Modeling Uncertainty and Imprecision in Nonmonotonic Reasoning using
  Fuzzy Numbers
  To deal with uncertainty in reasoning, interval-valued logic has been
developed. But uniform intervals cannot capture the difference in degrees of
belief for different values in the interval. To salvage the problem triangular
and trapezoidal fuzzy numbers are used as the set of truth values along with
traditional intervals. Preorder-based truth and knowledge ordering are defined
over the set of fuzzy numbers defined over $[0,1]$. Based on this enhanced set
of epistemic states, an answer set framework is developed, with properly
defined logical connectives. This type of framework is efficient in knowledge
representation and reasoning with vague and uncertain information under
nonmonotonic environment where rules may posses exceptions.
