretations. The question of weather classical approaches, first and foremost Dempster’s conditioning, can be reduced to same form of distance minimization remains open: the generation of families of combination rules generated by (geometrical) conditioning appears to be the natural prosecution of the presented research.
منابع مشابه
Geometric conditional belief functions in the belief space
In this paper we study the problem of conditioning a belief function (b.f.) b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the space of all belief functions. Defining geometric conditional b.f.s by minimizing Lp distances between b and the conditioning simplex in such “belief” space (rather than in the “mass” space) produces c...
متن کاملGeometry of Dempster’s Rule
In this paper we analyze the nature of Shafer’s belief functions as geometric entities. We focus on the geometric behavior of Dempster’s rule of combination in the context of the belief space, i.e. the set of all the admissible belief functions defined over a given finite domain. After showing how convex closure and orthogonal sum commute in the belief space and introducing the concept of condi...
متن کاملGeometric conditioning of belief functions
In this paper we study the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the simplex of all belief functions. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We sh...
متن کاملEvidential Reasoning with Conditional Belief Functions
In the existing evidential networks with belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions to represent such relations in the network and show some relations of these two kinds of representations. We also present a propagation algorithm for such n...
متن کامل