Fuzzy Multi-Context Systems

—Multi-context systems provide an effective represen- tation and reasoning framework for integrating heterogeneous knowledge obtained from different sources and have been applied in different ﬁelds. Because many application ﬁelds in real life have to deal with uncertain and fuzzy knowledge, the present work aims to combine the multi-context system and fuzzy logic theory effectively and systematically to deal with the representation and reasoning of uncertainty in heterogeneous contexts. The current research in this area is still relatively limited, especially in terms of systematic integration. Speciﬁcally, the present work proposes a class of heterogeneous non-monotonic fuzzy multi- context systems based on non-monotonic multi-context systems, in which an abstract logic is proposed to capture different types of logic and is used as a theoretical basis for fuzzy multi-context knowledge representation and setting up bridging rules to integrate heterogeneous knowledge. Fuzzy equilibria are used to describe the semantics of fuzzy multi-context systems. The syntactic and semantic framework of heterogeneous nonmonotonic fuzzy multi-context systems is then systematically established. Finally, we show that the proposed fuzzy multi-context system not only extends the non-monotonic multi-context system to fuzzy settings, but also could expand the probabilistic multi-context system and the possibility multi-context system in the similar way.