Type-2 Fuzzy Probabilistic System for Proactive Monitoring of Uncertain Data-intensive Seasonal Time Series
This research realises a type-2 fuzzy probabilistic system for proactive monitoring of uncertain data-intensive seasonal time series in both theoretical and practical implications. In this thesis, a new form of representation, J˜-plane, is proposed for concave and unnormalized type-2 fuzzy events as well as convex and normalized ones, which facilitates bridging the gaps between higher order fuzzy probability realizations and real world problems. Since J˜-plane representation, the investigation of type-2 fuzzy probability theory and the proposal of a type-2 fuzzy probabilistic system become possible. Based on J˜-plane representation, a new fuzzy systemmodel - a type-2 fuzzy probabilistic system is proposed incorporating probabilistic inference with type-2 fuzzy sets. A special case study, a type-2 fuzzy SARIMA system is proposed and experimented in forecasting singleton and uncertain non-singleton bench mark data - Mackey-Glass time series. The results show that the type-2 fuzzy SARIMA system has achieved significant improvements beyond its predecessors - the classical statistical model - SARIMA, type-1 and general type-2 fuzzy logic systems, no matter whether in the singleton or the non-singleton experiments, whereas a SARIMA model cannot forecast non-singleton data at all. The type-2 fuzzy SARIMA system is applied in a real world scenario - WSS CAPS proactive monitoring, and compared with the results of the statistical model SARIMA, type-1 and general type-2 fuzzy logic systems to show that, the type-2 fuzzy SARIMA system can monitor practical uncertain data-intensive seasonal time series proactively and accurately, whereas its predecessors - the statistical model SARIMA, type-1 and general type-2 fuzzy logic systems - cannot deal with this at all. As a series of concepts, algorithms, experiments, practical implements and comparisons prove that, a type-2 fuzzy probabilistic system is viable in practice which realises that type-2 fuzzy systems evolve from rule-based fuzzy systems to the systems incorporating probabilistic inference with type-2 fuzzy sets.
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