Combining various types of belief structures

Abstract

We first discuss the basic ideas of the Dempster–Shafer belief structure. We particularly emphasize the associated measures of plausibility and belief. We discuss the cumulative distribution function associated with a belief structure. We next turn to the issue of combining multiple belief structures. Two different types of combination of belief structures are investigated. The first, which we refer to as the fusion of belief structures, occurs when the belief structures being combined are providing information about the same variable. Here we make use of the Dempster rule. The second type, which we refer to as the joining of belief structures, occurs when the belief structures being combined are providing information about different variables. Here we make use of a belief structures cumulative distribution function and the Sklar theorem. The classic belief structures typically have a finite number of focal elements; here we began to look at belief structures which have a continuum of focal elements.