Cancellativity properties for t-norms and t-subnorms

Authors:
Koen C. Maes;Andrea Mesiarová-Zemánková
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Computer Science, O'Reilly Institute, Trinity College, Dublin 2, Ireland and Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 81473 Bratislava, Slovaki ...
Venue:
Information Sciences: an International Journal
Year:
2009

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Abstract

On the one hand, cancellativity properties are mainly used to express to which extend the partial functions of a t-subnorm T are injective. On the other hand, the zooms of T corresponding to its non-trivial Archimedean components are t-subnorms that largely determine T. Fixing one out of four basic types of cancellativity (cancellativity, conditional cancellativity, weak cancellativity and weak conditional cancellativity) we figure out which less restrictive type of cancellativity expresses that all maximal Archimedean zooms of T satisfy the given cancellativity property. We lay bare the mutual relationships between all these types of cancellativity and solve an open problem posed by Klement et al.