Cancellativity properties for t-norms and t-subnorms (Q1006740)

The authors establish that the zooms corresponding to non-trivial Archimedean classes of a t-subnorm are Archimedean t-subnorms. Further, they characterize those t-subnorms whose Archimedean components are cancellative, conditionally cancellative, weakly cancellative, or weakly conditionally cancellative, and the relationships between these types of cancellativity are established. An open problem of \textit{E. P. Klement, R. Mesiar} and \textit{E. Pap} [Fuzzy Sets Syst. 145, No.~3, 471--479 (2004; Zbl 1050.03019)] is also solved negatively.