Extended threshold generation of a new class of fuzzy implications

Abstract

The threshold generation of a new implication from two given ones is introduced by Massanet and Torrens. Along the lines of the ordinal sum method in the construction of fuzzy connectives, the paper deals with generalization of the e-threshold generation method by applying the scaling method in the second variable, which can generate some implications different from usual implications, such as f -, g-implications, R-implications, S-implications and the ones derived from the ordinal sum method. And generated implications are characterized.