A note on computing lower and upper bounds of subjective probability from masses of belief

Abstract

This short note shows on a very simple example the consistency of free DSm model encountered in Dezert-Smarandache Theory (DSmT) [2] with a refined model for computing lower and upper probability bounds from basic belief assignments (bba). The belief functions have been introduced in 1976 by Shafer in Dempster-Shafer Theory (DST), see [1] and [2] for definitions and examples. Let’s consider the simplest free model for the frame Θ = {A, B} with A ∩ B = ∅, and let’s consider the following bba defined on the hyper-power set of Θ (its Dedekind’s lattice

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