Abstract
Since Fuzzy Event was proposed by Zadeh, the use of higher order fuzzy events to present real-valued problems is always an inhibitor of fuzzy probability in practice. This paper proposes a new concept, Type-2 Fuzzy Event, and the type-2 fuzzy probability for it. The new concept of Membership Probability Density Function (Mpdf) and a new Representation form - J-plane for type-2 fuzzy set are also presented. As a proof-of-concept application, Type-2 Fuzzy ARIMA is developed and a 36 month forecast of a real-valued problem is carried out. The forecast results are much better than classic Box-Jenkins Model (SARIMA). Also investigated is the gap between higher order fuzzy events realizations and real-valued problems in which type-2 fuzzy algorithms are replaced by classic numerical algorithms to circumvent artificial uncertainty growth.
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