Development of an Algorithm to Convert Linear Belief Function inputs to Exponential Conditional Probability Functions for Multiple Method Applications

Abstract

Evidential Reasoning (ER), based on the Dempster-Schafer theory of evidence, and Bayesian Networks (BN) are two distinct theories and methodologies for modelling and reasoning with data regarding propositions in uncertain domains. Both ER and BNs incorporate graphical representations and quantitative approaches of uncertainty. BNs are probability models consisting of a directed acyclic graph, which represents conditional independence assumptions in the joint probability distribution. Whereas ER graphically describes knowledge through an evaluation hierarchy and the relationships of the attributes based on Dempster-Shafer theory of belief functions. Therefore, this paper proposes an algorithm, which allows for the conversion of the linear input data of ER (belief degrees and relative weights) to the exponential data input of BNs (conditional probability tables (CPTs)). The algorithm is applied to a validated case study where the ER approach has been utilized for decision-making.