Contrapositive symmetry of distributive fuzzy implications revisited

In this paper, we explore the solution of functional equations I(x,T(y,z)) = T(I(x,y),I(x,z)) and I(x,y) = I(N(y),N(x)) satisfied simultaneously, where T is a strict t-norm, I a fuzzy implication and N a strong negation. Under the assumptions of I continuous except the points (0, 0) and (1, 1), we get the full characterizations of the solutions for this functional equations.