In a previous paper we explored the notion of coherent fuzzy consequence operator. Since we did not know of any example in the literature of non-coherent fuzzy consequence operator, we also showed several families of such operators. It is well-known that the operator induced by a fuzzy preorder through Zadeh's compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent. The aim of this paper is to show a parametric family of non-coherent fuzzy consequence operators which induce a preorder and also a family of non-coherent fuzzy consequence operators which do not induce a preorder. These families of operators can be implemented through very simple algorithms.
@article{urn:eudml:doc:39273,
title = {Parametric families of fuzzy consequence operators.},
journal = {Mathware and Soft Computing},
volume = {11},
year = {2004},
pages = {83-91},
zbl = {1075.03008},
mrnumber = {MR2139290},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39273}
}
Elorza, Javier; Burillo, Pedro. Parametric families of fuzzy consequence operators.. Mathware and Soft Computing, Tome 11 (2004) pp. 83-91. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39273/