Fuzzy Aggregates in Fuzzy Answer Set Programming

TL;DR

This paper extends fuzzy answer set programming by introducing fuzzy aggregates, enabling more natural problem modeling and reasoning in fuzzy environments, while maintaining desirable semantic properties.

Contribution

It defines fuzzy answer set semantics for DFLP with arbitrary fuzzy aggregates, unifying and extending previous semantics and classical answer set frameworks.

Findings

Fuzzy aggregates are incorporated into DFLP.

The semantics subsume previous fuzzy and classical answer set semantics.

Fuzzy answer sets are minimal fuzzy models, supporting nonmonotonic reasoning.

Abstract

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.