Notes on “pseudo-t-norms and implication operators on a complete Brouwerian lattice” and “pseudo-t-norms and implication operators: direct products and direct product decompositions”

This paper shows by examples that Theorems 4.1-4.3, 4.5 in [Fuzzy Sets and Systems 132 (2002) 113] and Theorems 2.1, 2.2, 3.1 in [Fuzzy Sets and Systems 139 (2003) 673] about pseudo-t-norms and implication operators are false, and gives a necessary condition for them being true.