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Generating theorems for s-norms and t-norms

The s-norm and t-norm operators are generalization of the union and intersection operators 
respectively for fuzzy sets. Thus various alternative operators have been proposed by several 
authors since the introduction of fuzzy sets by Zadeh in 1965. In this paper we give generating 
theorems for s-norms and t-norm, namely given an s-norm we can generate a class of s-norms 
and t-norms, and given a t-norm we can generate a class of t-norms and s-norms. We also give 
bijective generating theorems for s-norms and t-norms. Given two bijective functions on [0, 1] 
under certain conditions, from an s-norm, we generate an s-norm and a t-norm, and from a 
t-norm we generate a t-norm and an s-norm