Abstract
The paper proposes a new type-2 fuzzy logic system, Type-2 Fuzzy Probabilistic System, coupled with type-2 fuzzy probability, to deal with higher order fuzzy events with fuzzy sub-events together. The new concepts of Membership Probability Density Function (Mpdf) and J-plane Representation for type-2 fuzzy set are also presented. A special Type-2 Fuzzy Probabilistic Model, Type-2 Fuzzy ARIMA, is proposed. As a proof-of-concept application, an experiment with a 36 month forecast of a real-valued problem is conducted showing some improvement over Box-Jenkins Model (SARIMA). As series of concepts and results prove, Type-2 Fuzzy Probabilistic System can be determined by fuzzy statistical evaluation of high order fuzzy events and process. This paper realises type-2 fuzzy logic systems evolving from rule-based fuzzy systems to the systems based on type-2 fuzzy probability.
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