How does Dempster-Shafer theory work in representing ignorance in AI field?
Dempster-Shafer Theory was studied fairly seriously in AI through the 70's and 80's. However, Dempster-Shafer theory has some serious shortcomings, that will cause an agent that uses it to make irrational decisions. These were uncovered by Pearl and others in the 80's, with more problems emerging in later years.
See Cheeseman for a summary of the arguments that probability is the only suitable framework for reasoning under-uncertainty in AI (which is the current orthodox view), along with Josang & Harkin 2012 (which develops a theory that subsumes Dempster-Shafer, and under which DS can be shown to lead to poor decisions), and Pearls' On Probability Intervals.