Fuzzy Aggregates in Fuzzy Answer Set Programming
This work addresses a limitation in fuzzy answer set programming for researchers in knowledge representation and nonmonotonic reasoning, but it appears incremental as it builds on existing frameworks by adding fuzzy aggregates.
The paper tackles the problem of representing knowledge in fuzzy environments by extending disjunctive fuzzy logic programs (DFLP) to include arbitrary fuzzy aggregates, such as monotone, antimonotone, and nonmonotone types, and defines fuzzy answer set semantics for these programs. The result shows that this new semantics subsumes both the original fuzzy answer set semantics of DFLP and the classical answer set semantics of classical disjunctive logic programs with aggregates, and ensures that the fuzzy answer sets are minimal fuzzy models and incomparable.
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.