On generalized Hamacher families of triangular operators

A general functional connective generator is proposed for the Hamacher family in this short study. The connective generator generates a variety of different families in which the original Hamacher family can be observed as a special case. Although the original additive connective generator that was proposed by Dombi is also capable of generating Hamacher norms, we show that there is yet another connective generator that uses simple, monotonic, and continuous functions that are both bounded in the domain and range of [0,1] in contrast to the properties of the functions that used in the additive connective generator. © 1998 Elsevier Science Inc. All rights reserved.