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Discrete triangular norms. (English) Zbl 1037.03046
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, 389-400 (2003).
The paper is devoted to t-norms in the discrete setting. The relationship between discrete t-norms (t-norms on a finite chain) and t-norms on the real closed unit interval is studied. Possible extension(s) of a discrete t-norm to a t-norm on $$[0, 1]$$ are investigated. On this base an interesting open problem is formulated: characterize the discrete t-norms admitting a continuous extension. The converse problem - discretization of t-norms is also studied.
For the entire collection see [Zbl 1020.00006].

##### MSC:
 3e+72 Theory of fuzzy sets, etc.
##### Keywords:
discrete t-norm; continuous extension; discretization