Generalizing evidence theory to lattices to manage uncertainty

The Dempster-Shafer theory of evidence has been found to be promising for a variety of inexact reasoning applications. Many attempts have been made to generalize the theory to problem spaces which are not just the power sets of finite sets, which the original Dempster-Shafer theory addresses, but general Boolean algebras. However, some most important structures in applications to expert systems such as Gordon-Shortliffe´s tree hierarchy (J. Gordon & E.H. Shortliffe 1985), are lattices rather than Boolean algebras. It is interesting to generalize evidence theory to general lattices. The authors generalize the theory by reworking some of the conventional theorems in evidence theory and establish the relationships between weaker forms of the familiar evidential functions.