Solution to an open problem: A characterization of conditionally cancellative t-subnorms

In this work we solve an open problem of U. Höhle (Klement et al. Fuzzy Sets Syst 145:471-479, 2004, Problem 11). We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition under which a conditionally cancellative t-subnorm has 1 as its neutral element and hence show that conditionally cancellative t-subnorms whose natural negations are strong are, in fact, t-norms