  An interval-valued fuzzy answer set programming paradigm is proposed for
nonmonotonic reasoning with vague and uncertain information. The set of
sub-intervals of $[0,1]$ is considered as truth-space. The intervals are
ordered using preorder-based truth and knowledge ordering. The preorder based
ordering is an enhanced version of bilattice-based ordering. The system can
represent and reason with prioritized rules, rules with exceptions. An
iterative method for answer set computation is proposed. The sufficient
conditions for termination of iterations are identified for a class of logic
programs using the notion of difference equations.
