By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions.
We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to a triangular norm and conorm.
Moreover we discuss the problem of characterization of the approximate solutions of fuzzy equations.
Finally, the role of the equations considered here in creation of a formal framework for copying with fuzziness is illustrated by various examples in some well known schemes in applications of fuzzy set theory.
@article{urn:eudml:doc:38901,
title = {Fuzzy relation equation under a class of triangular norms: A survey and new results.},
journal = {Stochastica},
volume = {8},
year = {1984},
pages = {99-145},
zbl = {0581.04002},
mrnumber = {MR0783401},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38901}
}
Di Nola, Antonio; Pedrycz, Witold; Sessa, Salvatore; Pei Zhuang, Wang. Fuzzy relation equation under a class of triangular norms: A survey and new results.. Stochastica, Tome 8 (1984) pp. 99-145. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38901/