Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied by M.J. Frank (Aequationes Math. 19, 194-226, 1979). Finally, some open problems are formulated.
@article{urn:eudml:doc:39122,
title = {On some geometric transformation of t-norms.},
journal = {Mathware and Soft Computing},
volume = {5},
year = {1998},
pages = {57-67},
zbl = {0932.03066},
mrnumber = {MR1632763},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39122}
}
Klement, Erich Peter; Mesiar, Radko; Pap, Endre. On some geometric transformation of t-norms.. Mathware and Soft Computing, Tome 5 (1998) pp. 57-67. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39122/