Ranks of additive generators

Authors:
A. Mesiarová-Zemánková
Affiliations:
Department of Computer Science, Trinity College, Dublin, Ireland and Mathematical Institute of Slovak Academy of Sciences, Bratislava, Slovakia
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

For additive generators of t-norms and t-conorms, the concept of a rank is introduced. It is shown that cancellative and conditionally cancellative t-norms have only additive generators with an infinite rank. The conditions for additive generators with finite ranks are introduced and several examples are given. It is shown that the pseudo-inverse to the Cantor function is an additive generator with rank 2 of a t-conorm C and that for all m@?N,m=2 this t-conorm has an additive generator with rank m.