Analytical Solution of the Simplest Entropiece Inversion Problem.

In this paper, we present a method to solve analytically the simplest Entropiece Inversion Problem (EIP). This theoretical problem consists in finding a method to calculate a Basic Belief Assignment (BBA) from the knowledge of a given entropiece vector which quantifies effectively the measure of uncertainty of a BBA in the framework of the theory of belief functions. We give an example of the calculation of EIP solution for a simple EIP case, and we show the difficulty to establish the explicit general solution of this theoretical problem that involves transcendental Lambert’s functions.