A characterization of the Hamacher family of t -norms

Abstract Starting from a fuzzy conjunction, there are two main ways of defining a fuzzy implication operator. A functional equation for t-norms is obtained and studied which describes the equality of these two implications when the underlying conjunction has a particular form defined from a t-norm. The solution makes clear that this functional equation, together with an additional condition, provides a complete characterization of the Hamacher family of t-norms having positive parameter.