Representation of interrelationships among binary variables under dempster-shafer theory of belief functions

This paper presents an algorithm for developing models under Dempster-Shafer theory of belief functions for categorical and 'uncertain' logical relationships among binary variables. We illustrate the use of the algorithm by developing belief-function representations of the following categorical relationships: 'AND', 'OR', 'Exclusive OR (EOR)' and 'Not Exclusive OR (NEOR)', and 'AND-NEOR' and of the following uncertain relationships: 'Discounted AND', 'Conditional OR', and 'Weighted Average'. Such representations are needed to fully model and analyze a problem with a network of interrelated variables under Dempster-Shafer theory of belief functions. In addition, we compare our belief-function representation of the 'Weighted Average' relationship with the 'Weighted Average' representation developed and used by Shenoy and Shenoy. We find that Shenoy and Shenoy representation of the weighted average relationship is an approximation and yields significantly different values under certain conditions.