Fuzzy Aggregates in Fuzzy Answer Set Programming
  Fuzzy answer set programming is a declarative framework for representing and
reasoning about knowledge in fuzzy environments. However, the unavailability of
fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer
set semantics prohibits the natural and concise representation of many
interesting problems. In this paper, we extend DFLP to allow arbitrary fuzzy
aggregates. We define fuzzy answer set semantics for DFLP with arbitrary fuzzy
aggregates including monotone, antimonotone, and nonmonotone fuzzy aggregates.
We show that the proposed fuzzy answer set semantics subsumes both the original
fuzzy answer set semantics of DFLP and the classical answer set semantics of
classical disjunctive logic programs with classical aggregates, and
consequently subsumes the classical answer set semantics of classical
disjunctive logic programs. We show that the proposed fuzzy answer sets of DFLP
with fuzzy aggregates are minimal fuzzy models and hence incomparable, which is
an important property for nonmonotonic fuzzy reasoning.
