A GENERALIZED ALGEBRAIC APPROACH TO UNCERTAINTY PROCESSING IN RULE-BASED EXPERT SYSTEMS (DEMPSTEROIDS)

Algebraic analysis of compositional rule-based expert systems presented in HAJEK - VALDES [16] is generalized here by allowing the weights of the rules and propositions be elements of a semigroup called Dempster's semigroup (the semigroup operation is the celebrated Dempster rule). Dempster's semigroup is generalized to an infinite class of algebras called dempsteroids which relate to Dempster's semigroup like ordered Abelian groups to PROSPECTOR's group. Expert systems with weights in a dempsteroid are related to expert systems with weights in an ordered Abelian group and most theorems of [16] are generalized in our present more general case.