In [12] Trillas proved that (P(X),∩,U,-n) is a quasi-Boolean algebra if and only if its negation has an additive generator. In this paper such result is generalized to PJ(X) and the symmetry of J is analized.
From the results of Esteva ([11]) weak negations on [0,1] are studied; it is proved that such functions are monotonic, non-increasing, left-continuous and symmetrical with respect to y=x. Their classification relative to C([0,1]) is also given and a canonical element of each class is found. Finally strong and weak negations on a finite J are studied.
@article{urn:eudml:doc:38822,
title = {Sobre funciones de negaci\'on en [0,1].},
journal = {Stochastica},
volume = {4},
year = {1980},
pages = {141-166},
zbl = {0448.03047},
mrnumber = {MR0599138},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38822}
}
Esteva, Francesc; Domingo, Xavier. Sobre funciones de negación en [0,1].. Stochastica, Tome 4 (1980) pp. 141-166. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38822/