# zbMATH — the first resource for mathematics

Structure of Girard monoids on $$[ 0,1 ]$$. (English) Zbl 1036.03035
Rodabaugh, Stephen Ernest (ed.) et al., Topological and algebraic structures in fuzzy sets. A handbook of recent developments in the mathematics of fuzzy sets. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1515-1/hbk). Trends Log. Stud. Log. Libr. 20, 277-308 (2003).
This work is a continuation of previous papers of the same author [see, e.g., Fuzzy Sets Syst. 110, No. 2, 157–174 (2000; Zbl 0941.03059); ibid. 124, No. 1, 35–41 (2001; Zbl 0989.03059)]. The notion of a Girard monoid coincides, when the underlying lattice structure is the unit real interval, with the notion of a left-continuous triangular norm with induced strong negation. A complete and detailed geometrical description illustrates the construction and the decomposition of such triangular norms.
For the entire collection see [Zbl 1020.00006].

##### MSC:
 03E72 Theory of fuzzy sets, etc. 06F07 Quantales