On a family of connectives for fuzzy sets

In this paper we find the general solution of the functional equation $\text{S}{}^1\text{(T(x, y), T(x, N(y))) = x}$, where $\text{S}{}^1$ is a t-conorm, T is a t-norm and N is a strong negation on the unit interval. In particular the result yields a family of connectives for fuzzy sets.