J̃-plane - a new form of representation for Type-2 Fuzzy Probability

The use of higher order fuzzy events to represent real-world problems is always an inhibitor of practical fuzzy probability. In this paper, a new form of representation J̃-plane is proposed for Type-2 Fuzzy Probability. Based on the J̃-plane representation, the type-2 fuzzy computation and type-2 fuzzy characteristic moments are investigated and applied in a case of type-2 fuzzy probabilistic computational model - Type-2 Fuzzy SARIMA. This model is implemented in Wireless Soft-Switch communication network CAPS (Call Attempt Per Second) prediction to show that Type-2 Fuzzy SARIMA is much better than the classic statistical model SARIMA with more accurately and timely forecast results, along with the infinite maximum supported seasonality and less errors. As the series of algorithms and results prove in this paper, J̃-plane representation is viable in real-world problems which facilitate bridging the gap between higher order fuzzy probability realizations and real-world problems.