Multiple fuzzy implications and their generating methods

Abstract

By means of multiple iteration about the first variable of a known fuzzy implication, a new fuzzy implication is introduced. It is proved that the new implication preserves some important properties of the original implication. These properties include the identity principle (IP), the left neutrality property (NP), the exchange principle (EP), and so on. Based on this idea, by considering multiple iteration about the second variable of the known fuzzy implications, another new kind of fuzzy implications are similarly introduced, main properties of this kind of new implications are analyzed. This work is beneficial to enhance applications of fuzzy implications in other fields.