In [6] an approach to the representation of synonyms and antonyms via the automorphisms of the De Morgan Algebra [0,1]X was suggested. In [3], Ovchinnikov established a representation theorem for automorphisms of the function's complete and completely distributive lattice [0,1]X with the pointwise extension of Min and Max operations in [0,1]. Ovchinnikov results are now inmediately generalized by using a positive t-norm T and its dual eta-dual t-conorm T*. These results are applied to study the automorphism of [0,1] with different t-norms. Finally, the transformation by means of automorphisms of a given fuzzy on another given fuzzy set is studied.
@article{urn:eudml:doc:39015,
title = {Ovchinnikov's automorphisms revisited.},
journal = {Mathware and Soft Computing},
volume = {1},
year = {1994},
pages = {83-92},
zbl = {0814.04006},
mrnumber = {MR1301962},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39015}
}
Trillas, Enric; Rodríguez de Soto, Adolfo; Cubillo, Susana. Ovchinnikov's automorphisms revisited.. Mathware and Soft Computing, Tome 1 (1994) pp. 83-92. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39015/