Triple-Ⅰ Method Research Based On Residual Implication Operator

As one of the high and new techniques that develop modern industry and new products, fuzzy control technique has attracted so much attention and obtained the outstanding success in the applied areas, since Zadeh brought up the concept of fuzzy sets in 1965. Professor Wang Guojun set forth a new triple-I algorithm for the defect of CRI method applied extensively in control areas. This new method is more reasonable and has better logic foundation.The selection of implication has closely related with the result of fuzzy reasoning. Now R0 and Rl operators, which belong to special residual implication operator and have many fine properties, are used mostly in fuzzy control. So this research has important and extensive significance to combine fuzzy reasoning with fuzzy logic and fuzzy control. The textual purpose is to discuss the triple-I algorithm of fuzzy reasoning based on residual implication operator.Firstly, this text further develops the triple-I theory of fuzzy reasoning based on the defect of CRI algorithm, gives the formula of triple-I FMP and FMT based on residual implication operator and discusses their reducible properties. Secondly, the sustaining and restraining theories of triple-I method are discussed and the formula of a-FMP and FMT are provided. Then the reverse triple-I algorithm are discussed based on residual implication operator. Finally, because common fuzzy reasoning is special interval fuzzy reasoning, we set up the interval fuzzy reasoning based on residual implication operator by introducing the relation of partial order.