A parameterized implication function derived from the relations to be satisfied between a premise and the conclusion

There are a lot of implication functions in the field of fuzzy logic, and the nature of the fuzzy inference changes variously depending on the implication function to be used. However, it is very difficult to select a suitable implication function for actual applications. The authors intend to define a parameterized implication function whose nature changes variously depending on the values of the parameters, and adjust the parameters so that the implication function has a suitable nature for actual applications using a parameter tuning method. The authors think this work can reduce the efforts to select a suitable implication function. Moreover, it can clarify the nature of the rule to select a suitable implication function by parameter tuning. Therefore, the tuning of the parameters can be regarded as a kind of quantification of the meaning of the natural language sentences expressed in IF-THEN rules. The authors propose a parameterized implication function, defined to satisfy some desirable relations between the premise and the conclusion of rules used in fuzzy inference. The desirable relations are defined using some parameters indicating the nature of the implication. The authors also demonstrate some tuning simulations of the parameters used in the implication function using the tuning mechanism of a fuzzy inference tool named FINEST