We discuss the properties of two types of construction of a new t-norm from a given t-norm proposed recently by B. Demant, namely the dilatation and the contraction. In general, the dilatation of a t-norm is an ordinal sum t-norm and the continuity of the outgoing t-norm is preserved. On the other hand, the contraction may violate the continuity as well as the non-continuity of the outgoing t-norm. Several examples are given.
@article{urn:eudml:doc:39029,
title = {On some constructions of new triangular norms.},
journal = {Mathware and Soft Computing},
volume = {2},
year = {1995},
pages = {39-45},
zbl = {0837.47056},
mrnumber = {MR1366378},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39029}
}
Mesiar, Radko. On some constructions of new triangular norms.. Mathware and Soft Computing, Tome 2 (1995) pp. 39-45. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39029/